MCQ Questions for Class 8 Maths Rational Numbers Quiz 9

Which of the following statements is always true ?

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$\dfrac{x - y}{2}$ is a rational number between x and y
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$\dfrac{x + y}{2}$ is a rational number between x and y
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$\dfrac{x \times y}{2}$ is a rational number between x and y
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$\dfrac{x \div y}{2}$ is a rational number between x and y

$x + 0 = 0 + x = x,$ which is rational number, then

$0$ is called

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Identity for addition of rational numbers.
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Additive inverse of x.
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Multiplicative inverse of x.
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Reciprocal of x.

Explanation

Sum of any rational number and zero is always equal to that rational number.

Hence,

$0$ is called the identity for addition of rational numbers.

$\therefore$ Option A is the correct answer.

Which of the following is not true ?

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Rational numbers are closed under addition
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Rational numbers are closed under subtraction
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Rational numbers are closed under multiplication
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Rational numbers are closed under division

Explanation

Rational numbers are not closed under division.

Here,

$\dfrac{1}{0}$ is not defined but 1 and 0 are rational numbers.

$\therefore$ Option D is the correct answer.

The multiplicative inverse of

$-1 \dfrac{1}{7}$ is

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$\dfrac{8}{7}$
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$\dfrac{-8}{7}$
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$\dfrac{7}{8}$
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$\dfrac{7}{-8}$

Explanation

Given number is

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

$-1\dfrac{1}{7}=-\dfrac{7+1}{7}$

$=-\dfrac{8}{7}$

Since we know that the multiplicative inverse of any non-zero number

$a$ is

$\dfrac{1}{a}$

$\therefore$ the multiplicative inverse of

$-\dfrac{8}{7}$ is

$\dfrac{1}{-\dfrac{8}{7}}$

$=-\dfrac{7}{8}$

State whether the statements are true (T) or false (F).
The multiplicative inverse of

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

$\dfrac{5}{3}.$

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True
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False

State whether the statement is true (T) or false (F).

$\dfrac{9}{6}$ lies between

$1$ and

$2$ .

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True
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False

Explanation

1 and 2 The mean of

$1$ and

$2$ is

$\cfrac{1+2}{2}=\cfrac{3}{2}$ .

State whether the statements are true (T) or false (F).
If

$a \neq 0$ the multiplicative inverse of

$\dfrac{a}{b}$ is

$\dfrac{b}{a}.$

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True
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False

State whether the statement is true (T) or false (F).

$\dfrac{5}{10}$ lies between

$\dfrac{1}{2}$ and

$1.$

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True
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False

Explanation

Required rational number

$\displaystyle =\frac{1}{2}\left ( \frac{1}{2}+\frac{1}{1} \right )=\frac{1}{2}\left ( \frac{2+1}{2} \right )=\frac{3}{4}$

1886583_1791871_ans_7d0f0a8975584a7a8046b6933bc88f8f.pdf

State whether the statement is true (T) or false (F).

$\dfrac{5}{6}$ lies between

$\dfrac{2}{3}$ and

$1$ .

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True
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False

Explanation

Required rational number

$\displaystyle =\frac{1}{2}\left ( \frac{2}{3}+\frac{1}{1} \right )=\frac{1}{2}\left ( \frac{2+3}{3} \right )=\frac{5}{6}$

State whether the statements are true (T) or false (F).
Between any two rational numbers there are exactly ten rational numbers.

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True
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False

State whether the statements are true (T) or false (F).
For all rational numbers x and y,

$x \times y = y \times x.$

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True
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False

State whether the statement is true (T) or false (F).

$\dfrac{-7}{2}$ lies between

$-3$ and

$-4.$

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True
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False

Explanation

-3 and -4 The mean of

$-3$ and

$-4$ is

$\cfrac{-3-4}{2}=-\cfrac{7}{2}$ .

State whether the statement is true (T) or false (F).
The rational number

$\dfrac{57}{23}$ lies to the left of zero on the number line.

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True
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False

Explanation

The given rational number

$\dfrac{57}{23}$ is a positive rational number that lies on the right side of zero in the number line.

Hence the given statement is false.

State whether the statements are true (T) or false (F).
All positive rational numbers lie between

$0$ and

$1000.$

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True
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False

Explanation

There are infinite positive rational numbers beyond

$1000$ and beween

$0$ and

$1000$

Rational numbers are closed under addition and multiplication but not under subtraction.

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True
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False

State whether the statement are true (T) or false (F).
The rational numbers

$\dfrac{1}{2}$ and

$-1$ are on the opposite sides of zero on the number line.

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True
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False

Explanation

Since

$\dfrac {1}{2}$ is a positive number, all the positive numbers are

$> 0$ and so all the positive numbers lie to the right of

$0$ on the number line.

Since -1 is a negative number, all the negative numbers are

$< 0$ and so all the negative numbers lie to the left of

$0$ on the number line.

$\therefore$ The above statement is true both the rational numbers lie on opposite sides.

The multiplication inverse of

$10^{-100}$ is

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$10$
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$100$
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$10^{100}$
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$10^{-100}$

Explanation

For multiplicative inverse, let

$a$ be the multiplicative of

$10^{-100}$
So,

$a\times b=1$
Therefore

$a\times\ 10^{-100}=1$

$\Rightarrow \ a=\dfrac {1}{10^{-100}} =\dfrac {1}{\dfrac {1}{10^{100}}}=10^{100}$

The multiplicative inverse of

$(-4)^{-2}$ is

$(4)^{2}$ .

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True
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False

Explanation

True

multiplicative inverse of

$4^{-2}$

$=\dfrac{1}{(-4)^{-2}}=\dfrac{1}{\dfrac{1}{(-4)^{2}}}=\dfrac{1}{\dfrac{1}{4^{2}}}=4^2=RHS$

The multiplicative inverse of

$\left(\dfrac{3}{2}\right)^{2}$ is not equal to

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

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True
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False

Explanation

True.

$\Rightarrow \left(\dfrac{3}{2}\right)^{2}\times \left(\dfrac{2}{3}\right)^{-2}=\left(\dfrac{3}{2}\right)^{2}\times\left(\dfrac{3}{2}\right)^{2}\neq 1$

The multiplicative inverse of

$\left(-\dfrac {5}{9} \right)^{99}$ is

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$\left(-\dfrac {5}{9} \right)$
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$\left(-\dfrac {5}{9} \right)^{99}$
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$\left(-\dfrac {9}{-5} \right)^{99}$
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$\left(-\dfrac {9}{5} \right)^{99}$

Explanation

For multiplicative inverse

$a$ is called multiplicative inverse

$b$ , if

$a\times b=1$
Put

$\Rightarrow a\times \left(\dfrac {-5}{9}\right)^{99}=1\quad \left[As, a^{-m}=\dfrac {1}{a^m}\right]$

$\Rightarrow a=\dfrac {1}{\left(\dfrac {-5}{9}\right)^{99}}\Rightarrow a=\left(-\dfrac {5}{9}\right)^{-99}=\left(-\dfrac {9}{5}\right)^{99}$

State whether the following statement is true of false? Justify your answer.

$\dfrac {\sqrt {12}}{\sqrt {3}}$ is not a rational number as

$\sqrt {12}$ and

$\sqrt {3}$ are not integers.

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True
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False

Explanation

Rational number is a number which can be written in form

$\cfrac pq$ , where

$p,q$ are both integers.

The given statement is false.

Because,

$\dfrac{\sqrt{12}}{\sqrt3}=\sqrt {\dfrac {12}{3}} = \sqrt {4} = 2$ , which can be wriiten as

$\cfrac21$ which is a rational number.

So,

$\dfrac{\sqrt{12}}{\sqrt3}$ can be written as

$\cfrac{p}q$ form with

$p,q$ both integers, so it is a raional number.

The product of rational number

$\dfrac{-2}{5}$ and its multiplicative inverse is

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1
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0
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$\dfrac{4}{25}$
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$\dfrac{2}{5}$

Explanation

Product of
rational number $\dfrac{-2}{5}$ and its

multiplicative
inverse is $\dfrac{-2}{5} \times \dfrac{-5}{2}=1$

The Multiplicative inverse of $\dfrac{-4}{9}$ is

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$\dfrac{4}{9}$
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$\dfrac{-9}{4}$
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$\dfrac{9}{4}$
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none of these

Explanation

Multipiicative
inverse of $\dfrac{-4}{9}$

$=\dfrac{9}{-4}=\dfrac{9(-1)}{-4(-1)}=\dfrac{-9}{4}$

State whether the statements are true (T) or false (F).

The rational number

$\dfrac{-13}{-5}$ lies to the right of zero in the number line.

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True
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False

Explanation

On a number line,

$\because \dfrac{-13}{-5}=\dfrac{13}{5}$
which lies to the right side of zero.

The Additive inverse of

$\dfrac{-7}{12}$
is

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$\dfrac{12}{-7}$
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$\dfrac{-7}{12}$
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$\dfrac{-5}{12}$
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$\dfrac{7}{12}$

State true or false.

There exists at least one integer between two different rational numbers

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True
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False

The product of rational number

$\dfrac{-2}{3}$ and its additive inverse is

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1
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$\dfrac{2}{3}$
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$\dfrac{4}{9}$
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$\dfrac{-4}{9}$

Explanation

Additive
inverse of $\dfrac{-2}{3}$ is $\dfrac{2}{3}$

$\dfrac{-2}{3}$
is $\dfrac{2}{3}=\dfrac{-4}{9}$

State whether the statement are true (T) or false (F).

The rational numbers

$\dfrac{-17}{6}$ and

$\dfrac{8}{-15}$ lie on opposite sides of zero on the number line.

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True
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False

Explanation

On a number line,

$\dfrac{-17}{6}$ and $\dfrac{8}{-15}=\dfrac{-8}{15}$ both are negative so lie on the same side of zero.

On opposite sides is false.

State true or false.

For each rational number, one can find the next rational number

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True
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False

Find,

$\dfrac { -2 }{ 3 } \times \dfrac { 3 }{ 5 } +\dfrac { 5 }{ 2 } -\dfrac { 3 }{ 5 } \times \dfrac { 1 }{ 6 }$

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

CBSE Questions for Class 8 Maths Rational Numbers Quiz 9 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

CBSE Questions for Class 8 Maths Rational Numbers Quiz 9 - MCQExams.com

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Practice Class 8 Maths Quiz Questions and Answers

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