MCQ Questions for Class 8 Maths Rational Numbers Quiz 4

There exists ....... number of rational numbers between

\frac{2}{5}

$\dfrac {2}{5}$ and

$\dfrac {4}{5}.$

0%
$0$
0%
$1$
0%
$5$
0%
infinite

Explanation

There exists infinite number of rational numbers between any two rational numbers. i.e. in this case between

$\dfrac {2}{5}$ and

$\dfrac {4}{5}$ .

Which of the following rational numbers lies between

$0$ and

$-1$ ?

0%
$0$
0%
$-1$
0%
$\dfrac {-1}{4}$
0%
$\dfrac {1}{4}$

Explanation

Clearly,

$0$ and

$-1$ cannot lie between

$0$ and

$-1$ .

Also,

$0=\dfrac{0}{4}$ and

$-1=\dfrac{-4}{4}$

We can clearly see that

$\dfrac {-1}{4}$ lies between

$0$ and

$-1$ .

Which of the following rational numbers lies between

$\dfrac {3}{2}$ and

$4$ ?

0%
$\dfrac {1}{2}$
0%
$3$
0%
$\dfrac {8}{2}$
0%
$\dfrac {9}{2}$

Explanation

We have to find a rational number between

$\dfrac {3}{2}$ and

$4$ . The L.C.M. of the denominators of both numbers is

$2$ .

$\therefore \dfrac {3}{2} = \dfrac {3}{2}$ and

$4\times \dfrac {2}{2} = \dfrac {8}{2}$ .

$\therefore$ From the above given options, only

$\dfrac {6}{2}$
i.e.

$=3$ lies between

$\dfrac {3}{2}$ and

$4$ .

There are ....... rational number which when multiplied by

$0$ , gives product as

$1.$

0%
$0$
0%
$2$
0%
$4$
0%
infinite

Explanation

There are no rational numbers which when multiplied by

$0$ gives product as

$1$ because the product of

$0$ and any number is always

$0.$

The number

$\dfrac {13}{15}$ is correctly represented on number line

Explanation

To represent

$\dfrac{13}{15}$ on a number line, divide the space from

$0$ to

$1$ in

$15$ equal parts

The thirteenth part will represent a rational number

$\dfrac{13}{15}$ .

As we can see,

$\dfrac{11}{15}$ come after

$\dfrac{10}{15}$ , then

$\dfrac{12}{15}$ and then

$\dfrac{13}{15}$ .

Hence, the above line is the correct representation of

$\dfrac{13}{15}$

$1$ is the multiplicative identity for ........

0%
whole numbers
0%
integers
0%
rational numbers
0%
all of the above

Explanation

${\textbf{Step - 1: Defining Multiplicative identity}}$

${\text{Multiplicative identity is a number which when multiplied by another number gives}}$

${\text{the another number again as result}}{\text{.}}$

${\text{For example, if x }} \times {\text{ y = x then y is multiplicative identity of x}}$

${\textbf{Step - 2: Identifying multiplicative identity}}$

${\text{We know that, any number multiplied by 1 gives the number itself}}{\text{.}}$

$\Rightarrow {\text{ 1 is the multiplicative identity for any real number}}$

${\textbf{Hence correct option is (D) all of the above}}$

$\dfrac {3x}{y}\times 1 = ..........$ is stated by multiplicative identity property.

0%
$3x$
0%
$y$
0%
$\dfrac {3x}{y}$
0%
$1$

Explanation

The multiplicative identity property states that when we multiply a number by

$1,$ then the product is the number itself.

So,

$\dfrac {3x}{y} \times 1 = \dfrac {3x}{y}$ .

The sum of two rational numbers is

$-5$ . If one of the numbers is

$\dfrac {-3}{5}$ , find the other number

0%
$-4\dfrac {2}{5}$
0%
$4\dfrac {8}{5}$
0%
$\dfrac {-6}{5}$
0%
$4\dfrac {6}{5}$

Explanation

$Let\quad other\quad will\quad be\quad x\\ then\quad x+\dfrac { -3 }{ 5 } =-5\\ x=-5+\dfrac { 3 }{ 5 } =\dfrac { -22 }{ 5 } =-4\dfrac { 2 }{ 5 }$

So correct answer will be option A

Which pair of numbers are rationalising factors to one another

0%
$2\sqrt{3}$ and $\sqrt{3}$
0%
${3}^{1/3}-{3}^{-1/3}$ and ${3}^{2/3}+1+{3}^{-2/3}$
0%
${x}^{1/x}-{x}^{-1/n}$ and $\left( { x }^{ \cfrac { n-1 }{ n } }-{ x }^{ \cfrac { n-2 }{ n } }+........{ x }^{ -\left( \cfrac { n-1 }{ n } \right) } \right)$
0%
$\sqrt [ 3 ]{ 5 } +\cfrac{1}{\sqrt [ 3 ]{ 5 } }$ and $\sqrt [ 3 ]{ {5}^{2} } +1-\cfrac{1}{\sqrt [ 3 ]{ {5}^{2} } }$

Which are three rational numbers between

$-2$ and

$-1$ ?

0%
$\dfrac { -1 }{ 2 } ,\dfrac { -1 }{ 3 } ,\dfrac { -1 }{ 5 }$
0%
$\dfrac { -3 }{ 2 } ,\dfrac { -7 }{ 4 } ,\dfrac { -5 }{ 4 }$
0%
$\dfrac { -12 }{ 5 } ,\dfrac { -22 }{ 5 } ,\dfrac { 12 }{ 5 }$
0%
$\dfrac { 3 }{ 2 } ,\dfrac { 7 }{ 4 } ,\dfrac { 5 }{ 4 }$

Explanation

Mean

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

$\frac{(-2)+\dfrac{-3}{2}}{2}$ =

$\dfrac {-7}{4}$

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

$\dfrac {-5}{4}$

Mean of numbers lies between the two numbers.

So, answer is option

$B.$

How many rational numbers exist between any two distinct rational numbers?

0%
$2$
0%
$3$
0%
$10$
0%
Infinite

Explanation

Rational numbers are those numbers which can be expressed in the form of

$\dfrac{p}{q}$ where

$p$ and

$q$ are integers. Hence between two rational numbers there can be infinite rational numbers

So correct answer is option D

The multiplicative inverse of

$-7$ is _____

0%
$7$
0%
$\dfrac {1}{7}$
0%
$-7$
0%
$\dfrac {-1}{7}$

Explanation

Multiplicative inverse means the same thing as reciprocal.

And the product of a number and its multiplicative inverse is 1.

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

Hence multiplicative inverse of -7 is

$\frac{-1}{7}$

Out of the following numbers, which can be represented on a number line?

$0, \dfrac56, 1, \dfrac24$

0%
$0$
0%
$\dfrac56$
0%
$1$
0%
All of these

Explanation

Given numbers are

$0,\dfrac{5}{6} ,1,\dfrac{2}{4}$

$0,1$ are integers and

$\dfrac{5}{6}, \dfrac{2}{4}$ are rational numbers.

As, rationals and integers are subset of reals.

Thus, all the above numbers are real.

Hence, we can represent all above numbers on a number line.

Say true or false
The distributive property can work if there is multiplication or division inside the parentheses

0%
True
0%
False

Explanation

If there is multiplication or division inside the parentheses, distribution property cannot work

For example

$a(b\times c)\ne (ab\times ac)$

While representing

$\dfrac23$ on a number line, between which two integers does the point lie?

0%
$1$ and $2$
0%
$0$ and $1$
0%
$2$ and $3$
0%
$1$ and $3$

Explanation

$\dfrac{2}{3}=0.67$

It is clear that 0.67 lies between 0 and 1

So correct answer will be option B

The additive inverse of

$\dfrac {-3}{5}$ is ________

0%
$\dfrac {-3}{5}$
0%
$\dfrac {5}{3}$
0%
$\dfrac {3}{5}$
0%
$\dfrac {-5}{3}$

Explanation

We know that for any real number

$a$ , the additive number inverse is given by

$-a$ such that

$a+( -a) =0.$

As,

$\dfrac{-3}{5}+\dfrac{3}{5}=0$

Then additive inverse of

$\dfrac{-3}{5}$ is

$\dfrac{3}{5}$ .

Hence, option

$C$ is correct.

The given property

$a+b=b+a$ is known as:

0%
Commutative property
0%
Distributive Property
0%
Associative Property
0%
Closure property

Explanation

Commutative property says that the numbers can be added in any order, and you will still get the same answer.

$a+b = b+a$ is a clear example of commutative property

The rational number between the pair of number

$\dfrac{1}{2}$ and

$\sqrt 1$ is:

0%
$\dfrac{9}{4}$
0%
$\dfrac{3}{4}$
0%
$\dfrac{5}{4}$
0%
$\dfrac{7}{4}$

Explanation

The rational number between

$\dfrac12$ and

$\sqrt1$ :

Since,

$\sqrt1=1$

So. the rational number between

$\dfrac12$ and

$1=\dfrac12\times \left(\dfrac12+1\right)$

$=\dfrac12 \times \dfrac32$

$=\cfrac34$

So,

$B$ is the correct option.

Find the additive inverse of the following rational numbers:
(i)

$-\dfrac{2}{3}$

0%
$\dfrac{2}{3}$
0%
$\dfrac{4}{3}$
0%
$\dfrac{5}{3}$
0%
$\dfrac{7}{3}$

Explanation

Additive inverse of

$\dfrac{2}{-3}= -\left ( \dfrac{2}{-3} \right )= \dfrac{2}{3}$

Where does a rational number

$\displaystyle\frac{-2}{3}$ lies on the number line?

0%
Lies to the left side of $0$ on the number line
0%
Lies to the right side of $0$ on the number line
0%
It is not possible to represent on the number line
0%
Cannot be determined on which side the number lies

Explanation

$\dfrac{-2}{3}=-0.667$

$-0.667<0$

Hence it will lie to the left side of

$0$ on the number line.

Name the property of rational numbers illustrated by the given statement.

$\displaystyle\frac{-3}{2}\times \frac{5}{4}+\frac{-3}{2}\times \frac{-7}{6}=\frac{-3}{2}\times \left(\displaystyle\frac{5}{4}+\frac{-7}{6}\right)$ .

0%
Associativity
0%
Distributivity
0%
Commutativity
0%
None of these

Explanation

Associative property

$(a+b)+c =a+(b+c)$

$(a \times b) \times c = a \times (b \times c)$

Distributive property

$a \times (b+c)=a \times b +a \times c$

Commutative property

$a+b=b+a$

$a \times b =b \times a$

so the given equation follows:

$a\times (b+c)=a\times b +a \times c$

$a=-\dfrac{3}{2}$

$b=\dfrac{5}{4}$

$c=-\dfrac{7}{6}$

The additive identity of rational number is ______.

0%
$0$
0%
$1$
0%
$-1$
0%
$2$

Explanation

The set of rational numbers forms a group with respect to the addition of rational number in which the additive identity is

$0$ .

$a+0=0+a=a$ for all rational

$a$ .

So the additive identity is

$0$ .

Hence option (A) is correct

Name the property of rational numbers illustrated by the given statement.

$\displaystyle\frac{7}{4}\times \left(\displaystyle\frac{-8}{3}+\frac{-13}{12}\right)=\frac{7}{4}\times \frac{-8}{3}+\frac{7}{4}\times \frac{-13}{12}$ .

0%
Commutativity
0%
Associativity of multiplication
0%
Distributivity of multiplication over addition
0%
Distributivity of addition over multiplication

Explanation

Distributivity of multiplication over addition

$a(b+c)=a\times b +b \times c$

(X + Y) + Z = X + (Y + Z) means

0%
Operator OR is distributive
0%
Operator OR is associative
0%
Operator AND is associative
0%
None of the above

A: Rational numbers are always closed under division.

R: Division by zero is not defined.

0%
A is true and R is the correct explanation of A
0%
A is false and R is false
0%
A is true and R is false
0%
A is false and R is true

Explanation

Statement A: False

$0$ is a rational number because it can be written as

$\dfrac{0}{1}$ . When we divide any rational number by

$0$ which is also a rational number, then the resultant number is of the form

$\dfrac{m}{0}$ where

$m$ is any rational number.

So, the resultant is not defined and hence rational numbers are not closed under division

Statement R: True

Any Real number divided by

$0$ is not defined.

In the number line, the rational numbers represented by

$'A'$ is

0%
$\dfrac {2}{8}$
0%
$\dfrac {3}{8}$
0%
$\dfrac {1}{8}$
0%
$\dfrac {2}{3}$

Explanation

Consider the given figure,

Distance between

$0$ to

$3$ is divided in equal

$8$ part

So, each part is equal to

$=\dfrac{3}{8}$

Hence, point

$A$ is at

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

Hence, this is the answer.

1056990_1086170_ans_e14d215cd3204e2e84b0bfc60eb25e2a.png

Between two rational numbers, there exists-

0%
No rational number
0%
Only one rational number
0%
Infinite numbers of rational numbers
0%
No irrational number

Explanation

Between two rational numbers there are infinitely many rational number for example between

$4$ and

$5$ there are

$4.1, 4.2, .4.22, 4.223 .....$
Hence,

$(C)$ is the correct answer.

State whether the following statement is true/ false?

$0$ is the identity element for subtraction of rational numbers.

0%
True
0%
False

Explanation

Let us take a rational number as

$7/8$ ,

now

$7/8 - 0 = 7/8$

But

$0 - 7/8 = -7/8$

Since,

$7/8\neq -7/8$
Therefore, the given statement is false.

State true or false

The multiplicative inverse of

$\dfrac {-1}4$ is

$\dfrac{-1}{8}$ .

0%
True
0%
False

Express the following decimal in the form

$\dfrac{p}{q}$ :

$9.90$

0%
$\dfrac{99}{10}$
0%
$\dfrac{999}{100}$
0%
$\dfrac{99}{1000}$
0%
None of the above

Explanation

Given,

$9.90$

multiply and divide by

$1000$

$=9.90 \times \dfrac{100}{100}$

$=\dfrac{990}{100}$

$=\dfrac{99}{10}$

CBSE Questions for Class 8 Maths Rational Numbers Quiz 4 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Rational Numbers Quiz 4 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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