Class 7 Maths - Fractions And Decimals

$23.2\div 100 =x$ . Find $1000x$

We have,

$\Rightarrow x = 23.2 \div 100$

$=0.232$

Then,

$\Rightarrow 1000x = 0.232 \times 1000$

$\Rightarrow \dfrac{{232}}{{1000}} \times 1000$

$=232$

Hence,

$1000x=232$

Convert the given mixed fractions into improper
$2\dfrac {1}{5}$

Given mixed friction:

$2\dfrac{1}{5}$

Improper friction

$=\dfrac{5\times 2+1}{5}=\dfrac{11}{5}$

Hence, this is the answer.

Convert the given mixed fractions into improper
$2\dfrac {1}{2}$

Given mixed friction:

$2\dfrac{1}{2}$

Improper friction

$=\dfrac{2\times 2+1}{2}=\dfrac{5}{2}.$

Convert the given mixed fractions into improper
$3\dfrac {1}{6}$

Given mixed friction:

$3\dfrac{1}{6}$

Improper friction

$=\dfrac{3\times 6+1}{6}=\dfrac{19}{6}.$

Convert the given mixed fractions into improper
$7\dfrac {2}{9}$

Given mixed friction:

$7\dfrac{2}{9}$

Improper friction

$=\dfrac{9\times 7+2}{9}=\dfrac{65}{9}.$

Convert the given mixed fractions into improper
$6\dfrac {1}{10}$

Given mixed friction:

$6\dfrac{1}{10}$

Improper friction

$=\dfrac{10\times 6+1}{5}=\dfrac{61}{10}.$

Convert the given mixed fractions into improper
$4\dfrac {2}{3}$

Given mixed friction:

$4\dfrac{2}{3}$

Improper friction

$=\dfrac{4\times 3+2}{3}=\dfrac{14}{3}.$

Find $2\dfrac{1}{2}%$ of $320$ people.

$2\dfrac{1}{2}=\frac{5}{2}$

$=\frac{5}{2}\times 320=800$

find : $2.5 \times 0.3$

$2.5\times0.3 =0.75$

$18.368\div 14$ .

$18.368\div 14=1312$

Divide each of the given numbers by $10,100,1000$ and 10000 $:$
$2.1$
$8.64$
$5.01$
$0.0906$
$0.125$
$111.11$

1211753_1320020_ans_4ea5dc1bf8e24a0a86925fac35585c5a.jpg

Solve : $0.5\times 0.05$

We have,

$0.5 \times 0.05$

$\begin{array}{l} =\cfrac { 5 }{ { 10 } } \times \cfrac { 5 }{ { 100 } } \\ =\cfrac { { 25 } }{ { 1000 } } \\ =0.025 \end{array}$

Hence,

We get

$0.025$

Solve
(i) $1.5\times 0.3$

$\begin{array}{l} We\, \, have, \\ 1.5\times 0.3 \\ =\cfrac { { 15 } }{ { 10 } } \times \cfrac { 3 }{ { 10 } } \\ =\cfrac { { 45 } }{ { 100 } } \\ =0.45 \\ Hence, \\ We\, \, get=0.45 \end{array}$

Solve: $1.07\times 0.02$

We have,

$1.07 \times 0.02$

$\begin{array}{l} =\cfrac { { 107 } }{ { 100 } } \times \cfrac { 2 }{ { 100 } } \\ =\cfrac { { 214 } }{ { 10000 } } \\ =0.0214 \end{array}$

Hence,

We get

$0.0214$

Solve: $4.3\times 3.4$

Given that,

$4.3 \times 3.4$

$\begin{array}{l} =\cfrac { { 43 } }{ { 10 } } \times \cfrac { { 34 } }{ { 10 } } \\ =\cfrac { { 1462 } }{ { 100 } } \\ =14.62 \end{array}$

Hence,

We get

$14.62$ as final answer

Solve: $0.1\times 47.5$

Given that,

$0.1 \times 47.5$

$\begin{array}{l} =\cfrac { 1 }{ { 10 } } \times \cfrac { { 475 } }{ { 10 } } \\ =\cfrac { { 475 } }{ { 100 } } \\ =4.75 \end{array}$

Hence,

We get

$4.75$

Solve:
$10.05\times 1.05$

We have,

$10.05 \times 1.05$

$\begin{array}{l} =\cfrac { { 1005 } }{ { 100 } } \times \cfrac { { 105 } }{ { 100 } } \\ =\cfrac { { 105525 } }{ { 10000 } } \\ =10.5525 \end{array}$

Hence,

We get

$10.5525$

Solve : $70.01\times 1.1$

We have,

$70.01 \times 1.1$

$\begin{array}{l} =\cfrac { { 7001 } }{ { 100 } } \times \cfrac { { 11 } }{ { 10 } } \\ =\cfrac { { 77011 } }{ { 1000 } } \\ =77.011 \end{array}$

Hence,

We get

$77.011$

Find:
$0.2\times 6$

$0.2\times6$ =

$1.2$

Find
$651.2 \div 4$

Given

$651.2 \div 4$

$=651.2 \times {\dfrac14}$

$={\dfrac{6512}{10}} \times {\dfrac14}$

$=\dfrac{1628}{10}$

$=162.8$

Hence,

$651.2 \div 4=162.8$ .

Convert the following into a vulgar fraction:
$2.\overline { 13 }$

Let

$y=2.131313$

$\Rightarrow 100y=213.131313$

$-99y=-211$

$\Rightarrow y=\dfrac{211}{99}$ .

1214449_1396056_ans_8c31d5c2ee34438a939812b75e6a6038.jpg

Fill in the blank.
$1.1 \times 100=$ ______

Now,

$1.1 \times 100=\dfrac{11}{10}\times 100=110$ .

Convert the following into a vulgar fraction:
$0.\bar { 8 }$

Let

$y=0.8888$

$\Rightarrow 10y=8.888$

$-9y=-8$

$\Rightarrow y=\dfrac{8}{9}$ .

1214445_1396044_ans_a5d7e39f43c342fb92f85de1d6f009b9.jpg

Multiply : $0.1\times 51.7$

$0.1\times 51.7$

$5.17$

Simplify: $9\displaystyle \dfrac{5}{10}$

$9\dfrac{5}{10}=9\dfrac{1}{2}=9+\dfrac{1}{2}=\dfrac{18+1}{2}=\dfrac{19}{2}$

$\implies 9\dfrac{5}{10}=\dfrac{19}{2}$

Convert the following into a vulgar fraction:
$0.\overline { 34 }$

Let

$y=0.343434$

$100y=34.343434$

$-99y=-34$

$\Rightarrow y=\dfrac{34}{99}$ .

1214446_1396049_ans_1cf591ba804741b3838aca8968130a53.jpg

Fill in the blank.
$0.345 \times 1000=$ ______

Now,

$0.345 \times 1000=\dfrac{345}{1000}\times 1000=345.$

Fill in the blank.
$5.9 \times 1000=$ _____

Now,

$5.9 \times 1000=\dfrac{59}{10}\times 1000=5900$ .

Fill in the blank.
$10.056 \times 100=$ ______

Now,

$10.056 \times 100=\dfrac{10056}{1000}\times 100=\dfrac{10056}{10}=1005.6$

Fill in the blank.
$5.76 \times 10=$ ________

Now,

$5.76 \times 10=\dfrac{576}{100}\times 10=\cfrac{576}{10}=57.6$ .

What is the value when $442.36\ km$ is divided by $2$ .

Dividing

$442.36$ by

$2$ .

$\dfrac{442.36}{2}\, km$

$=221.18\, km$

What is $10$ times of $50.30$ kg.

Multiplying

$50.30$ by

$10$

$50.30\times10$

$=503\,kg$

Convert $\dfrac{87}{7}$ into mixed fraction.

$\therefore \dfrac {87}{7}$ in mixed fraction

$= 12 \dfrac {3}{7}$
1708525_1788421_ans_db92b62ad3544c3b9a7dd275a9f0fb47.png

To multiply a decimal number by 1000, we move
the decimal point in the number to the right by three places.

True

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, (a + a^{1/2} b^{1/2})(a + b)^{-1}(\sqrt{a}(\sqrt{a} -\sqrt{b})^{-1} - (\frac{\sqrt{a} + \sqrt{b}}{\sqrt{b}})^{-1})$

1313389_884361_ans_6ded26194d3342fbb65fc1b7611a8392.jpg

Convert the following into a vulgar fraction:
$0.\bar { 6 }$

Let

$y=0.6666$

$\Rightarrow 10y=6.6666$

$\Rightarrow -9y=-6$

$\Rightarrow y=\dfrac{6}{9}=\dfrac{2}{3}$

$\Rightarrow y=\dfrac{2}{3}$ .

$2.4\div 10=$

2045325_1570264_ans_7d8d8fd0a32e47b1b8a8a4a92e90091e.jpg

Simplify:
$3.24\div 0.0016$

$3.24\div 0.0016$

$=\dfrac{3.24}{0.0016}$

$=\dfrac{3.24\times 10000}{0.0016\times 10000}$ by multiplying and dividing by

$10000$

$=\dfrac{32,400‬}{16}$

$=2,025‬$

Divide $0.57$ by $10$ .

If we divide

$0.57$ by

$10,$ then we get,

$\dfrac{0.57}{10}$

$=\dfrac{57}{10\times 100}$

$=\dfrac{57}{1000}$

$=0.057$

Hence, the required answer is

$0.057\ .$

Find:
$211.9 \times 1.13$

1498994_1676165_ans_216363157e4749e8a7f8626acc057227.jpg

Divide $54.25$ by $10$ .

Now if we divide

$54.25$ by

$10$ then we get,

$\dfrac{54.25}{10}$

$=\dfrac{5425}{1000}$

$=5.425$

Divide $0.004$ by $10$ .

If we divide

$0.004$ by

$10$ then we get,

$\dfrac{0.004}{10}$

$=\dfrac{4}{10,000}$

$=0.0004$

Divide:
$0.45$ by $9$

If we divide

$0.45$ by

$9$ we get,

$\dfrac{0.45}{9}$

$=\dfrac{45}{900}$

$=\dfrac{5}{100}$

$=0.05$

Divide $0.48$ by $100$ .

If we divide

$0.48$ by

$100$ we get,

$\dfrac{0.48}{100}$

$=\dfrac{48}{10,000}$

$=0.0048$

Divide:
$40.32$ by $9.6$

If we divide

$40.32$ by

$9.6$ then we get,

$\Rightarrow \dfrac{40.32}{9.6}$

$=\dfrac{403.2}{96}\\=\dfrac {4032}{960}\\=\dfrac {21}{5}$

$=4.2$

Divide $0.71$ by $1000$ .

If we divide

$0.71$ by

$1000$ then we get,

$\dfrac{0.71}{1000}$

$=\dfrac{71}{100,000}$

$=0.00071$

Divide $3.8$ by $1000$ .

If we divide

$3.8$ by

$1000$ then we get,

$\dfrac{3.8}{1000}$

$=\dfrac{38}{10,000}$

$=0.0038$

Divide $74.3$ by $100$ .

If we divide

$74.3$ by

$100$ then we get,

$\dfrac{74.3}{100}$

$=\dfrac{743}{1000}$

$=0.743$

Divide $0.7$ by $100$ .

If we divide

$0.7$ by

$100$ we get,

$\dfrac{0.7}{100}$

$=\dfrac{7}{1000}$

$=0.007$

Divide:
$217.44$ by $9$

If we divide

$217.44$ by

$9$ then we get,

$\dfrac{217.44}{9}=\dfrac {21744}{900}=\dfrac {604}{25}$

$=24.16$

Divide: $319.2$ by $2.28$

If we divide

$319.2$ by

$2.28$ then we get,

$=\dfrac{319.2}{2.28}$

$=\dfrac{31920}{228}$ {multiplying numerator and denominator by 100}

$=140$

Divide $29.5$ by $1000$ .

If we divide

$29.5$ by

$1000$ then we get,

$\dfrac{29.5}{1000}$

$=\dfrac{295}{10,000}$

$=0.0295$

Divide:
$31.92$ by $228$

If we divide

$31.92$ by

$228$ then we get,

$\dfrac{31.92}{228}$

$=\dfrac {3192}{100}\times \dfrac{1}{228}=\dfrac {14}{100}$

$=0.14$

Divide:
$403.2$ by $96$

If we divide

$403.2$ by

$96$ then we get,

$\dfrac{403.2}{96}$

$=\dfrac {4032}{960}=\dfrac {21}{5}$

$=4.2$

Divide:
$0.765$ by $0.9$

If we divide

$0.765$ by

$0.9$ then we get,

$\dfrac{0.765}{0.9}$

$=\dfrac{7.65}{9}$

$=0.85$

Divide:
$15.68$ by $20$

If we divide

$15.68$ by

$20$ then we get,

$\dfrac{15.68}{20}$

$=\dfrac {1568}{100}\times \dfrac{1}{20}=\dfrac {789}{1000}$

$=0.784$

Divide:

$0.08 \quad by \quad 10$

On dividing a decimal by

$10$ , the decimal point is shifted to the left by one place.

$\therefore 0.08 \div 10$

$= \cfrac{0.08}{10}\\$

$= 0.008$ ....

$\{$ Decimal point shifted one place to left

$\}$

Divide:

$23.4 \quad by \quad 100$

On dividing a decimal by

$100$ , the decimal point is shifted to the left by two places.

$$ \therefore 23.4 \div 100 $$

$= \cfrac{23.4}{100}\\$

$=0.234$ ....

$\{$ Decimal point shifted two places to left

$\}$

Divide:

$137.2 \quad by \quad 100$

On dividing a decimal by

$100$ , the decimal point is shifted to the left by two places.

$\therefore 137.2 \div 100$

$= \cfrac{137.2}{100}\\$

$=1.372$ ....

$\{$ Decimal point shifted two places to left

$\}$

Divide:

$32.56 \quad by \quad 10$

On dividing a decimal by

$10$ , the decimal point is shifted to the left by one place.

$\therefore 32.56 \div 10$

$= \cfrac{32.56}{10}\\$

$= 3.526$ ....

$\{$ Decimal point shifted one place to left

$\}$

Divide:

$0.062 \quad by \quad 10$

On dividing a decimal by

$10$ , the decimal point is shifted to the left by one place.

$\therefore 0.062 \div 10$

$= \cfrac{0.062}{10}\\$

$= 0.0062$ ....

$\{$ Decimal point shifted one place to left

$\}$

Express the following improper fractions as mixed fractions:
$25/6$

When we divide

$25$ by

$6$ it leaves a remainder of

$1$ i.e,

$25 = 4\times 6 +1$ .

Therefore,

$25/6$ can be express as mixed fractions as

$4 \dfrac{1}{6}$ .

Express the following improper fractions as mixed fractions:
18/5

$18/5$ can be expressed as mixed fractions as

$3 \dfrac{3}{5}.$

Express the following mixed fractions as improper fractions:
$3 \dfrac{1}{4}$

$3 \dfrac{1}{4}$
It can be written as

$= \left(3 \times 4 + 1\right)/4$
By further calculation

$= \left(12 + 1\right)/4$

$= 13/4$

Express the following improper fractions as mixed fractions:
$22/5$

$22/5$ can be express as mixed fractions as

$4\dfrac{ 2}{5.}$

Express the following improper fractions as mixed fractions:
$38/5$

$38/5$ can be express as mixed fractions as

$7 \dfrac{3}{5}$ .

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$0.112$

$0.112$
It can be written as

$0.112 \times 10=1.12$

$0.112 \times 100=11.2$

$0.112 \times 1000=112$

Multiply each number by $10,100,1000 :$
$0.5$

$0.5$
It can be written as

$0.5 \times 10=5$

$0.5 \times 100=50$

$0.5 \times 1000=500$

Multiply:
$0.568$ by $6.4$

$0.568$ by

$6.4$
It can be written as

$0.568 \times 6.4=3.6352$

$\begin{array}{l l}& \,\,0.568 \\\times& \,\,\,\,\,\,\,6.4 \\\hline & \,\,\,\,2272 \\\times& \,3408 \\ \hline& 3.6352 \end{array}$

Express the following mixed fractions as improper fractions:
$12\dfrac{ 7}{11}$

$12\dfrac{ 7}{11}$
It can be written as

$= \left(12 \times 11 + 7\right)/11$
By further calculation

$= \left(132 + 7\right)/11$

$= 139/11$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$4.8$

$4.8$
It can be written as

$4.8 \times 10=48$

$4.8 \times 100=480$

$4.8 \times 1000=4800$

Multiply:
16.32 by 28

$16.32$ by

$28$
It can be written as

$16.32 \times 28=456.96$

$\begin{array}{l l}& 16.32 \\\times&28 \\\hline & 130.56 \\ & 326.4 \\ \hline & 456.96 \end{array}$

Divide:
$324.76$ by $1000$

$324.76$ by

$1000$
It can be written as

$324.76 \div 1000=\dfrac{324.76}{1000}=0.32476$

Divide:
4.8432 by 0.08

$4.8432$ by

$0.08$
It can be written as

$4.8432 \div 0.08$
Multiplied by

$10000$
So we get

$48432 \div 800=60.54$
1744066_1827783_ans_f955e709135648c49c2f4c61dbd96933.png

Evaluate :
$0.125 \div 25$

$0.125 \div 25$
We get

$0.125 \div 25=0.005$
1744168_1827811_ans_ec93f10677ef479d827987bb8ec7c06c.png

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$16.27$

It can be written as

$16.27 \times 10=162.7$

$16.27 \times 100=1627$

$16.27 \times 1000=16270$

Evaluate:
$5.897 \times 2.3$

$5.897 \times 2.3$
We know that

$5.897 \times 2.3=13.5631$

$\begin{array}{l l}& \,\,\,\,5.897 \\ \times& \,\,\,\,\,\,\,\,2.3 \\ \hline & \,\,\,\,17691 \\ \times& \,\,11794 \\ \hline & 13.5631 \end{array}$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$234.8$

$234.8$
It can be written as

$234.8 \times 10=2348$

$234.8 \times 100=23480$

$234.8 \times 1000=234800$

Evaluate :
$20.64 \div 16$

$20.64 \div 16$
We get

$20.64 \div 16=1.29$
1744136_1827804_ans_bad8cef9579c4ef7ba7f9322f9be665e.png

Divide:
$27.918$ by $9$

$27.918$ by

$9$
It can be written as

$\dfrac{27918}{1000} \div 9$

$=\dfrac{27918}{1000}\times \dfrac19$

$=\dfrac{3102}{1000}=3.102$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$0.0359$

$0.0359$
It can be written as

$0.0359 \times 10=0.359$

$0.0359 \times 100=3.59$

$0.0359 \times 1000=35.9$

Evaluate :
$19.25 \div 25$

$19.25 \div 25$
We get

$19.25 \div 25=0.77$

1744124_1827802_ans_1c40357819e840e1bdb1035846f33035.png

Evaluate :
$257.894 \div 0.169$

$257.894 \div 0.169$
Multiplying by 1000

$257894 \div 169=1526$
1744228_1827816_ans_569d1457fccd4687a186e2d36fddd543.png

Solve : $13 \dfrac{5}{6} \times 1\dfrac{5}{26}$

$13\dfrac{5}{6}\times 1\dfrac{5}{26}$

$=\dfrac{83}{6}\times \dfrac{31}{26}$

$=\dfrac{2573}{156}$

$=16\dfrac{77}{156}$

Divide the following numbers by $10, 100$ and $1000$ ( orally):
$3.45$

$3.45$

$3.45\div 10=0.345$

$3.45\div 100=0.0345$

$3.45\div 1000=0.00345$

Evaluate :
$9.75 \div 5$

$9.75 \div 5$
We get

$9.75 \div 5 =1.95$
1744086_1827797_ans_8e6205986ee049e2beaffee3ee30fb7c.png

For the celebration class $VII$ bought sweets for $Rs.740.25$ and cold drink for $Rs.70$ . If $35$ students contributed equally what amount was contributed by each student.

$740.25+70=810.25$

then

$810.25 \div 35 = 23.15$

Fill in the blank.
$32.4 \times 10=$ ______

Now,

$32.4 \times 10=\dfrac{324}{10}\times 10=$

$324$ .

Fill in the blank.
$0.369 \times 10=$ ________

Now,

$0.369 \times 10=\dfrac{369}{1000}\times 10=\dfrac{369}{100}=3.69$ .

Fill in the blank.
$2.35 \times 1000=$ ____

Now,

$2.35 \times 1000=\dfrac{235}{100}\times 1000=2350$ .

Fill in the blank.
$0.25 \times 100=$ _____

Now,

$0.25 \times 100=25.$

Divide $0.043$ by $10$ .

If we divide

$0.043$ by

$10$ then we get,

$\dfrac{0.043}{10}$

$=\dfrac{43}{10,000}$

$=0.0043$

$8.892\div 19=x$ . Find $1000x$

We have,

$\Rightarrow x = 8.892 \div 19$

$\Rightarrow 0.468$

Then,

$\Rightarrow 100x = 0.468 \times 1000$

$\Rightarrow \dfrac{{468}}{{1000}} \times 1000$

$=468$

Hence,

$1000x=468$

$324.4\div 100 =x$ . Find $1000x$

We have,

$\Rightarrow x = 324.4 \div 100$

$=3.244$

Then,

$\Rightarrow 1000x = 3.244 \times 1000$

$\Rightarrow \dfrac{{3244}}{{1000}} \times 1000$

$=3244$

Hence,

$1000x=3244$

$35.7\div 10 =x$ . Find $100x$

We have,

$\Rightarrow x = 35.7 \div 10$

$=3.57$

Then,

$\Rightarrow 100x = 3.57 \times 100$

$\Rightarrow \dfrac{{357}}{{100}} \times 100$

$=357$

Hence,

$100x=357$

If $0.24\div 0.6=x$ . Find $10x$

We have,

$x = 0.24 \div 0.6$

$=0.4$

Then,

$10x=0.4 \times10=4$

Hence,

$10x=4$

Find $1.5\div 0.05=$

We have,

$1.5 \div 0.05$

$= \dfrac{{1.5}}{{0.05}} \times \dfrac{{100}}{{10}}$

$=30$

If cost of a pen is $Rs. 6.25$ then the cost of $14$ such pens is

The cost of

$1$ pen

$=Rs.6.25$

Then,

The cost of

$14$ such pens

$=6.25 \times14$

$=87.5$

Find $3.6\div 0.6$ .

We have,

$3.6 \div 0.6$

$= \dfrac{{3.6}}{{0.6}}$

$= \dfrac{{36}}{6} \times \dfrac{{10}}{{10}}$

$=6$

$0.2\div 10 =x$ . Find $100x$

We have,

$\Rightarrow x = 0.2 \div 10$

$=0.02$

Then,

$\Rightarrow 100x = 0.02 \times 100$

$\Rightarrow \dfrac{2}{{100}} \times 100$

$=2$

Hence,

$100x=2$

Solve $6.69\div 3=x$ . Find $100x$

We have,

$\Rightarrow x = 6.69 \div 3$

$\Rightarrow 2.23$

Then,

$100x = 2.23 \times 100$

$\Rightarrow \dfrac{{223}}{{100}} \times 100$ [Divide

$100$ by

$100$ we get

$1$ ]

$\Rightarrow 223 \times 1$

$\Rightarrow 223$

Solve : $\dfrac{9}{46} \times 7\dfrac{2}{3}$

$\dfrac{9}{46}\times 7\dfrac{2}{3}$

$=\dfrac{9}{46}\times \dfrac{23}{3}$

$=\dfrac{3}{2}\times \dfrac{1}{1}$

$=\dfrac{3}{2}$

$2.214 \div 18=x$ . Find $1000x$

We have,

$\Rightarrow x = 2.214 \div 18$

$\Rightarrow 0.123$

Then,

$\Rightarrow 100x = 0.123 \times 100$

$\Rightarrow \dfrac{{123}}{{1000}} \times 1000$

$= 123$

Hence,

$1000x= 123$

Express the septenary fraction $\cfrac{1552}{2626}$ as a denary vulgar fraction in its lowest terms.

$1552$ from the scale of seven to decimal is

$2\times7^0+5\times7^1+5\times7^2+1\times7^3=625$

$2626$ from the scale of seven to decimal is

$6\times7^0+2\times7^1+6\times7^2+2\times7^3=1000$

Hence, the fraction is

$\dfrac{625}{1000}=\dfrac58$

Solve the following:
$168.07\times 100$

1496809_703925_ans_1134101f188949fa9d952eef0abdd9cf.PNG

Solve the following:
$131.1\times 100$

$131.1\times 100$

There is one decimal digit in the factor

$131.1$

Now, we are going to remove that decimal digit.

$\Rightarrow$

$\dfrac{1311}{10}\times 100$

$\Rightarrow$

$1311\times 10$

$\Rightarrow$

$13110$

$\therefore$

$131.1\times 10=13110$

Solve the following:
$53.7\times 10$

1305115_703924_ans_f068dbda801d484bba07e49c94830e0d.jpeg

Solve the following:
$36.8\times 10$

$36.8×10$

$=368.0$

So the correct answer is

$368$

Solve the following:
$21.3\times 10$

To find

$21.3\times 10$

$21.3×10$

$=213.0$

Hence, the answer is

$213$

Solve the following:
$0.08\times 100$

1496806_703932_ans_20d8d22e4f6a4bd7a42ecb6c751e3915.PNG

Solve the following:
$0.03\times 1000$

1305123_703937_ans_03e7550533f54829889b86c5607829e3.jpeg

Solve the following:
$88.5\div 0.15$

Given,

$88.5\div 0.15$

Could be written as,

$= \dfrac{855}{10}\times \dfrac{100}{15}$

$= 590$

So, given statement is true.

$\dfrac {6}{15}\times \dfrac {5}{18}=$ $\dfrac {x}{9}$ . Find x.

For the value of

$X$ ,we have to solve the given equation.

$\Rightarrow \dfrac{6}{{15}} \times \dfrac{5}{{18}} = \dfrac{x}{9}$

$\Rightarrow \dfrac{6}{{15}} \times \dfrac{5}{{18}} = \dfrac{x}{9}\,\,\,\,\left[ {divide\,\,18\,\,by\,\,6 = 3\& \,divide\,\,15\,\,by\,\,5\, = 3} \right]$

$\Rightarrow \dfrac{1}{3} \times \dfrac{1}{3} = \dfrac{x}{9}$

$\Rightarrow \dfrac{1}{9} = \dfrac{x}{9}\,\,\,\,\,\,\,\,\,\,\therefore cancle\,\,\,9\,\,both\,\,side$

$\therefore x = 1$

Hence, the value of

$X=1$

Solve $50\dfrac{1}{2}\times 49\dfrac{1}{2}$ .

$50 \dfrac{1}{2} \times 49 \dfrac{1}{2}$

$= \dfrac{101}{2} \times \dfrac{99}{2}$

$=\dfrac{9999}{4}$

$\dfrac {9}{10}\times \dfrac {5}{9}\times \dfrac {15}{25}=$ $\dfrac {x}{10}$ . Find x.

For the value of

$X$ , we solve the given equation:-

$\Rightarrow \dfrac{9}{{10}} \times \dfrac{5}{9} \times \dfrac{{15}}{{25}} = \dfrac{x}{{10}}$

$\Rightarrow \dfrac{9}{{10}} \times \dfrac{5}{9} \times \dfrac{{15}}{{25}} = \dfrac{x}{{10}}\,\,\,\,\left[ {cancle\,\,9\,by\,9\,,\,\,25\,by\,\,5\,\& 15\,\,by\,\,5} \right]$

$\Rightarrow \dfrac{3}{{10}} = \dfrac{x}{{10}}\,\,\,\left[ {cancle\,\,10\,\,both\,\,sides} \right]$

Hence, the value of

$X=3$ .

$\therefore x = 3$

Calculate $4.203\times 15000$ .

Mutliply of

$4.203 \times 15000$

$= \cfrac{{4203}}{{1000}} \times 15000$

$= \cfrac{{63045000}}{{1000}}$

$={63045}$

Hence, the solution is

$63045$

Calculate $0.035\times 1200$ .

Multiply

$0.035 \times 1200$

$= \dfrac{{35}}{{1000}} \times 1200$

$= \dfrac{{42000}}{{1000}}$

$=42$

Hence, the solution is

$42$

Evaluate $2.25\times 4$ .

Multiply

$2.25 \times 4$

$= \dfrac{{225}}{{100}} \times 4$

$= \dfrac{{900}}{{100}}$

$=9$

Hence, the solution is

$9$

$3.4\times 10 =$ ________.

Multiply

$3.4 \times 10$

$= \cfrac{{34}}{{10}} \times 10$

$=34$

Hence, the solution is

$34$

$2.97\times 100 =$ _______.

Multiply of

$2.97 \times 100$

$= \cfrac{{297}}{{100}} \times 100$

$=297$

Hence, the solution is

$297$

$3.4\times 1000 =$ _______.

We have,

$\Rightarrow 3.4 \times 1000 = \dfrac{{34}}{{10}} \times 1000$ [Divide

$1000$ by

$10$ we get

$10$ ]

$\Rightarrow 34 \times 100$

$\Rightarrow 3400$

Calculate $3.5\times 24$ .

Multiply

$3.5 \times 24$

$=\cfrac{{35}}{{10}} \times 24$

$=\cfrac{{840}}{{10}}$

$=84$

Hence, the solution is

$84$ ,

$0.46\times 100 =$ _________.

Multiply of

$0.46 \times 100$

$= \cfrac{{46}}{{100}} \times 100$

$=46$

Hence, the solution is

$46$

$0.5\times 10 =$ ____________.

Multiply

$0.5 \times 10$

$= \cfrac{5}{{10}} \times 10$

$=5$

Hence, the solution is

$5$

Calculate $6.54\times 50$ .

Given multiply of

$6.54 \times 50$

$= \cfrac{{654}}{{100}} \times 50$

$= \cfrac{{32700}}{{100}}$

$=327$

Hence, the solution is

$327$ ,

$0.25\times 1000 =$ __________.

Multiply of

$0.25 \times 1000$

$= \cfrac{{25}}{{100}} \times 1000$

$=250$

Hence, the solution is

$250$

Solve $2.1\times 100 =$ ______.

We have,

$\Rightarrow 2.1 \times 100 = \dfrac{{21}}{{10}} \times 100$ [Divide

$100$ by

$10$ we get

$10$ ]

$\Rightarrow 21 \times 10$

$\Rightarrow 210$

Calculate $7.604\times 0$ .

Multiply of

$\cfrac{{7604}}{{1000}} \times 0$

$=\cfrac{{7604}}{{1000}} \times 0$

$=0$

Hence, the solution is

$0$

$14.63\div 11=x$ . Find $100x$

We have,

$\Rightarrow x = 14.63 \div 11$

$\Rightarrow 1.33$

Then,

$\Rightarrow 100x = 1.33 \times 100$

$\Rightarrow \dfrac{{133}}{{100}} \times 100$ [Divide

$100$ by

$100$ we get

$1$ ]

$\Rightarrow 133 \times 1$

$\Rightarrow 133$

$\therefore x = 133$

$13.92\div 12=x$ . Find $100x$

We have,

$\Rightarrow x = 13.92 \div 12$

$\Rightarrow 1.16$

Then,

$\Rightarrow 100x = 1.16 \times 100$

$\Rightarrow \dfrac{{116}}{{100}} \times 100$ [Divide

$100$ by

$100$ we get

$1$ ]

$=116$

$\therefore x = 116$

$48.3\div 14=x$ . Find $100x$

We have,

$\Rightarrow x = 48.3 \div 14$

$\Rightarrow 3.45$

Then,

$\Rightarrow 100x = 3.45 \times 100$

$\Rightarrow \dfrac{{345}}{{100}} \times 100$ [Divide

$100$ by

$100$ we get

$1$ ]

$\therefore x = 345$

$45.645 \div 15=x$ . Find $1000x$

We have,

$\Rightarrow x = 45.645 \div 15$

$\Rightarrow 3.043$

Then,

$\Rightarrow 1000x = 3.043 \times 1000$

$\Rightarrow \dfrac{{3043}}{{1000}} \times 1000$

Hence,

$1000x=3043$

$39.39\div 13=x$ . Find $100x$

We have,

$\Rightarrow x = 39.39 \div 13$

$=3.03$

Then,

$\Rightarrow 100x = 3.03 \times 100$

$\Rightarrow \dfrac{{303}}{{100}} \times 100$

$=303$

Hence,

$100x=303$

Solve $2.24\times 100 =$ ______.

We have,

$\Rightarrow 2.24 \times 100 = \dfrac{{224}}{{100}} \times 100$ [Cancle

$100$ by

$100$ ]

$\Rightarrow 224 \times 1$

$\Rightarrow 224$

$24.6\div 100 =x$ . Find $1000x$

We have,

$\Rightarrow x = 24.6 \div 100$

$=0.246$

Then,

$\Rightarrow 1000x = 0.246 \times 1000$

$\Rightarrow \dfrac{{246}}{{1000}} \times 1000$

$=246$

Hence,

$1000x=246$

Hitesh and Hiral goes to market to buy some items for their home. Rate of items are in kg. Answer the following question on its base. How much is the price of $4\ kg$ Rice in rupees?

The Price of

$4kg$ Rice

$=4 \times$ cost of

$1kg$ Rice.

$=4 \times20.50$

$Rs.82.00$

$620.5 \div 10 =x$ . Find $100x$

We have,

$\Rightarrow x = 620.5 \div 10$

$=62.05$

Then,

$\Rightarrow 100x = 62.05 \times 100$

$\Rightarrow \dfrac{{6205}}{{100}} \times 100$

$=6205$

Hence,

$100x=6205$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \frac{x^{1/2} + 1}{x + x^{1/2} + 1} : \frac{1}{x^{1/2} - 1}$

1313391_884210_ans_4cd52dd013474453ac1d354c5e62ba04.jpg

Divide $3.96$ by $4$

$3.96 \div 4$ can be written as

$\dfrac{{3.96}}{4}$

$\Rightarrow \dfrac{{396}}{{400}}$

$\Rightarrow \dfrac{396}{4}\times \dfrac{1}{100}$

$\Rightarrow 99\times 0.01=0.99$

Hence,

$3.96 \div 4$ =

$0.99$

Convert each of the following into mixed fraction :
$(1)\dfrac{17}{5}$ $(2)\dfrac{62}{7}$    $(3)\dfrac{101}{8}$

$(4)\dfrac{95}{13}$    $(5)\dfrac{81}{11}$    $(6)\dfrac{87}{16}$

$(7)\dfrac{113}{12}$    $(8)\dfrac{117}{20}$

We know that, an improper fraction can be converted to a mixed fraction by dividing the numerator with the denominator.

The mixed fraction is formed as

$\text{Quotient}\dfrac{\text{Remainder}}{\text{Divisor}}$

Now, let's convert each of the given fraction into a mixed fraction.

$(1)$

$\dfrac{17}{5}$

$17=3\times 5+2$

Hence, quotient

$=3$ and remainder

$=2$

$\therefore\ \dfrac{17}{5}=3\dfrac25$

$(2)$

$\dfrac{62}{7}$

$62=8\times 7+6$

Hence, quotient

$=7$ and remainder

$=6$

$\therefore\ \dfrac{62}{7}=8\dfrac67$

$(3)$

$\dfrac{101}{8}$

$101=12\times 8+5$

Hence, quotient

$=12$ and remainder

$=5$

$\therefore\ \dfrac{101}{8}=12\dfrac58$

$(4)$

$\dfrac{95}{13}$

$95=7\times 13+4$

Hence, quotient

$=7$ and remainder

$=4$

$\therefore\ \dfrac{95}{13}=7\dfrac{4}{13}$

$(5)$

$\dfrac{82}{11}$

$81=7\times 11+4$

Hence, quotient

$=7$ and remainder

$=4$

$\therefore\ \dfrac{81}{11}=7\dfrac{4}{11}$

$(6)$

$\dfrac{87}{16}$

$87=5\times 16+7$

Hence, quotient

$=5$ and remainder

$=7$

$\therefore\ \dfrac{87}{16}=5\dfrac{7}{16}$

$(7)$

$\dfrac{113}{12}$

$113=9\times 12+5$

Hence, quotient

$=9$ and remainder

$=5$

$\therefore\ \dfrac{113}{12}=9\dfrac{5}{12}$

$(8)$

$\dfrac{117}{20}$

$117=5\times 20+17$

Hence, quotient

$=5$ and remainder

$=17$

$\therefore\ \dfrac{117}{20}=5\dfrac{17}{20}$

Simplify $7\dfrac {1}{2} \times 3\dfrac {1}{3}$

$7\cfrac{1}{2} \times 3\cfrac{1}{3}$

$= \cfrac{{7 \times 2 + 1}}{2} \times \cfrac{{3 \times 3 + 1}}{3}$

$= \cfrac{{15}}{2} \times \cfrac{{10}}{3}$

$= \cfrac{{150}}{6}$

Evaluate $9\dfrac {1}{11}\times 10\dfrac {1}{12}$

Let

$=9\cfrac{1}{{11}} \times 10\cfrac{1}{{12}}$

$\Rightarrow$

$= \cfrac{{99 + 1}}{{11}} \times \cfrac{{120 + 1}}{{12}}$

$= \cfrac{{100}}{{11}} \times \cfrac{{121}}{{12}}=\dfrac{12100}{132}$

Find the value of :
(i) ${(82)^2} - {(18)^2}$
(ii)   $\,\,{(128)^2} - {(72)^2}$
(iii)   $\,197 \times 203\,\,$
(iv)   $\dfrac{{198 \times 198 - 102 \times 102}}{{96}}$
(v) $(14.5 \times 15.3)\,$
(vi) $\,\,\,\,\,{(8.63)^2} - {(1.37)^2}$

$(82)^2-(18)^2\ \ \ \ (\text{using}\quad a^2-b^2=(a+b)(a-b))$

$=(82+18)(82-18)$

$=100\times 64\\=6400$

ii)

$(128)^2-(72)^2$

$(128+72)(128-72)$

$=200\times 56$

$=11200$

iii)

$197\times 203$

$=(200-3)(200+3)$

$=200^2-3^2$

$=40000-9$

$=39991$

iv)

$\dfrac{198\times198-102\times102}{96}$

$=\dfrac{198^2-102^2}{96}\\=\dfrac{(198+102)(198-102)}{96}$

$=\dfrac{300\times 96}{96}\\=300$

$(14.5\times 15.3)=221.85$

vi)

$(8.63)^2-(1.37)^2$

$=(8.63+1.37)(8.63-1.37)$

$=10\times 7.26$

$=72.6$

Solve $45.30 \div 15$

$45.30 \div 15$ can be written as

$\dfrac{45.30}{15}$

$= \dfrac{4530}{1500}$

Dividing both numerator and denominator by

$15$ , we get

$= \dfrac{302}{100}$

$= 3.02$ Answer

Multiply: $\dfrac { 4 }{ 5 } \times 6\dfrac { 1 }{ 4 }$

Here,

$\dfrac{4}{5} \times 6\dfrac{1}{4}$

$= \dfrac{4}{5} \times \dfrac{{25}}{4}$

$= \dfrac{{100}}{{20}}$

$= 5$

Find

(i) $0.4\, \div \,\,2$

(ii) $0.35\, \div \,\,5$

(iii) $2.48\, \div \,\,4$

(iv) $65.4\, \div \,\,6$

(v)   $651.2\, \div \,\,4$

(vi)   $14.49\, \div \,\,7$

(vii)   $3.96\, \div \,\,4$

(viii)   $0.80\, \div \,\,5$

$(i){{0.4} \over 2} = 0.2$

$(ii){{0.35} \over 5} = 0.07$

$\left( {iii} \right){{2.48} \over 4} = 0.62$

$\left( {iv} \right){{65.4} \over 2} = 10.9$

$(v){{651.2} \over 4} = 162.8$

$(vi){{14.49} \over 7} = 2.07$

$(vii){{3.96} \over 4} = 0.99$

$(viii){{0.80} \over 5} = 0.16$

Find
(i) $7.9\, \div \,1000$
(ii) $128.9\, \div \,10$

On solving the given expression,

1.) $\dfrac{7.9} {1000}= 0.0079$

2.) $\dfrac{128.9} {10}= 12.89$

Work out the following division.
a. $0.6\div2$
b. $0.625 \div 5$
c. $17.28 \div 9$
d. $7.2 \div 4$

1326008_1064923_ans_05ac5fff0dcc4195a75ac9d40fa81a62.jpg

Rishi bought six school bags for Rs. $712.02$ . What is the cost of each bag?

$6\>bags\longrightarrow712.02\>Rs\\\therefore 1\>bag\longrightarrow(\cfrac{712.02}{6})\\=118.67\>Rs$

solve:
(i) $6\frac{1}{4}\div 1\frac{1}{3}$
(ii) $12\div 1\frac{3}{4}$
(iii) $\frac{1}{3}\times 2\frac{1}{3}$

(i)

$6\frac {1}{4} \div 1\frac {1}{3}$

$= \frac {{25}}{{4}} \div \frac {4}{3}$

$= \frac {{25}}{{4}} \div \frac {3}{4}$

$= \frac {{25}}{{3}}$

(ii)

$12 \div 1\frac {3}{4}$

$= 12 \div \frac {7}{4}$

$= 12 \times \frac {4}{7}$

$= \frac{{48}}{{7}}$

(iii)

$\frac {1}{3} \div 2\frac{1}{3}$

$= \frac{1}{3} \div \frac {7}{3}$

$= \frac{1}{3} \times \frac {3}{7}$

$= \frac {1}{7}$

Multiply:
$2.57$ by $1.8$

On multiplying we get,

$2.57\times1.8$

$\implies 4.626$

Find the product of $\dfrac {12}{15}$ & $\dfrac {14 }{ 10}$

$\cfrac{12}{15}\times \cfrac{14}{10}$

$=\cfrac{4}{5}\times \cfrac{14}{10}$ ( dividing

$12$ and

$15$ by

$3$ )

$=\cfrac{4}{5}\times \cfrac{7}{5}$ ( dividing

$14$ and

$10$ by

$2$ )

$=\cfrac{28}{25}$

$\cfrac{0.036}{4}$

The pronblem given

$\cfrac {0.036}{4}$

$= \cfrac {36}{4000}$

$= .009$

Find the value of
$3.852\div 1.8$

According to question,

$\dfrac{3.852}{1.8}$

$=\dfrac{38520}{18000}$

$= 2.14$

Multiply:
$1.5$ by $0.9$

On multiplying , we get

$1.5$

$\times$

$0.9$

$\implies 1.35$

$4\frac { 1 }{ 2 } \quad :\quad 1\frac { 1 }{ 8 }$

$4\dfrac{1}{2}:1\dfrac{1}{8}=\dfrac{9}{2}:\dfrac{9}{8}=\dfrac{1}{2}:\dfrac{1}{8}$

Solve: $42.435 \times 10=?$

$42.435\times 10$

$\Rightarrow 42.435\times 10$

______________

$00000$

$42435\times$

______________

$424.350$ Ans

1148540_1183118_ans_a47beda07043424fa8bf00b21e30de09.jpg

Convert $4\dfrac{11}{7}$ into improper fraction:

$4\dfrac{11}{7} = \dfrac{(4\times 7) + 11}{7} = \dfrac{39}{7}$

Solve: $4\dfrac{3}{5}\times 2\dfrac{3}{7}=\dfrac{23}{5}\times \dfrac{17}{7}= ?$

$\displaystyle 4\frac{3}{5}\times 2\frac{3}{7} = \frac{23}{5}\times \frac{17}{7} = \frac{391}{35}$ Ans
1159134_1182906_ans_3d35c9a2871b473798e183a944cf0b3e.jpg

Find the product :
$3.762\times 10$

$3.762 \times 10 = 37.62$

$6.4 \div 0.4$

$\dfrac{6.4}{0.4}=\dfrac{64}{4}=16$

Simplify: $5 \dfrac { 1 } { 6 } - 3 \dfrac { 1 } { 4 } + 3 \dfrac { 1 } { 3 } + 4$

Given:

$\displaystyle5\frac{1}{6}-3\frac{1}{4}+3\frac{1}{3}+4$

$\\=\displaystyle\left(\frac{31}{6}\right)-\left(\frac{13}{4}\right)+\left(\frac{10}{3}\right)+\left(\frac{4}{1}\right)$

LCM of

$6,4,3 = 12$

$\\=\displaystyle\left(\frac{(31\times2)-(13\times3)+(10\times4)+(4\times12)}{12}\right)$

$\\=\displaystyle\left(\dfrac{62-39+40+48}{12}\right)$

$\\=\displaystyle\frac{111}{12}$

$\\=\dfrac{37}{4}$

Solve: $12.87 \times 4.2$

$12.87\times 4.2$

__________

$2574$

$5148 \times$

__________

$54.054$ Ans

1165163_1191287_ans_c458fd2d4d4a41c9a38678a780fcff1d.jpg

A student in a school pays $3\frac { 1 }{ 5 }$ as a fund. If the amount collected is $406\frac { 2 }{ 5 }$ , find the number of students in the school.

Total amount collected

$=406\dfrac{2}{5}=\dfrac{2032}{5}$

Amount paid by one student

$=3\dfrac{1}{5}=\dfrac{16}{5}$

Number of students

$=\dfrac{Total\ amount}{Amount\ paid \ by\ one\ student}$

$=\dfrac{2032/5}{16/5}$

$=\dfrac{2032}{16}$

$=127$

Hence, number of students are 127.

$3\dfrac{1}{2}\div \dfrac{3}{14}$

$3\frac{1}{2}\div \frac{3}{14}$

$\Rightarrow \frac{7}{2}\times \frac{14}{3} = \frac{49}{3}$

1111536_1204127_ans_e87863e8b62845889ccd034f1a7525e0.jpg

Simplify
$2\dfrac {2}{7} \div 1\dfrac {4}{11} \times 2\dfrac {4}{9}$

$2\cfrac { 2 }{ 7 } \div 1\cfrac { 4 }{ 11 } \times 2\cfrac { 4 }{ 9 }$

Applying

$BODMAS$ rule.

$\cfrac { 16 }{ 7 } \div \cfrac { 15 }{ 11 } \times \cfrac { 22 }{ 9 }$

$=\cfrac { 16 }{ 7 } \times \cfrac { 11 }{ 15 } \times \cfrac { 22 }{ 9 }$

$=\cfrac { 3872 }{ 945 }$

If in mixed fraction form $\dfrac {19}{6}$ is equal to $3\dfrac {x}{6}$ , then what is the value of $x$ ?

$\dfrac{19}{6}=\dfrac{18+1}{6}$

$=\dfrac{18}{6}+\dfrac{1}{6}$

$=3+\dfrac{1}{6}$

$=3\dfrac{1}{6}$

So the value of

$x$ will be

$1$

Find the product :
$19.638\times 10$

$19.638 \times 10 = 196.38$

Divide the following
$2.8 \div 0.7$

1146527_1215773_ans_cb98afdb96a546fea8ba630ee64a35a7.jpeg

Solve $\dfrac { 7 }{ 8 } +\dfrac { 5 }{ 12 } \times \dfrac { 9 }{ 10 } -\dfrac { 1 }{ 4 }$ .

Solution:- Given

$\Rightarrow \dfrac{7}{8} + \dfrac{5}{12} \times \dfrac{9}{10} - \dfrac{1}{4}$ by order of operation first, we do work of multiplication.

$\Rightarrow \dfrac{7}{8} + \dfrac{3}{8} - \dfrac{1}{4}$

$\Rightarrow \dfrac{7 + 3 - 2}{8}$

$\Rightarrow \dfrac{8}{8}$

$1 (Ans)$

Write these numbers in order, starting with the smallest.
$0.55$ $\dfrac{6}{11}$ $54\dfrac{1}{2}\%$
___ $<$ _ $<$ _____

$\dfrac 6{11}=0.5454\\54\dfrac 12\%=54.5\%=54.5\dfrac 1{100}=0.545$

So the gven numbers are

$0.55,0.5454,0.545$

The smallest one is

$0.545<0.5454<0.55$

So the order is

$54\dfrac 12\%,\dfrac 6{11},0.55$

Find :
$211.02 \times 4$

To find:

$211.02\times4$

$211.02\times4=\dfrac{21102\times 4}{100}$

$= \dfrac{84408}{100}$

$=844.08$

Find:
$20.1\times 4$

Given:

$20.1\times4$

$= \dfrac{201}{10}\times 4$

$= \dfrac{804}{10}$

$= 80.4$

Find :
$1.3\times 10$

$1.3\times10$

$= 13$

Find :
$0.05\times 5$

$0.05\times5$

$= 0.25$

Find:
$153.7\times 10$

$153.7\times 10 = 1537.0$

Find :
$2.71\times 5$

$2.71\times 5 = 13.55$

Find :
$2\times 0.86$

$2\times 0.86 = 1.72$ .

Find :
$11.2\times 0.15$ .

$11.2\times 0.15 = 1.680$ .

Find :
$1.3\times 3.1$ .

Given to find

$1.3\times3.1$

$=\dfrac{13}{10} \times \dfrac{31}{10}$

$=\dfrac{13 \times 31}{10 \times 10}$

$=\dfrac{403}{100}$

$=4.03$

Find :
$168.07\times 10$ .

$168.07\times10$

$= 1680.7$

Find :
$0.2\times 316.8$ .

The given numbers are

$0.2$ and

$316.8$

Multiplication gives

$=0.2\times316.8$

$=\dfrac{2}{10} \times \dfrac{3168}{10}$

$=\dfrac{6336}{100}$

$= 63.36$

Find :
$0.5\times 10$ .

$0.5\times10$

$=5$

Find :
$156.1\times 100$ .

$156.1\times 100 = 15610$ .

Find :
$31.3\times 100$ .

$31.3\times100$

$=3130$

Find :
$0.08\times 10$

$0.08\times10$

$=0.8$

Divide:

$43.2 \quad by \quad 6$

Perform the division by considering the dividend a whole number.
When the division of the whole-part of the dividend is complete, put the decimal point in the quotient and proceed with the division as in case of whole numbers.
we have,

$43.2 \div 6$

$43.2 \div 6=7.2$

1625893_1780047_ans_db84a5880ce946a3ab46a3c53c3da30f.PNG

Divide:

$60.48 \quad by \quad 12$

Perform the division by considering the dividend a whole number.
When the division of whole-part of the dividend is complete, put the decimal point in the quotient and proceed with the division as in case of whole numbers.
we have,

$60.48 \div 12$

$\therefore 60.48 \div 12 = 5.04$

1625936_1780057_ans_dd9300afc0584c558d2efaf9f88bd146.PNG

Divide:

$117.6 \quad by \quad 21$

$117.6 \div 21$

$\therefore 117.6 \div 21 = 5.6$

1626024_1780067_ans_ea85554cee5443c683674185f882f24f.PNG

Divide:

$2.575 \quad by \quad 25$

$2.575 \div 25$

$\therefore 2.575 \div 25 = 0.103$

1626104_1780089_ans_68e8e181417449848cb1b6f2ca4a55b3.PNG

Divide:

$0.765 \quad by \quad 9$

$0.765 \div 9$

$\therefore 0.765 \div 9 = 0.085$

1629868_1780109_ans_6d4ae88e38cc4fb1976add398641d0a3.PNG

Find the product: $\dfrac{5}{8}$ $\times$ $\dfrac{4}{7}$

By the rule of multiplication of fractions,

$\text{Product of fractions}=\dfrac{\text{product of numerators}}{\text{product of denominators}}$

$\therefore \dfrac58\times \dfrac47$

$=\dfrac{5\times4}{8\times7}$

$=\dfrac{5\times1}{2\times7}$

$=\dfrac5{14}$

Divide:

$6.08 \quad by \quad 8$

$6.08 \div 6$

$\therefore 6.08 \div 6 = 0.76$

1629853_1780104_ans_ac3b00f8e6d84f479820aff5b3ce6ff8.PNG

Divide:

$217.44 \quad by \quad 18$

$217.44 \div 18$

$\therefore 217.44 \div 18 = 12.08$

1626073_1780081_ans_c642e646d44941668919d936a84e4674.PNG

Evaluate the following:
$12.08\times 9.3$

$12.08\times 9.3$

$12.08$

$\ \ \ \times 9.3$

$\overline{\ \ \ \ \ 3624}$

$\ 10872\times$

$\overline{\underline{112.344}}$

Evaluate the following:
$238.06\times 7.5$

$238.06\times 7.5$

$238.06$

$\times 7.5$
_______________

$119030$

$166642\times$
________________

$1785.450$
________________

Evaluate the following:
$3.7\times 4.5$

$3.7\times 4.5$

$3.7$

$\times 4.5$

$\overline{\ \ 185}$

$148\times$

$\overline{\underline{16.65}}$

Work out the following:
$72.8\div 0.04$

$72.8\div 0.04$

$=\dfrac{72.8}{0.04}=\dfrac{7280}{4}$

$\left. 4 \right) \overline { 7280 } \left( 1820 \right. \\ -4\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 32\\ -32\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \ \ 8\\ \ \ -8\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \ \quad \times \\ \_ \_ \_ \_ \_ \_ \_ \_ \_$

Work out the following:
$8.64\div 3.6$

$8.64\div 3.6$

$=86.4\div 36$

$\left. 36 \right) \overline { 86.4 } \left( 2.4 \right. \quad \quad \quad \quad \quad \quad \quad \\ \ \ -72\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 144\\ \quad -144\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \quad \quad \times \\ \_ \_ \_ \_ \_ \_ \_ \_ \_$

Multiply the following number by $10, 100$ and $1000$ orally:
$.234$

$0.234$

$0.234\times 10=2.34$

$0.234\times 100=23.4$

$0.234\times 1000=234$

Work out the following:
$0.144\div 0.02$

$0.144\div 0.02$

$=14.4\div 2$

$\left. 2 \right) \overline { 14.4 } \left( 7.2 \right. \quad \quad \quad \quad \quad \quad \quad \\ -14\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 4\\ \quad -4\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \quad \quad \times \\ \_ \_ \_ \_ \_ \_ \_ \_ \_$

Multiply the following number by $10, 100$ and $1000$ orally:
$3.45$

$3.45$

$3.45\times 10=34.5$

$3.45\times 100=345$

$3.45\times 1000=3450$

Work out the following:
$70.756\div 4$

$70.756\div 4$

$\left. 4 \right) \overline { 70.756 } \left( 17.689 \right. \\ -4\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad 30\\ -28\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \ \ \ 27\\ \quad \ \ \ 24\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \ \ \ \ \ \ 35\\ \quad \ -32\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad \ \ \ \ 36\\ \quad \quad \ \ \ \ 36\\ \_ \_ \_ \_ \_ \_ \_ \_\_\_\_\_\\ \quad \quad \ \ \ \ \ \ \times \\ \_ \_ \_ \_ \_ \_ \_ \_ \_$

Work out the following:
$2.46\div 6$

$246\div 6$

$\left. 6 \right) \overline { 2.46 } \left( 0.41 \right. \quad \quad \quad \quad \quad \quad \quad \\ -2.4\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 6\\ \quad \quad 6\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \quad \quad \times \\ \_ \_ \_ \_ \_ \_ \_ \_ \_$

Evaluate the following:
$0.79\times 32.4$

$0.79\times 32.4$

$32.4$

$\times 0.79$
_______________

$2916$

$2268\times$
________________

$25.596$
________________

Work out the following:
$3.016\div 8$

$3.016\div 8$

$\left. 8 \right) \overline { 3.016 } \left( 0.377 \right. \\ -2.4\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad 61\\ \ \ \ -56\\ \quad \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \\ \quad \quad \ \ \ 56\\ \quad \ \ \ -56\\ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \_ \quad \\ \quad \quad \times \\ \_ \_ \_ \_ \_ \_ \_ \_ \_$

Convert the following mixed number into improper fractions :
$(i) 7\dfrac{2}{11}$
$(ii) 3\dfrac{5}{48}$
$(iii)13\dfrac{7}{64}$
$(iv) 7\dfrac{2}{3}$

$(i) 7\dfrac{2}{11} = \dfrac{11\times 7 + 2}{11} = \dfrac{79}{11}$

$(ii) 3\dfrac{5}{48} = \dfrac{48 \times 3 + 5}{48} = \dfrac{149}{48}$

$(iii)13\dfrac{7}{64} = \dfrac{64 \times 13 + 7}{64} = \dfrac{832 + 7}{64} = \dfrac{839}{64}$

$(iv) 7\dfrac{2}{3} = \left[7\dfrac{2}{3}\right] = \left[\dfrac{3 \times 7 + 2}{3}\right] = \dfrac{23}{3}$

Divide the following numbers by $10, 100$ and $1000$ ( orally):
$23.01$

$23.01$

$23.01\div 10=2.301$

$23.01\div 100=0.2301$

$23.01\div 1000=0.02301$

Evaluate the following :
$(i) \dfrac{2}{5} \times \dfrac{3}{7}$
$(ii) \dfrac{3}{5} \times \dfrac{8}{9}$
$(iii) 7 \times 1\dfrac{2}{3}$

$(i) \dfrac{2}{5} \times \dfrac{3}{7} \Rightarrow \dfrac{6}{35}$

$(ii) \dfrac{3}{5} \times \dfrac{8}{9} = \dfrac{8}{15}$

$(iii) 7 \times 1\dfrac{2}{3} = \dfrac{7}{1} \times \dfrac{5}{3} = \dfrac{35}{3} = 11 \dfrac{2}{3}$

Divide the following numbers by $10, 100$ and $1000$ ( orally):
$4.7$

$4.7$

$4.7\div 10=0.47$

$4.7\div 100=0.047$

$4.7\div 1000=0.0047$

Multiply:
$0.943$ and $62$

$0.943$ and

$62$
The multiplication of

$0.943$ and

$62$ is as follows

$943$

$62 ×$
________

$1886$

$5658 ×$
________

$58466$
________
We know that,

$.943 × 62 = 58.466$
Hence

$0.943 × 62 = 58.466$

If length of one bed-cover is $2.1 m,$ find the total length of $17$ bed-covers.

Given
Length of one bed-cover

$= 2.1 m$
The length of 17 bed-covers can be calculated as below

$= 17 × 2.1$

$= 35.7 m$
Therefore, the total length of

$17$ bed-covers is

$35.7$ m

Multiply:
$5.6$ and $8$

$5.6$ and

$8$
The multiplication of

$5.6$ and

$8$ is as follows

$5.6 × 8 = 44.8$
Hence,

$5.6 × 8 = 44.8$

Multiply:
$38.46$ and $9$

$38.46$ and

$9$
The multiplication of

$38.46$ and

$9$ is as follows

$38.46 × 9 = 346.14$
Hence,

$38.46 × 9 = 346.14$

Multiply:
$0.0453$ and $35$

We know that,

$453\times35=15855$

hence,

$0.0453\times35=1.5855$

Multiply:
$7.5$ and $2.5$

$7.5$ and

$2.5$
The multiplication of

$7.5$ and

$2.5$ is as follows

$75$

$25 ×$
________

$375$

$150 ×$
_________

$1875$
_________
We know that,

$75 × 25 = 1875$
Hence

$7.5 × 2.5 = 18.75$

Multiply:
$0.87$ by $10$

$0.87$ by

$10$
It can be written as

$0.87 \times 10=8.7$

Multiply:
$6.4$ by $1000$

$6.4$ by

$1000$
It can be written as

$6.4 \times 1000=6400$

Multiply:
$2.948$ by $100$

$2.948$ by

$100$
It can be written as

$2.948 \times 100=294.8$

Multiply:
$5.8$ by $4$

$5.8$ by

$4$
It can be written as

$5.8 \times 4=23.2$

$5.8$

$\times$

$4$

$\begin{array}{l l}\hline & 23.2 \end{array}$

Divide:
$12.8$ by $4$

$12.8$ by

$4$
It can be written as

$12.8 \div 4$

$=\dfrac{128}{10}\times\dfrac14$

$=\dfrac{32}{10}=3.2$

Divide:
$7.8$ by $100$

$7.8$ by

$100$
It can be written as

$7.8 \div 100=\dfrac{7.8}{100}=0.078$

Evaluate:
$0.01 \times 0.001$

$0.01 \times 0.001$
We know that

$0.01 \times 0.001=\dfrac{1}{100}\times\dfrac{1}{1000}$

$=\dfrac{1}{100000}=0.00001$

Divide:
4.32 by 1.2

$4.32$ by

$1.2$
It can be written as

$4.32 \div 1.2$
Multiplying by 100

$432 \div 120=3.6$
1744036_1827779_ans_42d06bdf797448cd8876b24919506572.png

Divide:
4.672 by 8

$4.672$ by

$8$
It can be written as

$4.672\div8=0.584$
1743512_1827778_ans_9ccdbfc31dfd471ca52da186cfd0ac22.png

Divide:
$54.9$ by $10$

$54.9$ by

$10$
It can be written as

$54.9 \div 10=\dfrac{54.9}{10}=5.49$

Multiply:
5.037 by 8

$5.037$ by

$8$
It can be written as

$5.037 \times 8=40.296$

$\begin{array}{l l}& 5.037 \\\times&8 \\\hline & 40.296 \end{array}$

Multiply:
$4.6$ by $2.1$

$4.6$ by

$2.1$
It can be written as

$4.6 \times 2.1=9.66$

$\begin{array}{l l}& \,\,\,4.6 \\\times& \,\,\,2.1 \\\hline & \,\,\,46 \\\times& \,92 \\ \hline& 9.66 \end{array}$

Evaluate:
$0.894 \times 87$

$0.894 \times 87$
We know that

$0.894 \times87=77.778$

Evaluate :
$3.204 \div 9$

$3.204 \div 9$
We get

$3.204 \div 9=0.356$
1744146_1827808_ans_24cfca680d94498396c4c64a5fe0740e.png

Evaluate :
$27.69 \div 30$

$27.69 \div 30$
We get

$27.69 \div 30=0.923$

1744109_1827800_ans_19a65eacd9e041e198b74acfdaac3288.png

Evaluate :
$4.4064 \div 4$

$4.4064 \div 4$
We get

$\dfrac{44064}{10000} \div 4$

$=\dfrac{44064}{10000}\times \dfrac{1}{4}$

$=\dfrac{11016}{10000}=1.1016$

Divide:
$7.644$ by $1.4$

$7.644$ by

$1.4$
It can be written as

$7.644 \div 1.4$
Multiplying by

$1000$

$7644 \div 1400=5.46$
1744048_1827780_ans_b3b4f4838c7244d5b8bb4bd9100f8392.png

If we multiply the fractions $\displaystyle\frac{1}{2}$ and $\displaystyle\frac{1}{3}$ we will get $\displaystyle\frac{1}{6}$ .If true enter 1 else 0.

We multiply the given fractions

$\dfrac {1}{2}$ and

$\dfrac {1}{3}$ as shown below:

$\dfrac { 1 }{ 2 } ×\dfrac { 1 }{ 3 } =\dfrac { 1\times 1 }{ 2×3 } =\dfrac { 1}{ 6 }=\dfrac {1}{6}$

Hence, the product of

$\dfrac {1}{2}$ and

$\dfrac {1}{3}$ is

$\dfrac {1}{6}$ .

Solve the following:
$0.5\times 10$

1305121_703930_ans_c15afd12e9084981891aa05fa28b0e0e.jpeg

Solve the following:
$3.62\times 100$

1305118_703928_ans_d83ca831ec534ef9a53c709a8d90cd7f.jpeg

A motor bike covers a distance of $62.5km$ consuming one litre of petrol. How much distance does it cover for $10$ litres of petrol? (In km)

Distance covered in

$1$ L of petrol

$= 62.5$ km
Distance covered in

$10$ L of petrol

$= 62.5 \times 10$ km

$= 625$ km

Solve the following:
$0.9\times 100$

1305122_703935_ans_5b0972bf64184c958a13491b3a9a15da.jpeg

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\left ( \frac{\sqrt{2}}{(1 - x^2)^{-1}} + \frac{3^{3/2}}{x^{-2}} \right ) : \left ( \frac{x^{-2}}{1 + x^{-2}} \right )^{-1}$

1694724_883648_ans_98086d63c21f475f8bf9e3ed1b17ea0b.jpg

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\frac{0.23 (7) + \frac{43}{450}}{0.5 (61) - \frac{113}{495}}$

fisrtly change the mixed infinite fraction into common fraction so

$.23(7)$

can be written in coomon fraction as

$\dfrac{214}{900}=\dfrac{107}{450}$

$0.5(61)$ can b written as common fraction is

$\dfrac{556}{900}$

now solve the given expression

$\dfrac{\dfrac{107}{450}+\dfrac{43}{450}}{\dfrac{556}{900}-\dfrac{113}{495}}$

$\dfrac{\dfrac{107+43}{450}}{\dfrac{556\times11-113\times20}{9900}}$

$\dfrac{\dfrac{150}{450}}{\dfrac{6116-2260}{9900}}$

$\dfrac{150}{450}\times\dfrac{9900}{3856}$

$\dfrac{3300}{3856}$ answer

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\left ( \frac{1}{a} + \frac{1}{b} - \frac{2c}{ab} \right )(a + b + 2c): \left ( \frac{1}{a^2} + \frac{1}{b^2} + \frac{2}{ab} - \frac{4c^2}{a^2 b^2} \right )$

$\bigg(\dfrac{1}{a}+\dfrac{1}{b}-\dfrac{2{c}}{a{b}}\bigg) (a+b+2{c})=\dfrac{(a+b-2{c})(a+b+2{c})}{a{b}}=\dfrac{(a+b)^{2}-4{c^{2}}}{a{b}}$

$\bigg(\dfrac{1}{a^{2}}+\dfrac{1}{b^{2}}+\dfrac{2}{a{b}}-\dfrac{4{c}^{2}}{a^{2}b^{2}}\bigg)=\dfrac{a^{2}+b^{2}+2{a}{b}-4{c^{2}}}{a^{2}b^{2}}=\dfrac{(a+b)^{2}-4{c^{2}}}{a^{2}b^{2}}$

$\implies \bigg(\dfrac{1}{a}+\dfrac{1}{b}-\dfrac{2{c}}{a{b}}\bigg)(a+b+2{c}):\bigg(\dfrac{1}{a^{2}}+\dfrac{1}{b^{2}}+\dfrac{2}{a{b}}-\dfrac{4{c}^{2}}{a^{2}b^{2}}\bigg)=1:\dfrac{1}{a{b}}=a{b}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\left ( 6a^2 + 5a - 1 + \frac{a + 4}{a + 1} \right ) : \left ( 3a - 2 + \frac{3}{a + 1} \right )$

1694720_883647_ans_0fcac4e6340b488d840855c999c64af3.jpg

$\displaystyle\frac{1}{1 + \sqrt{2} + \sqrt{3}}$

$\dfrac{1}{1+(\sqrt{2}+\sqrt{3})}$

$=\dfrac{1}{1+(\sqrt{2}+\sqrt{3})}\times \dfrac{(1+\sqrt{2}-\sqrt{3})}{(1+\sqrt{2}-\sqrt{3})}$

$=\dfrac{1+\sqrt{2}-\sqrt{3}}{3-2\sqrt{2}+3}$

$=\dfrac{1+\sqrt{2}-\sqrt{3}}{2\sqrt{2}}\times \dfrac{2\sqrt{2}}{2\sqrt{2}}$

$=\dfrac{1+\sqrt{2}-\sqrt{3}\times2\sqrt{2}}{8}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle( \sqrt{\sqrt{3} + \sqrt{2}} - (\sqrt{3} - \sqrt{2})^{1/2}) ((\sqrt{3} + \sqrt{2})^{1/2} + \sqrt{\sqrt{3} - \sqrt{2}})^{-1} - \cos \frac{5\pi }{4}$

Let

$a=\sqrt { 3 } ,b=\sqrt { 2 }$

$\therefore$ The given question becomes

$(\dfrac { \sqrt { a+b } -\sqrt { a-b } }{ \sqrt { a+b } +\sqrt { a-b } } )-\cos { \dfrac { 5\pi }{ 4 } }$

now rationalizing the numerator by multiplying and dividing the denominator

$\Rightarrow (\dfrac { \sqrt { a+b } -\sqrt { a-b } }{ \sqrt { a+b } +\sqrt { a-b } } )(\dfrac { \sqrt { a+b } +\sqrt { a-b } }{ \sqrt { a+b } +\sqrt { a-b } } )-\cos { \dfrac { 5\pi }{ 4 } }$

$\Rightarrow [\dfrac { (a+b)-(a-b) }{ { (\sqrt { a+b } +\sqrt { a-b } ) }^{ 2 } } ]+\dfrac { 1 }{ \sqrt { 2 } }$

$\Rightarrow =[\dfrac { 2b }{ (2a+2\sqrt { { a }^{ 2 }-{ b }^{ 2 } } ) } ]+\dfrac { 1 }{ \sqrt { 2 } }$

We know that

$a^2-b^2=1$

On substituting the values of a,b we get

$\Rightarrow =[\dfrac { \sqrt { 2 } }{ (\sqrt { 3 } +1) } ]+\dfrac { 1 }{ \sqrt { 2 } }$

Now again rationalizing the denominator we get

$\Rightarrow \dfrac { \sqrt { 2 } (\sqrt { 3 } -1) }{ 2 } +\dfrac { \sqrt { 2 } }{ 2 } =\dfrac { \sqrt { 6 } -\sqrt { 2 } +\sqrt { 2 } }{ 2 } =\sqrt { \dfrac { 3 }{ 2 } }$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\frac{x^{1/2} + x^{-1/2}}{1 - x} + \frac{1 - x^{-1/2}}{1 + \sqrt{x}}$

$\dfrac{x^{1/2}+x^{-1/2}}{1-x}+\dfrac{1-x^{-1/2}}{1+\sqrt{x}}=\dfrac{1+x}{\sqrt{x}(1-x)}+\dfrac{\sqrt{x}-1}{\sqrt{x}(\sqrt{x}+1)}=\dfrac{1}{\sqrt{x}}\bigg(\dfrac{1+x}{1-x}-\dfrac{(\sqrt{x}-1)^2}{1-x}\bigg)=\dfrac{1+x-x-1+2\sqrt{x}}{(1-x)\sqrt{x}}=\dfrac{2}{1-x}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \frac{2 \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \left ( \frac{a^{3/2} + b^{3/2}}{\sqrt{a} + \sqrt{b}} - \frac{1}{(ab)^{-1/2}} \right )(a - b)^{-1}$

$\cfrac{2\sqrt b}{\sqrt a+\sqrt b}+(\cfrac{a^{\frac{3}{2}}+b^{\frac{3}{2}}}{\sqrt a+\sqrt b}-\cfrac{1}{(ab)^{\frac{-1}{2}}})(a-b)^{-1}$

$=\cfrac{2\sqrt b}{\sqrt a+\sqrt b}+(\cfrac{(\sqrt a+\sqrt b)(a+b-\sqrt ab)}{(\sqrt a+\sqrt b)}-\sqrt ab)(a-b)^{-1}$

$=\cfrac{2\sqrt b}{\sqrt a+\sqrt b}+\cfrac{(a+b-2\sqrt ab)}{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)}$

$=\cfrac{2\sqrt b}{\sqrt a+\sqrt b}+\cfrac{(\sqrt a-\sqrt b)^{2}}{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)}$

$=\cfrac{2\sqrt b+\sqrt a-\sqrt b}{\sqrt a+\sqrt b}$

$=\cfrac{\sqrt a+\sqrt b}{\sqrt a+\sqrt b}=1$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \frac{a - a^2}{a^{1/2} - a^{-1/2}} - \frac{2}{a^{3/2}} - \frac{1 - a^{-2}}{a^{1/2} + a^{-1/2}}$

1694727_884140_ans_fbeab2acce0c46f48951a880465f8b9f.jpg

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\frac{a \sqrt{a} + b \sqrt{b}}{(\sqrt{a} + \sqrt{b})(a - b)} + \frac{2\sqrt{b}}{\sqrt{a} + \sqrt{b}} - \frac{\sqrt{ab}}{a -b}$

$\dfrac{a\sqrt{a}}{(\sqrt{a}+\sqrt{b})(a-b)}+\dfrac{2\sqrt{b}}{\sqrt{a}+\sqrt{b}}-\dfrac{\sqrt{a{b}}}{a-b}=\dfrac{a\sqrt{a}+2{a}\sqrt{b}-2b\sqrt{b}-a\sqrt{b}-b\sqrt{a}}{(\sqrt{a}+\sqrt{b})(a-b)}=\dfrac{a\sqrt{a}+a\sqrt{b}-b\sqrt{a}-2{b}\sqrt{b}}{(\sqrt{a}+\sqrt{b})(a-b)}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, x^{1/2} + x^{-1/2} + \frac{(1 - x)(1 - x^{-1/3})}{1 + \sqrt{x}}$

1694729_884146_ans_f989e25c3db14db8a14e9bc7e4db2567.jpg

$1006.2 \div 39$

1698446_1026714_ans_80f9d8b1a52e49f3a764cbbe5f08ee3f.jpg

Express $32.12\bar{35}$ in the form of $\dfrac{p}{q}$ where $p$ and $q$ are integers.

1237693_1000329_ans_995a2cc17e0b48fa96c94040ba19cc20.jpeg

Convert each of the following into mixed fraction :
$(1)\frac{17}{5}$ $(2)\frac{62}{7}$ $(3)\frac{101}{8}$ $(4)\frac{95}{13}$
$(5)\frac{81}{11}$ $(6)\frac{87}{16}$ $(7)\frac{113}{12}$ $(8)\frac{117}{20}$

$(1) \dfrac{17}{5}=3\dfrac{2}{5}$

$(2) \dfrac{62}{7}=8\dfrac{6}{7}$

$(3) \dfrac{101}{8}=12\dfrac{5}{8}$

$(4) \dfrac{95}{13}=7\dfrac{4}{13}$

$(5) \dfrac{81}{11}=7\dfrac{4}{11}$

$(6) \dfrac{87}{16}=5\dfrac{7}{16}$

$(7) \dfrac{113}{12}=9\dfrac{5}{12}$

$(8) \dfrac{117}{20}=5\dfrac{17}{20}$

Find $0.1\times 71.3$

$=0.1\times 71.3$

$=7.13$

In order to make a shirt $2\,m\,\,\,25\,cm$ cloth is needed. What length of cloth is required to make $18$ such shirt ?

1868661_1103638_ans_864ced7557474275a4d987f0ca90ff0b.jpg

Find: $100.01\times 0.01$

Given:

$100.01\times 0.01$

On expanding the decimals we get,

$=\dfrac{10001}{100}\times \dfrac{1}{100}=1.0001$

Find $101.01 \times 0.01$

$101.01 \times 0.01$

$=1.0101$

Find $0.2\times 312.4$

$=0.2\times 312.4$

$=62.48$

$5.04 \div 0.8=?$

$5.04\div0.8$

$=\dfrac{504}{100}\times\dfrac{10}{8}=\dfrac{63}{10}=\boxed{6.3}$

Find $3.3\times 0.3$

$=3.3\times0.3$

$=0.99$

In mixed fraction form $\dfrac {35}{9}$ is equal to $3\dfrac {y}{9}$ .
What is the value of $y$ ?

$\dfrac{35}{9}=\dfrac{27+8}{9}$

$=\dfrac{27}{9}+\dfrac{8}{9}$

$=3+\dfrac{8}{9}$

$=3\dfrac{8}{9}$

So, the value of

$y$ is

$8$

Solve:
$84.9 \div 30$

$=\dfrac{84.9}{30}$

$=\dfrac{849}{300}$

$=\dfrac{283}{100}$

$=2.83$

Hence, the answer is

$2.83.$

$14.9\div 0.64$ .

$\begin{matrix} \Rightarrow 14.9\div 0.64 \\ \Rightarrow \cfrac { { 14.9 } }{ { 0.64 } } \\ \Rightarrow \cfrac { { 14.90 } }{ { 0.64 } } \\ \Rightarrow \cfrac { { 1490 } }{ { 64 } } \\ \Rightarrow 23.25\, \, Ans. \\ \end{matrix}$

Find :
1) $\dfrac{2}{5} \times \dfrac{1}{8}$
ii) $\dfrac{1}{5} \times \dfrac{3}{4}$
iii) $\dfrac{5}{8} \times \dfrac{8}{15}$

(i)

$\dfrac{2}{5}\times \dfrac{1}{84}=\dfrac{1}{20}$

(ii)

$\dfrac{1}{5}\times \dfrac{3}{4}=\dfrac{3}{20}$

(iii)

$\dfrac{5}{8}\times \dfrac{8}{15}=\dfrac{1}{3}$ .

$2\dfrac {1}{2}:3\dfrac {1}{3} > 3.5:4.5$
State true or false.

$2\dfrac{1}{2}:3\dfrac{1}{3} > 3.5 : 4.5$

$\dfrac{5}{2}:\dfrac{10}{3} > 3.5 : 4.5$

$2.5 : 3.33 > 3.5 : 4.5$

$\therefore 2.5 : 3.33$ is not greater than

$3.5 : 4.5$

$\therefore$ It is false.

Draw representations to multiply :
(a) $3$ and $2.6$
(b) $4$ and $1.3$

$(a)3 \quad and\quad 2.6=3\times2.6=7.8\\(b)4\quad and\quad 1.3=4\times1.3=5.2$

Multiply of the following numbers by $10,\ 100$ and $1000$ :
(i) $3.9$
(ii) $2.89$
(iii) $0.0829$
(iv) $40.3$
(v) $0.3725$

(i)

$3.9$

$3.9 \times 10 = 39$

$3.9 × 100 = 390$

$3.9 × 1000 = 3900$
Hence,

$39, 390$ and

$3900$ are the required numbers
(ii)

$2.89$

$2.89 × 10 = 28.9$

$2.89 × 100 = 289$

$2.89 × 1000 = 2890.00$

$= 2890$
Hence,

$28.9, 289$ and

$2890$ are the required numbers
(iii)

$0.0829$

$0.0829 × 10 = 0.829$

$0.0829 × 100 = 8.29$

$0.0829 × 1000 = 82.9$
Hence,

$0.829, 8.29$ and

$82.9$ are the required numbers
(iv)

$40.3$

$40.3 × 10 = 403$

$40.3 × 100 = 4030$

$40.3 × 1000 = 40300$
Hence,

$403, 4030$ and

$40300$ are the required numbers
(v)

$0.3725$

$0.3725 × 10 = 3.725$

$0.3725 × 100 = 37.25$

$0.3725 × 1000 = 372.5$

Express the following as improper fractions:
$10\dfrac {3}{5}$

An Improper Fraction has a top number larger than (or equal to) the bottom number.

$10\dfrac {3}{5}$

$= \dfrac {(5\times 10) + 3}{5}$

$= \dfrac {53}{5}$ .

The following fractions represent just three different numbers. Separate them in to three groups of equal fractions by changing each one to its simplest form:
$\dfrac {15}{75}$

1502081_1658007_ans_8feaf7c2a5c44e8c815c1093b3d5ffb5.jpg

Change the following fraction into its simplest form:
$\dfrac {4}{25}$

Since,

$4$ and

$25$ have no factor in common hence, the fraction is already in it's simplest form:

So,

$\dfrac{4}{25}$ is the simplest form.

Multiply :
$3\dfrac{1}{8}$ $\times 4\dfrac{10}{11}$

Given,

$3\dfrac{1}{8}$

$\times 4\dfrac{10}{11}$

$=\dfrac{25}{8} \times \dfrac {54}{11}$

$=\dfrac {675}{44}$

$=15\dfrac{15}{44}$

Find the product:
$3\dfrac{6}{7}\times 4\dfrac{2}{3}$

1498980_1675978_ans_e5aa1848e7fd4b0daf62e9cc32751da1.jpg

Find the product:
$7\dfrac{1}{2}\times 2\dfrac{4}{15}$

Now,

$7\dfrac{1}{2}\times 2\dfrac{4}{15}$

$=\dfrac{(7\times 2)+1}{2}\times \dfrac{(2\times 15)+4}{15}$

$=\dfrac{15}{2}\times \dfrac{34}{15}$

$=\dfrac{34}{2}$

$=17$ .

Find the product:
$4.74\times 10$

1498983_1676009_ans_e55691ec46b644d0b3f3cc256740f6e2.jpg

Find the product:
$42.5 \times 100$

Now,

$42.5\times 100$

$=\dfrac{425}{10}\times 100$

$=425\times 10$

$=4250$

Find the product:
$0.0054 \times 10$

Now,

$0.0054\times 10$

$=\dfrac{54}{1,000}\times 10$

$=\dfrac{54}{100}$

$=0.054$

Find the product:
$0.45 \times 10$

Now,

$0.45\times 10$

$=\dfrac{45}{100}\times 10$

$=\dfrac{45}{10}$

$=4.5$ .

Find the product:
$35.853 \times 100$

Now,

$35.853\times 100$

$=\dfrac{35853}{1,000}\times 100$

$=\dfrac{35853}{10}$

$=3585.3$

Find the product:
$12.075 \times 100$

Now,

$12.075\times 100$

$=\dfrac{12075}{1000}\times 100$

$=\dfrac{12075}{10}$

$=1207.5$

Find the product:
$0.0529 \times 1000$

Now,

$0.0529\times 1000$

$=\dfrac{529}{10,000}\times 1000$

$=\dfrac{529}{10}$

$=52.9$

Find the product:
$28.73 \times 47$

1498990_1676137_ans_bab1c87474cb47b0af5e7dd0f4195e10.jpg

Find the product:
$20.708 \times 1000$

Now,

$20.708\times 1000$

$=\dfrac{20708}{1000}\times 1000$

$=20708$

Find the product:
$100 \times 0.005$

Given:

$100\times 0.005$

$=100\times \dfrac{5}{1000}$

$=\dfrac{5}{10}$

$=0.5$

Find the product:
$1000 \times 0.1$

1498988_1676123_ans_7140960b0fc94ffbb160d58f1522838e.jpg

Find:
$13.01 \times 50.01$

1498996_1676178_ans_ed3675a1a13641328399546ee68ad0ef.jpg

Divide $142.45$ by $10$ .

Now if we divide

$142.45$ by

$10$ then we get,

$\dfrac{142.45}{10}$

$=\dfrac{14245}{1000}$

$=14.245$

Find the product:
$0.0415 \times 59$

1498991_1676145_ans_5b5acf3721e94ad6adde8942d23d454c.jpg

Divide $3.45$ by $10$ .

Now if we divide

$3.45$ by

$10$ then we get,

$\dfrac{3.45}{10}$

$=\dfrac{345}{1000}$

$=0.345$

Find the area of a square plot of land whose each side measures $8\dfrac {1}{2}$ meters.

We know that the given details are

One side measures

$= 8 \dfrac 12m$

By using the formula,

Area of square

$= side \times side$

Area of square plot

$= 8 \dfrac {1}{2}m \times 8 \dfrac {1}{2}m$

$= 17/2 m\times 17/2\ m$

$= 289/ 4m^{2} = 72\dfrac {1}{4} m^{2}$

$\therefore$ Area of square plot is

$72\dfrac {1}{4} m^{2}$ .

Divide:
$16.64$ by $20$

If we divide

$16.64$ by

$20$ then we get,

$\dfrac{16.64}{20}$

$=\dfrac{8.32}{10}$

$=0.832$

Divide:
$164.6$ by $200$

If we divide

$164.6$ by

$200$ then we get,

$\dfrac{164.6}{200}$

$=\dfrac {1646}{10}\times \dfrac{1}{200}=\dfrac {823}{1000}$

$=0.823$

Divide:
$403.80$ by $30$

If we divide

$403.80$ by

$30$ then we get,

$\dfrac{403.8}{30}$

$=\dfrac{134.6}{10}$

$=13.46$

Divide:
$163.44$ by $24$

1499027_1676259_ans_f6d1af365e324903bb0284cce043d8ad.jpg

Multiply:
$\dfrac{7}{11}$ by $\dfrac{5}{4}$

1516664_1676809_ans_b5c6766f4da241d6bb54b47b7c647e8a.jpg

Find the product :

$7.54 \times 10$

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
we have,

$7.54 \times 10=75.4$

Find the product :

$2.397 \times 100$

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.
We have,

$2.397 \times 100 = 239.7$

Find the product :

$0.08 \times 100$

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.
we have,

$0.08 \times 100 = 8$

Find the product :

$6.83 \times 100$

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.
we have,

$6.83 \times 100 = 683$

Find the product :

$0.7 \times 10$

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
we have,

$0.7 \times 10 = 7$

Find the product :

$0.83 \times 10$

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
we have,

$0.83 \times 10 = 8.3$

Find the product :

$73.92 \times 10$

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
we have,

$73.92 \times 10 = 739.2$

Find the product :

$84.003 \times 10$

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
we have,

$84.003 \times 10 = 840.03$

Find the product :

$0.032 \times 10$

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.
we have,

$0.032 \times 10 = 0.32$

Find the product :

$0.076 \times 1000$

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.
we have,

$0.076 \times 1000 = 76$

Find the product :

$6.25 \times 1000$

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.
we have,

$6.25 \times 1000 = 6250$

Find the product :

$0.03 \times 100$

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.
we have,

$0.03 \times 100 = 3$

Find the product:
$4.8 \times 1000$

$4.8 \times 1000 = \dfrac{48}{10}\times 1000$

$=48\times 100=4800$

Find the product :

$5.4 \times 1.6$

Multiply the decimal without the decimal point by the given whole number.
we have,

$54 \times 16 = 864$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 5.4 \times 1.6 = 8.64$

Find the product :

$0.182 \times 1000$

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.
we have,

$0.182 \times 1000 = 182$

Find the product :

$0.06 \times 1000$

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.
we have,

$0.06 \times 1000 =60$

Find the product :

$0.6 \times 100$

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.
we have,

$0.6 \times 100 = 60$

Find the product :

$6.7314 \times 1000$

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.
we have,

$6.7314 \times 1000 = 6731.4$

Find the product :

$3.65 \times 19$

Multiply the decimal without the decimal point by the given whole number.
we have,

$365 \times 19 = 6935$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 3.65 \times 19 = 69.35$

Find the product :

$7.6 \times 2.4$

Multiply the two decimal without the decimal point just like whole numbers.

$76$

$\times 24$
____________

$+ 304$

$+152$
____________

$= 1824$

$\therefore 76 \times 24 = 1824$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=2$

$\therefore 7.6 \times 2.4 = 18.24$

Find the product :

$0.54 \times 0.27$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 54 \times 27 = 1458$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=4$

$\therefore 0.54 \times 0.27 = 0.1458$

1626450_1779758_ans_a7f1efccd777442490b1cee95be1d38b.PNG

Find the product :

$6.032 \times 124$

Multiply the decimal without the decimal point by the given whole number.
we have,

$6.032 \times 124 = 747968$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 6.032 \times 124 = 747.968$

Find the product :

$0.0146 \times 69$

Multiply the decimal without the decimal point by the given whole number.
we have,

$146 \times 69 = 10074$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 0.0146 \times 69 = 1.0074$

Find the product :

$3.45 \times 6.3$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 345 \times 63 = 21735$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=3$

$\therefore 3.45 \times 6.3 = 21.735$
1626359_1779755_ans_881c77353d8e496193d987ee144fc6c5.PNG

Find the product :

$0.854 \times 12$

Multiply the decimal without the decimal point by the given whole number.
we have,

$854 \times 12 = 10248$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 0.854 \times 12 = 10.248$

Find the product :

$0.00125 \times 327$

Multiply the decimal without the decimal point by the given whole number.
we have,

$125 \times 327 = 40875$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 0.00125 \times 327 = 0.40875$

Find the product :

$4.125 \times 86$

Multiply the decimal without the decimal point by the given whole number.
we have,

$4125 \times 86 = 354750$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 4.125 \times 86 = 35.4750$

Find the product :

$36.73 \times 48$

Multiply the decimal without the decimal point by the given whole number.
we have,

$3673 \times 48 = 176304$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 36.73 \times 48 = 1763.04$

Find the product :

$104.06 \times 75$

Multiply the decimal without the decimal point by the given whole number.
we have,

$10406 \times 75 = 780.450$
Mark the decimal point in the product to have as many places of decimal as are there are in the given decimal.

$\therefore 104.06 \times 75 = 780.450$

Find the product :

$0.623 \times 0.75$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 623 \times 75 = 46725$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$= 5$

$\therefore 0.623 \times 0.75 = 0.46725$

1626475_1779763_ans_2b4d5089557b404bbecb16961cd80bc4.PNG

Find the product :

$0.06 \times 0.38$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 6 \times 38 = 228$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=4$

$\therefore 0.06 \times 0.38 = 0.0228$

1626470_1779762_ans_5947229ae2d44a2393ac0993963f290f.PNG

Divide:

$4.7 \quad by \quad 100$

On dividing a decimal by

$100$ , the decimal point is shifted to the left by two places.

$\therefore 4.7 \div 100$

$= \cfrac{4.7}{100}\\$

$=0.047$ ....

$\{$ Decimal point shifted two places to left

$\}$

Find the product :

$54.5 \times 1.76$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 547 \times 176 = 95920$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$= 3$

$\therefore 54.5 \times 1.76 = 95.92$

1626492_1779767_ans_b99d486fabea4fc59bdd4942552640c0.PNG

Find the product :

$1.245 \times 6.4$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 1245 \times 64 = 79680$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$= 4$

$\therefore 1.245 \times 6.4 = 7.9680$

1626503_1779769_ans_f23651d677bf4700aef780f41745e53e.PNG

Find the product :

$0.014 \times 0.46$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 14 \times 46 = 644$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$= 5$

$\therefore 0.014 \times 0.46 = 0.00644$
1626484_1779764_ans_b84f28945f6d4aec87204df878bc028d.PNG

Find the product :

$0.568 \times 4.9$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 568 \times 49 = 27832$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=4$

$\therefore 0.568 \times 4.9 = 2.7832$

1626455_1779759_ans_6980d16518d1486fa32bcf0e9769e77a.PNG

Find the product :

$6.54 \times 0.09$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 654 \times 9 = 5886$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=4$

$\therefore 6.54 \times 0.09 = 0.5886$

1626461_1779760_ans_d208c52711ea4cfba5573f05f922ea79.PNG

Find the product :

$3.87 \times 1.25$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 387 \times 125 = 48375$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$=4$

$\therefore 3.87 \times 1.25 = 4.8375$

1626465_1779761_ans_b6b3cea6503949c68da8851cb088057c.PNG

Find the product :

$0.045 \times 2.4$

Multiply the two decimal without the decimal point just like whole numbers.

$\therefore 45 \times 24 = 1080$
Mark the decimal point in the product in such a way that the number of decimal places in the product is equal to the sum of the decimal place in the given decimals.
Sum of decimal places in the given decimals

$= 4$

$\therefore 0.045 \times 2.4 = 0.108$

1626497_1779768_ans_94d85016493a4858bfccae388fa32f42.PNG

Divide:

$131.6 \quad by \quad 10$

On dividing a decimal by

$10$ , the decimal point is shifted to the left by one place.

$\therefore 131.6 \div 10$

$= \cfrac{131.6}{10}$

$= 13.16$ ....

$\{$ Decimal point shifted one place to left

$\}$

Divide:

$0.3 \quad by \quad 100$

On dividing a decimal by

$100$ , the decimal point is shifted to the left by two places.

$\therefore 0.3 \div 100$

$= \cfrac{0.3}{100}\\$

$=0.003$ ....

$\{$ Decimal point shifted two places to left

$\}$

Divide:

$0.34 \quad by \quad 10$

On dividing a decimal by

$10$ , the decimal point is shifted to the left by one place.

$\therefore 0.34 \div 10$

$= \cfrac{0.34}{10}\\$

$= 0.034$ ....

$\{$ Decimal point shifted one place to left

$\}$

Divide:

$4.38 \quad by \quad 10$

On dividing a decimal by

$10$ , the decimal point is shifted to the left by one place.

$\therefore 4.38 \div 10$

$= \cfrac{4.38}{10}\\$

$= 0.438$ ....

$\{$ Decimal point shifted one place to left

$\}$

Divide:

$0.58 \quad by \quad 100$

On dividing a decimal by

$100$ , the decimal point is shifted to the left by two places.

$\therefore 0.58 \div 100$

$= \cfrac{0.58}{100}\\$

$=0.0058$ ....

$\{$ Decimal point shifted two places to left

$\}$

Multiply:
$\cfrac98$ by $\cfrac{32}3$

The product of two rational number =

$\cfrac{( \ product\ of\ their\ numerator\ )}{ (\ product\ of\ their\ denominator\ )}$

The above question can be written as

$\cfrac98\times \cfrac{32}3$

So, we have,

$=\cfrac98\times \cfrac{32}3$

$=\cfrac{9\times 32}{8\times 3}$

$=\cfrac{3\times 4}{1\times 1}$

$=12$

Multiply:
$\cfrac34$ by $\cfrac57$

The product of two rational number =

$\cfrac{( \ product\ of\ their\ numerator\ )}{ (\ product\ of\ their\ denominator\ )}$

The above question can be written as

$\cfrac34\times \cfrac57$

So, we have,

$=\cfrac34\times \cfrac57$

$=\cfrac{3\times 5}{4\times 7}$

$=\cfrac{15}{28}$

Divide:

$4.6 \quad by \quad 1000$

On dividing a decimal by

$1000$ , the decimal point is shifted to the left by three places.

$\therefore 4.6 \div 1000$

$= \cfrac{4.6}{1000}\\$

$=0.0046$ ....

$\{$ Decimal point shifted three places to left

$\}$

Divide:

$354.16 \quad by \quad 1000$

On dividing a decimal by

$1000$ , the decimal point is shifted to the left by three places.

$\therefore 354.16 \div 1000$

$= \cfrac{354.16}{1000}\\$

$=0.35416$ ....

$\{$ Decimal point shifted three places to left

$\}$

Divide:

$38.9 \quad by \quad 1000$

On dividing a decimal by

$1000$ , the decimal point is shifted to the left by three places.

$\therefore 38.9 \div 1000$

$= \cfrac{38.9}{1000}\\$

$=0.0389$ ....

$\{$ Decimal point shifted three places to left

$\}$

Divide:

$1286.5 \quad by \quad 1000$

On dividing a decimal by

$1000$ , the decimal point is shifted to the left by three places.

$\therefore 1286.5 \div 1000$

$= \cfrac{1286.5}{1000}\\$

$=1.2865$ ....

$\{$ Decimal point shifted three places to left

$\}$

Simplify: $=\dfrac{3}{20}\times$ $\dfrac{4}{5}$

The product of two rational number = ( product of their numerator)/ ( product of their denominator)

We have,

$=\dfrac{(3\times 4)}{ (20\times 5)}$

On simplifying,

$=\dfrac{(3\times 1)}{(5\times 5)}$

$=\dfrac{3}{25}$

Divide:

$0.8 \quad by \quad 1000$

On dividing a decimal by

$1000$ , the decimal point is shifted to the left by three places.

$\therefore 0.8 \div 1000$

$= \cfrac{0.8}{1000}\\$

$=0.0008$ ....

$\{$ Decimal point shifted three places to left

$\}$

Divide:

$0.02 \quad by \quad 100$

On dividing a decimal by

$100$ , the decimal point is shifted to the left by two places.

$\therefore 0.02 \div 100$

$= \cfrac{0.02}{100}\\$

$=0.0002$ ....

$\{$ Decimal point shifted two places to left

$\}$

Divide:

$0.768 \quad by \quad 16$

We perform the division by considering the dividend and divisor a whole number.

When the division in this form is complete.

we, subtract number of decimal points in dividend from number of decimal point in divisor. and that many decimal points we put in quotient of division.

So, we have,

$0.768 \div 16$

Now, we will do division

$768\div 16$

$768\div16=\cfrac{768}{16}=48$

Decimal points in dividend=

$3$

Decimal points in divisor=

$0$

subtraction=

$3-0=3$

So, we will put

$3$ decimal points in our answer

$48$

$\therefore 0.768 \quad by \quad 16 =0.048$

1636622_1780114_ans_20dc4f33c9d94a2697f52f9c6498d766.png

Divide:
$0.477 \quad by \quad 18$

Perform the division by considering the dividend a whole number.
When the division of thr whole-part of the dividend is complete, put the decimal point in the quotient and proceed with the division as in case of whole numbers.

Proceeding as above, We get

$0.477 \div 18 = 0.0265$
1626749_1780162_ans_bb4f657fe3ce4d75b01520e6e323ce9e.png

Divide:

$0.3322 \quad by \quad 11$

$0.3322 \div 11$

$\therefore 0.3322 \div 11 = 0.0302$

1626146_1780126_ans_7f7eeeb1a1144e2e869be6653d19457f.PNG

Divide:
$403.8 \div 30$

The above question can be written as,

$403.8 \div 30 =\dfrac{403.8}{30}$
Multiplying both numerator and denominator by 10, we get,

$= \dfrac{403.8 \times 10}{30 \times 10}=\dfrac{4038}{300}$

By long division (as shown in image), We get

$403.8\div30=\dfrac{4038 }{300} = 13.46$
1627677_1780191_ans_1738538d475d4631bbb99c9e8f90afe0.png

Divide:
$6.54 \hspace{2mm} by \hspace{2mm}12$

Perform the division by considering the dividend a whole number.
When the division of the whole part of the dividend is complete, put the decimal point in the quotient and proceed with the division as in case of whole numbers.

Proceeding as above, We get

$6.54 \div 12 = 0.545$

1626240_1780139_ans_34b298d57f194beab78126c37c70fdb2.png

Divide:
$1.001 \quad by \quad 14$

Proceeding as above, We get

$1.001 \div 14 = 0.0715$

1626416_1780150_ans_06327328b44544128c07af5cd0dc5f50.png

Divide:
$16.46 \div 20$

The above question can be written as,

$16.46\div20=\dfrac{16.46 }{ 20 }$
Multipling both numerator and denominator by 100 we get,

$= \dfrac{ 16.46 \times 100}{ 20 \times 100}$

$= \dfrac{1646 }{ 2000 }$

By long division (as shown in image), we get

$16.46\div20=\dfrac{ 1646 }{ 2000 } = 0.823$

1627581_1780184_ans_338e209dbc444381bc6c526b1ee0e9e1.png

Divide:

$0.175 \quad by \quad 25$

$0.175 \div 25$

$\therefore 0.175 \div 25 = 0.007$

1626113_1780119_ans_233c539783e946cd8c1c63c1e3429784.PNG

Divide:
$5.52 \quad by \quad 16$

$5.52 \div 16 = 0.345$
1626380_1780145_ans_bb079face51643229da941e59fea1de5.png

Divide:
$2.13$ by $15$

Perform the division by considering the dividend a whole number.

When the division of the whole-part of the dividend is complete, put the decimal point in the quotient and proceed with the division as in case of whole numbers.

$\therefore 2.13 \div 15 = 0.14$

1626100_1780135_ans_2cbaa57853904da79472d1a99bae563a.png

Find the product:
$\left(3\cfrac{6}{7}\right) \times\left(4\cfrac{2}{3}\right)$

By the rule Multiplication of fraction,

Product of fraction=

$\cfrac{product\ of\ numerator}{product\ of\ denominator}$

$1^{st}$ we will convert mixed fraction into improper fraction.

$3\cfrac{6}{7}=\cfrac{3\times 7+6}{7}=\cfrac{27}{7}$

And,

$4\cfrac{2}{3}=\cfrac{4\times 3+2}{3}=\cfrac{14}{3}$

Then,

$3\cfrac{6}{7} \times\left(4\cfrac{2}{3}\right)=\cfrac{27}{7}\times \cfrac{14}{3}$

$=\cfrac{(27\times 14)}{(7\times 3)}$

$=\cfrac{(9\times 2)}{(1\times 1)}$

$=\cfrac{18}{1}$

$=18$

Divide:

$18.08 \div 400$

$\dfrac{18.08}{400} = 0.0452$

1625676_1780211_ans_3114fde2c4a64678b20fae518bbe81a2.PNG

Find the product:
$\left(4\cfrac{1}{8} \right)\times\left(2\cfrac{10}{11}\right)$

By the rule Multiplication of fraction,

Product of fraction=

$\cfrac{product\ of\ numerator}{product\ of\ denominator}$

$1^{st}$ we will convert mixed fraction into improper fraction.

$4\cfrac{1}{8}=\cfrac{4\times 8+1}{8}=\cfrac{33}{8}$

And,

$2\cfrac{10}{11}=\cfrac{2\times 11+10}{11}=\cfrac{32}{11}$

Then,

$4\cfrac{1}{8} \times\left(2\cfrac{10}{11}\right)=\cfrac{33}{8}\times \cfrac{32}{11}$

$=\cfrac{(33\times 32)}{(8\times )}$

$=\cfrac{(3\times 4)}{(1\times 1)}$

$=\cfrac{12}{1}$

$=12$

Divide:

$3.28 \div 0.8$

1625682_1780213_ans_5b3793a481954428958a3df2521d1898.PNG

Find the product:
$\left(9\cfrac{1}{2}\right) \times\left(1\cfrac{9}{19}\right)$

By the rule Multiplication of fraction,

Product of fraction=

$\cfrac{product\ of\ numerator}{product\ of\ denominator}$

$1^{st}$ we will convert mixed fraction into improper fraction.

$9\cfrac{1}{2}=\cfrac{9\times 2+1}{2}=\cfrac{19}{2}$

And,

$1\cfrac{9}{19}=\cfrac{1\times 19+9}{19}=\cfrac{28}{19}$

Then,

$9\cfrac{1}{2} \times\left(1\cfrac{9}{19}\right)=\cfrac{19}{2}\times \cfrac{28}{19}$

$=\cfrac{(19\times 28)}{(2\times 19)}$

$=\cfrac{(1\times 14)}{(1\times 1)}$

$=\cfrac{14}{1}$

$=14$

Find the product:
$\left(5\cfrac{5}{6}\right)\times\left(1\cfrac{5}{7}\right)$

By the rule Multiplication of fraction,

Product of fraction=

$\cfrac{product\ of\ numerator}{product\ of\ denominator}$

$1^{st}$ we will convert mixed fraction into improper fraction.

$5\cfrac{5}{6}=\cfrac{5\times 6+5}{6}=\cfrac{35}{6}$

And,

$1\cfrac{5}{7}=\cfrac{1\times 7+5}{7}=\cfrac{12}{7}$

Then,

$\left(5\cfrac{5}{6}\right)\times\left(1\cfrac{5}{7}\right)=\cfrac{35}{6}\times \cfrac{12}{7}$

$=\cfrac{(35\times 12)}{(6\times 7)}$

$=\cfrac{(5\times 2)}{(1\times 1)}$

$=\cfrac{10}{1}$

$=10$

Divide:

$156.8 \div 200$

The above question can be written as,

$\Rightarrow ( \dfrac{156.8} {200} )$

Multiply by 10 for both numerator and denominator, then we get,

$= \dfrac{ ( 156.8 \times 10)} { ( 200 \times 10) }$

$=\dfrac{1568}{2000}$

$=0.784$

1624627_1780201_ans_057ee826ece540a6a70cc819152c14ec.PNG

Divide:

$12.8 \div 500$

$12.8\div 500= 0.0256$

1624666_1780208_ans_975d97f5d45c442c9459f970fe3023cc.PNG

Divide:
$19.2 \div 80$

The above question can be written as,

$19.2 \div 80 =\dfrac{19.2}{80}$
Multiplying both numerator and denominatorby 10, we get,

$= \dfrac{19.2 \times 10}{ 80 \times 10}$

$= \dfrac{192 }{800}$

By long division (as shown in image), We get

$19.2 \div80 =\dfrac{192}{800}= 0.24$

1627706_1780196_ans_f54dd346c2764dba8d61d77cb8e864a6.png

Divide:

$0.8085 \quad by \quad 0.35$

1625800_1780223_ans_f9ad2198d8ad40dcbdfbabbdd665939d.PNG

Divide:

$148 \quad by \quad 0.074$

$\dfrac{148}{0.074}=2000$
1626747_1780240_ans_8bcc75fdd35f45ada2799ca74296e111.PNG

Divide:

$6.612 \quad by \quad 11.6$

1625885_1780235_ans_ee2595fffcb94e048870cf12af5e7507.PNG

Divide:

$21.976 \quad by \quad 1.64$

1625815_1780226_ans_c227c8df9cb2439cabd98b02dac6343d.PNG

Divide:

$0.288\ by\ 0.9$

1625692_1780215_ans_cbace6a36acf492b8b39246293a071b0.PNG

Divide:

$11.04 \quad by \quad 1.6$

1625865_1780232_ans_146408443372444ea36ea65b1472202a.PNG

Divide:

$0.076 \quad by \quad 0.19$

1626594_1780237_ans_22d9fb426d7d48dfb65345ceb3235802.PNG

Divide:

$16.578 \quad by \quad 5.4$

1626770_1780243_ans_a873ad9cac5b4519b018157230bff286.PNG

Divide:

$25.395 by 1.5$

1625705_1780216_ans_3c9cdf93422745f59bd85ce15a260201.PNG

Divide:
$0.228$ by $0.38$

1625782_1780221_ans_59489b91b5e546979376dcde295ad0c7.PNG

The total cost of $24$ chairs is $9255.60.$ Find the cost of each chair.

The number of chairs

$= 24$
The cost of

$24$ chairs is = ₹

$9255.60$
Then the cost of each chair =

$\dfrac{9255.60}{24}$

$\therefore$ the cost of each chair is ₹

$385.65$

1626388_1780254_ans_2470fdeca969408abafc144f98d960c5.PNG

$8 \frac{2}{7}$ Is equal to the improper fraction_____.

$8 \dfrac{2}{7}$ Is equal to the improper fraction

$\Rightarrow 8 \dfrac {7}{2} = \dfrac {( 8 \times 7) + 7}{2} = \dfrac { 56 + 2 }{7} = \dfrac {58}{7}$

Write $\dfrac{129}{8}$ as a mixed fraction.

We have

$\dfrac {192}{8} = 16 \dfrac {1}{8}$

1642964_1788625_ans_9f2d6d0b06b649df94ed8df577c46f11.png

Grip size of a tennis racquet is $11 \dfrac{9}{80} cm$ . Express the size as an improper fraction.

Given , Grip size of tennis racquet is

$11 \dfrac {9}{80} cm$
Now,

$\Rightarrow 11 \dfrac {9}{80} = \dfrac {( 11 \times 80) + 9 }{80} = \dfrac {880 +9 }{80} = \dfrac {889}{80}$

$\dfrac {889}{80}$ this improper fraction.

Convert the following fractions into mixed fractions:
(i) $\dfrac{73}{8}$
(ii) $\dfrac{94}{13}$

(i) Mixed fraction of

$\dfrac{73}{8} = 9 \dfrac{1}{8}$
(ii) Mixed fraction of

$\dfrac{94}{13} = 7 \dfrac{3}{13}$

When 0.004 is divided by 0.02964, what will be the quotient?

1903699_1790261_ans_a77e6d451ccf4f839dcc24a0f855d763.jpeg

Convert the following fractions into improper fractions :
(i) $2 \dfrac{7}{9}$
(ii) $5 \dfrac{4}{11}$

(i) Improper fraction of

$2 \dfrac{7}{9} = \dfrac{2 \times 9 +7}{9} = \dfrac{25}{9}$
(ii) Improper fraction of

$5 \dfrac{4}{11} = \dfrac{5 \times 11 + 4}{11}$

$=\dfrac{59}{11}$

Find the following:
(i) $10.8 \div 4$
(ii) $126.35 \div 7$
(iii) $22.5 \div 1.5$
(iv) $4.28 \div 0.02$
(v) $3.645 \div 1.35$
(vi) $0.728 \div 0.04$
(vii) $13.06 \div 0.08$
(viii) $58.635 \div 4.5$

(i)

$\dfrac{10.8}{4}=2.7$

(ii)

$\dfrac{126.35}{7}=18.05$

(iii)

$\dfrac{225}{10} \times \dfrac{10}{15}= 15$

(iv)

$\dfrac{428}{100} \times \dfrac{100}{2}=214$

(v)

$\dfrac{3645}{1000} \times \dfrac{1000}{1350}= 2.7$

(vi)

$\dfrac{728}{1000} \times \dfrac{1000}{40} = 18.2$

(vii)

$\dfrac{1306}{100} \times \dfrac{100}{8} = 163.25$

(viii)

$\dfrac{58635}{1000} \times \dfrac{1000}{4500} = 13.03$

Multiply each of the following numbers by $10, 100$ and $1000$ (orally):
(i) $5.9$
(ii) $3.76$
(iii) $0.549$

(i)

$5.9 \times 10=59$

$5.9 \times 100=590$

$5.9 \times 1000=5900$

(ii)

$3.76 \times 10=37.6$

$3.76 \times 100=376$

$3.76 \times 1000=3760$

(iii)

$0.549 \times 10=5.49$

$0.549 \times 100=54.9$

$0.549 \times 1000=549$

Find the following:
(i) $2.7 \times 4$
(ii) $2.71 \times 5$
(iii) $2.5 \times 0.3$
(iv) $2.3 \times 4.35$
(v) $238.06 \times 7.5$
(vi) $0.79 \times 32.4$
(vii) $1.07 \times 0.02$
(viii) $10.05 \times 1.05$

(i)

$\dfrac{27}{10} \times 4=\dfrac{108}{10}=10.8$

(ii)

$=\dfrac{271}{100} \times 5 = \dfrac{1355}{100}=13.55$

(iii)

$\dfrac{25}{10} \times \dfrac{3}{10} = \dfrac{75}{100}=0.75$

(iv)

$= \dfrac{23}{10} \times \dfrac{435}{100} = \dfrac{10005}{1000}=10.005$

(v)

$\dfrac{23806}{100} \times \dfrac{75}{10}$

$=1785.45$

(vi)

$\dfrac{79}{100} \times \dfrac{324}{10}$

$=25.596$

(vii)

$=\dfrac{107}{100} \times \dfrac{2}{100}$

$=\dfrac{214}{10000}=0.0214$

(viii)

$\dfrac{1005}{100} \times \dfrac{105}{100}$

$=10.5525$

What is the cost of 27.5 m of cloth at 53.50 per metre?

1903336_1790236_ans_09e22965f90c4779bb367ce61d1f9894.jpg

What will be the total length of cloth required to make $5$ shirts, if $2.15 m$ of cloth is needed for each shirt?

Given
Cloth required for one shirt

$= 2.15$ m
Cloth required for 5 shirts can be calculated as below

$= 2.15 × 5$

$= 10.75 m$
Therefore, cloth required for

$5$ shirts is

$10.75 m$

The cost of a fountain pen is $Rs 13.25$ . Find the cost of $8$ such pens.

Given
The cost of a fountain pen

$= Rs 13.25$
The cost of

$8$ pens can be calculated as below
Cost of

$8$ fountain pens

$= 13.25 × 8$

$= 106.00$

$= Rs 106$
Therefore, the cost of

$8$ fountain pens is Rs

$106$

Find the area of a rectangle whose length is $5.7 \ cm$ and breadth is $3.5 \ cm$ .

Length of a rectangle

$=5.7 \ cm$
and Breadth

$=3.5 \ cm$

$Area = Length \times Breadth$

$=5.7 \times 3.5 \ sq. cm$

$=19.95 \ sq. cm$

If $Rs. 242.46$ are to be distributed among $6$ children equally, find the share of each.

$6$ children gets

$=Rs. 242.46$
One child will get

$= Rs. 242.46 \div 6= 40.41$

$83$ note-books are sold at $Rs 15.25$ each. Find the total money (in rupees) obtained by selling these note-books.

Given
Sale price of

$1$ note-book

$= Rs 15.25$
Sale price of

$83$ note-books can be calculated as below
Sale price of

$83$ books

$= Rs 15.25 × 83$

$= Rs 1265.75$ paise
Therefore, the total amount obtained by selling

$83$ note-books is Rs

$1265.75$ paise

The cost of one metre cloth is $Rs. 38.50$ . Find the cost of $3.6$ m cloth.

Cost of one metre of cloth

$= Rs. 38.50$
Cost of

$3.6 \ m$ of cloth

$=38.50 \times 3.6$

$= Rs. 138.60$

The length of an iron rod is $10.32 m$ . The rod is divided into $4$ pieces of equal lengths. Find the length of each piece.

Given
The length of an iron rod

$= 10.32$ m
The rod is divided into

$4$ pieces of equal length
The length of each piece can be calculated as below

$= \dfrac{10.32} {4}$

$= 2.58 m$
Therefore, the length of each piece of rod is

$2.58$

$m$

The cost of $25$ identical articles is $Rs 218.25.$ Find the cost of one article

Given
Cost of

$25$ articles

$=$ Rs

$218.25$
Cost of one article can be calculated as below
Cost of

$1$ article

$= \dfrac{218.25}{25}$

$=\dfrac{21825}{25 × 100}$
We get,

$= \dfrac{873}{100}$

$= Rs 8.73$
Therefore, the cost of one article is Rs

$8.73$

If the product of two decimal numbers is $38.745$ and one of the numbers is $2.7$ , find the other.

Product of two decimal numbers

$=38.745$
One number

$=2.7$
Second number

$=38.745 \div 2.7$

$=38.745 \div 2.70$

$\dfrac{38745}{2700} = 14.35$

Change the following mixed fractions to improper fractions:
(i) $2\frac { 1 }{ 5 }$
(ii) $3\frac { 1 }{ 4 }$
(iii) $7\frac { 1 }{ 8 }$
(iv) $2\frac { 1 }{ 11 }$

$2\frac { 1 }{ 5 }$

The conversion of mixed fraction to improper fraction is shown below

$2\frac { 1 }{ 5 } = \dfrac{(2 × 5 + 1) } 5$

$= (10 + 1) / 5$

$= 11 / 5$

(ii) $3\frac { 1 }{ 4 }$

The conversion of mixed fraction to improper fraction is shown below

$3\frac { 1 }{ 4 } = \dfrac{(3 × 4 + 1) } 4$

$= (12 + 1) / 4$

$= 13 / 4$

(iii) $7\frac { 1 }{ 8 }$

The conversion of mixed fraction to improper fraction is shown below

$7\frac { 1 }{ 8 } = \dfrac{(7 × 8 + 1) }8$

$= (56 + 1) / 8$

$= 57 / 8$

(iv) $2\frac { 1 }{ 11 }$

The conversion of mixed fraction to improper fraction is shown below

$2\frac { 1 }{ 11 } = \dfrac{(2 × 11 + 1) } 11$

$= (22 + 1) / 11$

$= 23 / 11$

Express the following improper fractions as mixed fractions:
$7/4$

$7/4$ can be express as mixed fractions as

$1 \dfrac{3}{4}$

Express the following mixed fractions as improper fractions:
$2 \dfrac{5}{48}$

$2 \dfrac{5}{48}$
It can be written as

$= \left(2 \times 48 + 5\right)/48$
By further calculation

$= \left(96 + 5\right)/48$

$= 101/48$

Express the following mixed fractions as improper fractions:
$2 \dfrac{4}{9}$

$2 \dfrac{4}{9}$
It can be written as

$= \left ( 2 \times 9 + 4\right) /9$
By further calculation

$= \left( 18 + 4 \right) /9$

$= 22/9$

Express the following mixed fractions as improper fractions:
$7 \dfrac{5}{13}$

$7 \dfrac{5}{13}$
It can be written as

$= \left(7 \times 13 + 5\right) / 13$
By further calculation

$= \left(91 + 5\right)/13$

$= 96/13$

Express the following as improper fractions:
a) $7\dfrac{3}{4}$ b) $5\dfrac{6}{7}$ c) $2\dfrac{5}{6}$ d) $10\dfrac{5}{3}$ e) $9\dfrac{3}{7}$ f) $8\dfrac{4}{9}$

$\displaystyle 7\frac{3}{4} = \frac{(4 \times 7) + 3}{4} = \frac{31}{4}$

$\displaystyle 5\frac{6}{7} = \frac{(7\times 5) + 6}{7} = \frac{41}{7}$

$\displaystyle 2\frac{5}{6} = \frac{(6 \times 2)+ 5}{6} = \frac{17}{6}$

$\displaystyle 10\frac{5}{3} = \frac{(3 \times 10)+ 5}{3} = \frac{35}{3}$

$\displaystyle 9\frac{3}{7} = \frac{(7 \times 9)+3}{7} = \frac{66}{7}$

$\displaystyle 8\frac{4}{9} = \frac{(8 \times 9)+4}{9} = \frac{76}{9}$

Evaluate :
$0.14616 \div 72$

$0.14616 \div 72$
We get

$0.14616 \div 72=0.00203$
1744186_1827813_ans_0a91c9bf1a11412db1496dee3dc99f89.png

Evaluate :
$0.6227 \div 1300$

$0.6227 \div 1300$
We get

$0.6227 \div 1300=0.000479$
1744211_1827814_ans_c538769339f04d3aa2fc83ad66351a68.png

Express the following as mixed fraction:

a) $\displaystyle \frac{20}{3}$ b) $\displaystyle \frac{11}{5}$ c) $\displaystyle \frac{17}{7}$ d) $\displaystyle \frac{28}{5}$ e) $\displaystyle \frac{19}{6}$ f) $\displaystyle \frac{35}{9}$

$\displaystyle \frac{20}{3} = \frac{18 + 2}{3} = \frac{18}{3}+ \frac{2}{3}$

$\displaystyle \frac{11}{5} = \frac{10+1}{5} = \frac{10}{5} + \frac{1}{5} = 2 + \frac{1}{5} = 2\frac{1}{5}$

$\displaystyle \frac{17}{7} = \frac{14+3}{7} = \frac{14}{7} + \frac{3}{7} = 2 + \frac{3}{7} = 2 \frac{3}{7}$

$\displaystyle \frac{28}{5} = \frac{25 + 3}{5} = \frac{25}{5} + \frac{3}{5} = 5+\frac{3}{5} = 5\frac{3}{5}$

$\displaystyle \frac{19}{6} = \frac{18+1}{6} = \frac{18}{6}+\frac{1}{6} = 3+\frac{1}{6} =3\frac{1} {6}$

$\displaystyle \frac{35}{9} = \frac{27+8}{9} = \frac{27}{9} + \frac{8}{9} = 3 + \frac{8}{9} = 3\frac{8}{9}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\frac{2b + a - \frac{4a^2 - b^2}{a}}{b^3 + 2ab^2 - 3a^2b} \cdot \frac{a^3b - 2a^2b^2 + ab^3}{a^2 - b^2}$

$\cfrac{2b+a-\cfrac{4a^{2}-b^{2}}{a}}{b^{3}+2ab^{2}-3a^{2}b}\cdot \cfrac{a^{3}b-2a^{2}b^{2}+ab^{3}}{a^{2}-b^{2}}$

$=\cfrac{\cfrac{2b+a^{2}-4a^{2}+b^{2}}{a}}{b(b^{2}+2ab-3a^{2})}\cdot \cfrac{ab(a^{2}-2ab+b^{2})}{a^{2}-b^{2}}$

$=\cfrac{2ab+b^{2}-3a^{2}}{ab(b^{2}+2ab-3a^{2})}\cdot \cfrac{ab(a-b)^{2}}{a^{2}-b^{2}}$

$=\cfrac{(a-b)^{2}}{(a+b)(a-b)}$

$=\cfrac{a-b}{a+b}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\left ( \frac{1}{a - \sqrt{2}} - \frac{a^2 + 4}{a^3 - \sqrt{8}} \right ) : \left ( \frac{a}{\sqrt{2}} + 1 + \frac{\sqrt{2}}{a} \right )^{-1}$

$(\cfrac{1}{a-\sqrt 2}-\cfrac{a^{2}+4}{a^{3}-\sqrt 8}):(\cfrac{a}{\sqrt 2}+1+\cfrac{\sqrt 2}{a})^{-1}$

$=(\cfrac{a^{2}+\sqrt 2a+2-a^{2}-4}{a^{3}-\sqrt 8})\times (\cfrac{a^{2}+\sqrt 2a+2}{\sqrt 2a})$

$=\cfrac{\sqrt 2a-2}{(a-\sqrt 2)(a^{2}+\sqrt 2a+2)}\times \cfrac{(a^{2}+\sqrt 2a+2)}{\sqrt 2a}$

$=\cfrac{\sqrt 2(a-\sqrt 2)}{\sqrt 2a(a-\sqrt 2)}$

$=\cfrac{1}{a}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\frac{(5 \sqrt{3} + \sqrt{50})\, (5 - \sqrt{24})}{\sqrt{75} - 5 \sqrt{2}}$

$\dfrac{\left(5\sqrt{3}+5\sqrt{2}\right)\left(5-2\sqrt{6}\right)}{\left(5\sqrt{3}-5\sqrt{2}\right)}$

$=\dfrac{ 5\left(\sqrt{3}+\sqrt{2}\right)\left(5-2\sqrt{6}\right)}{5\left(\sqrt{3}-\sqrt{2}\right)}$

$=\dfrac{\left(\sqrt{3}+\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)\left(5-2\sqrt{6}\right)}{\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)}$

$=\dfrac{\left(3+2+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}{3-2}$

$=\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)$

$=25-24= 1$ .

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\left ( \frac{1}{3} \right )^{-10}\, \cdot 27^{-3} + 0.2^{-4} \cdot 25^{-2} + (64^{-1/9})^{-3}$

$(3)^{10} . ((3)^3)^{-3} +$

$(\frac{10}{2})^4$

$(\frac{1}{25})^2$ +

$(((\frac{1}{2})^9)^{\frac{1}{9}})^{-3}$ {by using the property of

$x^{-1}=\frac{1}{x}$ } and vice varsa

$(3)^{10} .(3)^{-9}+ \frac{10000}{16} .( \frac{1}{25})^2+(2)^3$

$(3)^{10-9}+1+8$

$3+1+8=12.$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \frac{\sqrt{x} + 1}{1 + \sqrt{x} + x} : \frac{1}{x^2 - \sqrt{x}}$

$\cfrac{\sqrt x+1}{1+\sqrt x+x}:\cfrac{1}{x^{2}-\sqrt x}$

$=\cfrac{(\sqrt x+1)(\sqrt x-1)}{(1+\sqrt x+x)(\sqrt x-1)}:\cfrac{1}{\sqrt x(x^{2-\frac{1}{2}}-1)}$

$=\cfrac{(\sqrt x)^{2}-1}{(\sqrt x)^{3}-1}\times \sqrt x(x^{\frac{3}{2}}-1)$

$=\cfrac{(x-1)}{x^{\frac{3}{2}}-1}\sqrt x(x^{\frac{3}{2}}-1)$

$=\sqrt x(x-1)$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \left ( \frac{1}{m - \sqrt{mn}} + \frac{1}{m + \sqrt{mn}} \right )\cdot \frac{m^3 - n^3}{m^2 + mn + n^2}$

$(\cfrac{1}{m-\sqrt{mn}}+\cfrac{1}{m+\sqrt{mn}})$

$\cdot \cfrac{m^{3}-n^{3}}{m^{2}+mn+n^{2}}$

$=(\cfrac{m+\sqrt{mn}+m-\sqrt{mn}}{m^{2}-(\sqrt{mn})^{2}})\cdot \cfrac{(m-n)(m^{2}+mn+n^{2})}{(m^{2}+mn+n^{2})}$

$=\cfrac{2m}{m^{2}-mn}\cdot (m-n)$

$=\cfrac{2m(m-n)}{m(m-n)}$

$=2$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \left ( \frac{a^{1/2} + 2}{a + 2a^{1/2} + 1 } - \frac{a^{1/2} - 2}{a - 1} \right ) \cdot \frac{a^{1/2} + 1}{a^{1/2}}$

$(\cfrac{a^{\cfrac{1}{2}}+2}{a+2a^{\cfrac{1}{2}}+1}-\cfrac{a^{\cfrac{1}{2}}-2}{a-1})\cdot \cfrac{a^{\cfrac{1}{2}}+1}{a^{\cfrac{1}{2}}}$

$=(\cfrac{\sqrt a+2}{(\sqrt a)^{2}+2\sqrt a+1)}-\cfrac{\sqrt a-2}{(\sqrt a)^{2}-1)})\cdot \cfrac{\sqrt a+1}{\sqrt a}$

$=[\cfrac{\sqrt a+2}{(\sqrt a+1)^{2}}-\cfrac{\sqrt a-2}{(\sqrt a+1)(\sqrt a-1)}]\cdot \cfrac{\sqrt a+1}{\sqrt a}$

$=[\cfrac{\sqrt a+2}{\sqrt a+1}-\cfrac{\sqrt a-2}{\sqrt a-1}]\cfrac{\sqrt a+1}{\sqrt a(\sqrt a+1)}$

$=(\cfrac{(\sqrt a+2)(\sqrt a-1)-(\sqrt a-2)(\sqrt a+1)}{a-1})\cfrac{1}{\sqrt a}$

$=[\cfrac{a-\sqrt a+2\sqrt a-2-(a+\sqrt a-2\sqrt a-2)}{a-1}]\cfrac{1}{\sqrt a}$

$=[\cfrac{a+\sqrt a-2-a+\sqrt a+2}{a-1}]\cfrac{1}{\sqrt a}$

$=\cfrac{2\sqrt a}{(a-1)\sqrt a}=\cfrac{2}{a-1}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \frac{a -b}{a + b + 2\sqrt{ab}} : \frac{a^{-1/2} - b^{-1/2}}{a^{-1/2} + b^{-1/2}}$

$\cfrac{a-b}{a+b+2\sqrt{ab}}:\cfrac{a^{\frac{-1}{2}}-b^{\frac{-1}{2}}}{a^{\frac{-1}{2}}+b^{\frac{-1}{2}}}$

$=\cfrac{(\sqrt a)^{2}-(\sqrt b)^{2}}{(\sqrt a)^{2}+(\sqrt b)^{2}+2\sqrt a\sqrt b}\times \cfrac{\cfrac{1}{\sqrt a}+\cfrac{1}{\sqrt b}}{\cfrac{1}{\sqrt a}-\cfrac{1}{\sqrt b}}$

$=\cfrac{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)}{(\sqrt a+\sqrt b)(\sqrt a+\sqrt b)}\times \cfrac{\cfrac{\sqrt b+\sqrt a}{\sqrt{ab}}}{\cfrac{\sqrt b-\sqrt a}{\sqrt{ab}}}$

$=\cfrac{(\sqrt a-\sqrt b)}{(\sqrt a+\sqrt b)}\times \cfrac{(\sqrt b+\sqrt a)}{-(\sqrt a-\sqrt b)}$

$=-1$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \frac{b -x}{\sqrt{b} - \sqrt{x}} - \frac{b^{3/2} - x^{3/2}}{b - x}$

$\cfrac{b-x}{\sqrt b-\sqrt x}-\cfrac{b^{\frac{3}{2}}-x^{\frac{3}{2}}}{b-x}$

$=\cfrac{(\sqrt b)^{2}-(\sqrt x)^{2}}{\sqrt b-\sqrt x}-\cfrac{(\sqrt b-\sqrt x)(b+x+\sqrt bx)}{(\sqrt b)^{2}-(\sqrt x)^{2}}$

$=\sqrt b+\sqrt x-\cfrac{(b+x-\sqrt{bx})}{\sqrt b+\sqrt x}$

$=\cfrac{b+x+2\sqrt{bx}-b-x-\sqrt{bx}}{\sqrt b+\sqrt x}$

$=\cfrac{\sqrt{bx}}{\sqrt b+\sqrt x}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\,(x + \sqrt{x^2 - 1})^2 + (x + \sqrt{x^2 - 1})^{-2} + 2 (1 -2x^2)$

$(x+\sqrt{x^{2}-1}) + (x+\sqrt{x^{2}-1})^{-2}+2(1-2x^{2})$

$=(x+\sqrt {x^{2}-1)}^{-1}$ can be simplified

$\cfrac{1}{x+\sqrt{x^{2}-1}}$

$=\cfrac{x-\sqrt{x^{2}-1}}{(x)^{2}-(\sqrt{x^{2}-1})^{2}}$

$=\cfrac{x-\sqrt{x^{2}-1}}{x^{2}-x^{2}+1}=x-\sqrt{x^{2}-1}$

So,

$(x+\sqrt{x^{2}-1})^{2}+(x-\sqrt{x^{2}-1})^{2}+2-4x^{2}$

$=(x+\sqrt{x^{2}-1})^{2}+(x-\sqrt{x^{2}-1})^{2}+2(x+\sqrt{x^{2}-1})(x-\sqrt{x^{2}-1})-4x^{2}$

$=(x+\sqrt{x^{2}-1}+x-\sqrt{x^{2}-1})^{2}-4x^{2}$

$=(2x)^{2}-4x^{2}$

$=4x^{2}-4x^{2}=0$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\,\left ( \frac{x^{1/2} + y^{1/2}}{x^{1/2} - y^{1/2}} - \frac{x^{1/2} - y^{1/2}}{x^{1/2} + y^{1/2}} \right ) (y^{-1/2} - x^{-1/2})$

$(\cfrac{x^{\cfrac{1}{2}}+y^{\cfrac{1}{2}}}{x^{\cfrac{1}{2}}-y^{\cfrac{1}{2}}}-\cfrac{x^{\cfrac{1}{2}}-y^{\cfrac{1}{2}}}{x^{\cfrac{1}{2}}+y^{\cfrac{1}{2}}})(y^{\cfrac{-1}{2}}-x^{\cfrac{-1}{2}})$

$=\cfrac{(\sqrt x+\sqrt y)^{2}-(\sqrt x-\sqrt y)^{2}}{(\sqrt x)^{2}-(\sqrt y)^{2}}(\cfrac{1}{\sqrt y}-\cfrac{1}{\sqrt x})$

$=\cfrac{x+y+2\sqrt xy-x-y+2\sqrt 2}{x-y}\times \cfrac{\sqrt x-\sqrt y}{\sqrt {xy}}$

$=\cfrac{4\sqrt {xy}(\sqrt x-\sqrt y)}{(\sqrt x+\sqrt y)(\sqrt x-\sqrt y)\sqrt {xy}}$

$=\cfrac{4}{\sqrt x+\sqrt y}$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \left ( \frac{3}{\sqrt{1 + a}} + \sqrt{1 -a} \right ) : \left ( \frac{3}{\sqrt{1 - a^2}} + 1 \right )$

$(\cfrac{3}{\sqrt{1+a}}+\sqrt{1-a}):(\cfrac{3}{\sqrt{1-a^{2}}}+1)$

$=(\cfrac{3+\sqrt{1-a}\sqrt{1+a}}{\sqrt{1+a}})\times \cfrac{\sqrt{1-a^{2}}}{3+\sqrt{1-a^{2}}}$

$=\cfrac{(3+\sqrt{1-a^{2}})}{\sqrt{1+a}}\times \cfrac{\sqrt{1-a}\times\sqrt{1+a}}{(3+\sqrt{1-a^{2}})}$

$=\sqrt{1-a}$

A flower garden is 22.50 m long. Sheela wants to make a border along one side using bricks that are 0.25 m long. How many bricks will be needed?

1903684_1790269_ans_ee484228c9db49c7a982f671297dff9d.jpeg

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \left ( \frac{\sqrt{a}}{2} - \frac{1}{2 \sqrt{a}} \right )^2 \left ( \frac{\sqrt{a} - 1}{\sqrt{a} + 1} - \frac{\sqrt{a} + 1}{\sqrt{a} - 1} \right )$

$(\cfrac{\sqrt a}{2}-\cfrac{1}{2\sqrt a})^{2}(\cfrac{\sqrt a-1}{\sqrt a+1}-\cfrac{\sqrt a+1}{\sqrt a-1})$

$=(\cfrac{a-1}{2\sqrt a})^{2}[\cfrac{(\sqrt a-1)^{2}-(\sqrt a+1)^{2}}{a-1}]$

$=\cfrac{(a-1)^{2}}{4a}\cfrac{-4a}{(a-1)}$

$=(-a+1)$

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, \left ( \frac{P^{3/2} + q^{3/2}}{p - q} - \frac{p - q}{P^{1/2} + q^{1/2}} \right )\left ( \sqrt{pq} \frac{\sqrt{p} + \sqrt{q}}{p - q} \right )^{-1}$

$(\cfrac{P^{\cfrac{3}{2}}+q^{\cfrac{3}{2}}}{p-q}-\cfrac{p-q}{P^{\cfrac{1}{2}}+q^{\cfrac{1}{2}}})(\sqrt{pq}\cfrac{\sqrt p+\sqrt q}{p-q})^{-1}$

$=(\cfrac{(\sqrt p+\sqrt q)(p-\sqrt{pq}+q)}{(\sqrt p+\sqrt q)(\sqrt p-\sqrt q)}-\cfrac{(\sqrt p-\sqrt q)(\sqrt p+\sqrt q)}{(\sqrt p+\sqrt q)}) (\sqrt{pq}\cfrac{(\sqrt p+\sqrt q)}{(\sqrt p+\sqrt q)(\sqrt p-\sqrt q)})^{-1}$

$=(\cfrac{P-\sqrt{pq}+q}{\sqrt p-\sqrt q}-(\sqrt p-\sqrt q))(\cfrac{\sqrt{pq}}{\sqrt p-\sqrt q})^{-1}$

$=(\cfrac{P-\sqrt{pq}+q-P-q+2\sqrt{pq}}{\sqrt p-\sqrt q})\cfrac{(\sqrt p-\sqrt q)}{\sqrt{pq}}$

$=\cfrac{\sqrt{pq}}{\sqrt{pq}}=1$

Fractions And Decimals - Class 7 Maths - Extra Questions

23.2÷100=x23.2\div 100 =x. Find 1000x1000x

Convert the given mixed fractions into improper 2152\dfrac {1}{5}

Convert the given mixed fractions into improper 2122\dfrac {1}{2}

Convert the given mixed fractions into improper3163\dfrac {1}{6}

Convert the given mixed fractions into improper7297\dfrac {2}{9}

Convert the given mixed fractions into improper 61106\dfrac {1}{10}

Convert the given mixed fractions into improper4234\dfrac {2}{3}

Find 2122\dfrac{1}{2}% of 320320 people.

find : 2.5×0.32.5 \times 0.3

18.368÷1418.368\div 14.

Divide each of the given numbers by 10,100,100010,100,1000 and 10000::2.12.18.648.645.015.010.09060.09060.1250.125111.11111.11

Solve : 0.5×0.050.5\times 0.05

Solve(i) 1.5×0.31.5\times 0.3

Solve: 1.07×0.021.07\times 0.02

Solve: 4.3×3.44.3\times 3.4

Solve: 0.1×47.50.1\times 47.5

Solve:10.05×1.0510.05\times 1.05

Solve : 70.01×1.170.01\times 1.1

Find:0.2×60.2\times 6

Find651.2÷4651.2 \div 4

Convert the following into a vulgar fraction:2.¯132.\overline { 13 }

Fill in the blank.1.1×100=1.1 \times 100=______

Convert the following into a vulgar fraction:0.ˉ80.\bar { 8 }

Multiply : 0.1×51.70.1\times 51.7

Simplify:95109\displaystyle \dfrac{5}{10}

Convert the following into a vulgar fraction:0.¯340.\overline { 34 }

Fill in the blank.0.345×1000=0.345 \times 1000=______

Fill in the blank.5.9×1000=5.9 \times 1000=_____

Fill in the blank.10.056×100=10.056 \times 100=______

Fill in the blank.5.76×10=5.76 \times 10=________

What is the value when 442.36 km442.36\ km is divided by 22.

What is 1010 times of 50.3050.30 kg.

Convert 877 \dfrac{87}{7} into mixed fraction.

To multiply a decimal number by 1000, we move the decimal point in the number to the right by three places.

Represent the following mixed infinite decimal periodic fractions as common fractions:(a+a1/2b1/2)(a+b)−1(√a(√a−√b)−1−(√a+√b√b)−1)\displaystyle\, (a + a^{1/2} b^{1/2})(a + b)^{-1}(\sqrt{a}(\sqrt{a} -\sqrt{b})^{-1} - (\frac{\sqrt{a} + \sqrt{b}}{\sqrt{b}})^{-1})

Convert the following into a vulgar fraction:0.ˉ60.\bar { 6 }

2.4÷10=2.4\div 10=

Simplify:3.24÷0.00163.24\div 0.0016

Divide 0.570.57 by 1010.

Find:211.9×1.13211.9 \times 1.13

Divide 54.2554.25 by 1010.

Divide 0.0040.004 by 1010.

Divide:0.450.45 by 99

Divide 0.480.48 by 100100.

Divide:40.3240.32 by 9.69.6

Divide 0.710.71 by 10001000.

Divide 3.83.8 by 10001000.

Divide 74.374.3 by 100100.

Divide 0.70.7 by 100100.

Divide:217.44217.44 by 99

Divide: 319.2319.2 by 2.282.28

Divide 29.529.5 by 10001000.

Divide:31.9231.92 by 228228

Divide:403.2403.2 by 9696

Divide:0.7650.765 by 0.90.9

Divide:15.6815.68 by 2020

Divide:0.08by10 0.08 \quad by \quad 10

Divide:23.4by100 23.4 \quad by \quad 100

Divide:137.2by100 137.2 \quad by \quad 100

Divide:32.56by10 32.56 \quad by \quad 10

Divide:0.062by10 0.062 \quad by \quad 10

Express the following improper fractions as mixed fractions:25/625/6

Express the following improper fractions as mixed fractions:18/5

Express the following mixed fractions as improper fractions:3143 \dfrac{1}{4}

Express the following improper fractions as mixed fractions:22/522/5

Express the following improper fractions as mixed fractions:38/538/5

Multiply each number by (i)10,(ii)100,(iii)1000:(i)10, (ii)100, (iii)1000 : 0.1120.112

Multiply each number by 10,100,1000:10,100,1000 :0.50.5

Multiply:0.5680.568 by 6.46.4

Express the following mixed fractions as improper fractions:1271112\dfrac{ 7}{11}

Multiply each number by (i)10,(ii)100,(iii)1000:(i)10, (ii)100, (iii)1000 :4.84.8

Multiply:16.32 by 28

Divide:324.76324.76 by 10001000

Divide:4.8432 by 0.08

Evaluate :0.125÷25 0.125 \div 25

Multiply each number by (i)10,(ii)100,(iii)1000:(i)10, (ii)100, (iii)1000 :16.2716.27

Evaluate:5.897×2.3 5.897 \times 2.3

Multiply each number by (i)10,(ii)100,(iii)1000:(i)10, (ii)100, (iii)1000 : 234.8234.8

Evaluate :20.64÷16 20.64 \div 16

$23.2\div 100 =x$ . Find $1000x$

Convert the given mixed fractions into improper
$2\dfrac {1}{5}$

Convert the given mixed fractions into improper
$2\dfrac {1}{2}$

Convert the given mixed fractions into improper
$3\dfrac {1}{6}$

Convert the given mixed fractions into improper
$7\dfrac {2}{9}$

Convert the given mixed fractions into improper
$6\dfrac {1}{10}$

Convert the given mixed fractions into improper
$4\dfrac {2}{3}$

Find $2\dfrac{1}{2}%$ of $320$ people.

find : $2.5 \times 0.3$

$18.368\div 14$ .

Divide each of the given numbers by $10,100,1000$ and 10000 $:$
$2.1$
$8.64$
$5.01$
$0.0906$
$0.125$
$111.11$

Solve : $0.5\times 0.05$

Solve
(i) $1.5\times 0.3$

Solve: $1.07\times 0.02$

Solve: $4.3\times 3.4$

Solve: $0.1\times 47.5$

Solve:
$10.05\times 1.05$

Solve : $70.01\times 1.1$

Find:
$0.2\times 6$

Find
$651.2 \div 4$

Convert the following into a vulgar fraction:
$2.\overline { 13 }$

Fill in the blank.
$1.1 \times 100=$ ______

Convert the following into a vulgar fraction:
$0.\bar { 8 }$

Multiply : $0.1\times 51.7$

Simplify: $9\displaystyle \dfrac{5}{10}$

Convert the following into a vulgar fraction:
$0.\overline { 34 }$

Fill in the blank.
$0.345 \times 1000=$ ______

Fill in the blank.
$5.9 \times 1000=$ _____

Fill in the blank.
$10.056 \times 100=$ ______

Fill in the blank.
$5.76 \times 10=$ ________

What is the value when $442.36\ km$ is divided by $2$ .

What is $10$ times of $50.30$ kg.

Convert $\dfrac{87}{7}$ into mixed fraction.

To multiply a decimal number by 1000, we move
the decimal point in the number to the right by three places.

Represent the following mixed infinite decimal periodic fractions as common fractions:
$\displaystyle\, (a + a^{1/2} b^{1/2})(a + b)^{-1}(\sqrt{a}(\sqrt{a} -\sqrt{b})^{-1} - (\frac{\sqrt{a} + \sqrt{b}}{\sqrt{b}})^{-1})$

Convert the following into a vulgar fraction:
$0.\bar { 6 }$

$2.4\div 10=$

Simplify:
$3.24\div 0.0016$

Divide $0.57$ by $10$ .

Find:
$211.9 \times 1.13$

Divide $54.25$ by $10$ .

Divide $0.004$ by $10$ .

Divide:
$0.45$ by $9$

Divide $0.48$ by $100$ .

Divide:
$40.32$ by $9.6$

Divide $0.71$ by $1000$ .

Divide $3.8$ by $1000$ .

Divide $74.3$ by $100$ .

Divide $0.7$ by $100$ .

Divide:
$217.44$ by $9$

Divide: $319.2$ by $2.28$

Divide $29.5$ by $1000$ .

Divide:
$31.92$ by $228$

Divide:
$403.2$ by $96$

Divide:
$0.765$ by $0.9$

Divide:
$15.68$ by $20$

Divide:

$0.08 \quad by \quad 10$

Divide:

$23.4 \quad by \quad 100$

Divide:

$137.2 \quad by \quad 100$

Divide:

$32.56 \quad by \quad 10$

Divide:

$0.062 \quad by \quad 10$

Express the following improper fractions as mixed fractions:
$25/6$

Express the following improper fractions as mixed fractions:
18/5

Express the following mixed fractions as improper fractions:
$3 \dfrac{1}{4}$

Express the following improper fractions as mixed fractions:
$22/5$

Express the following improper fractions as mixed fractions:
$38/5$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$0.112$

Multiply each number by $10,100,1000 :$
$0.5$

Multiply:
$0.568$ by $6.4$

Express the following mixed fractions as improper fractions:
$12\dfrac{ 7}{11}$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$4.8$

Multiply:
16.32 by 28

Divide:
$324.76$ by $1000$

Divide:
4.8432 by 0.08

Evaluate :
$0.125 \div 25$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$16.27$

Evaluate:
$5.897 \times 2.3$

Multiply each number by $(i)10, (ii)100, (iii)1000 :$
$234.8$

Evaluate :
$20.64 \div 16$

Divide:
$27.918$ by $9$