1 Marks Question

Question 11 Mark

The product of two rational numbers is always a ___________.

Answer

The product of two rational numbers is always a rational number.

Question 21 Mark

'Rational numbers are commutative under addition but not commutative under subtraction.' Justify the statement with an example.

Answer

Let $\frac{1}{2}$ and $\frac{1}{4}$ be two rational numbers.
Now, $\frac{1}{2}+\frac{1}{4}=\frac{1}{4}+\frac{1}{2}=\frac{3}{4}$ which implies that rational numbers are commutative under addition.
Now, $\quad \frac{1}{2}-\frac{1}{4}=\frac{2-1}{4}=\frac{1}{4}$
But $\quad \frac{1}{4}-\frac{1}{2}=\frac{1-2}{4}=-\frac{1}{4}$
Thus, $\quad \frac{1}{2}-\frac{1}{4} \neq \frac{1}{4}-\frac{1}{2}$
So, rational numbers are not commutative under subtraction.

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Question 31 Mark

Find the value of $0+\frac{5}{4}$.

Answer

$ 0+\frac{5}{4}=0 \times \frac{4}{5}=0\quad$ [ $\because 0 \times x=0$, for all $x$ being a rational number]
Hence, 0 is the required answer.

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Question 41 Mark

Write the multiplicative and additive identity for rational numbers?

Answer

1 is the multiplicative identity of a rational number
$\because$ For all rational numbers let $x, x \times 1=x=1 \times x$ and 0 is the additive identity for a rational numbers.
$\because$ For all rational numbers let $x, x+0=x=0+x$

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Question 51 Mark

Give the reason why multiplicative inverse of 0 does not exist?

Answer

The multiplicative inverse for any rational number $x$ is $\frac{1}{x}$. Here, multiplicative inverse of 0 is $\frac{1}{0}$.
But $\frac{1}{0}$ is not defined.
So, multiplicative inverse of 0 is not defined.

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Question 61 Mark

Find the multiplicative inverse of $\frac{-11}{13}$.

Answer

The multiplicative inverse of $\frac{-11}{13}$ is $\frac{-13}{11}$.

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Question 71 Mark

Write the multiplicative inverse of 312 .

Answer

The multiplicative inverse of 312 is $\frac{1}{312}$.

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Question 81 Mark

Simplify $\frac{4}{5}+\frac{9}{2}+\left(\frac{-4}{5}\right)$.

Answer

$\frac{4}{5}+\frac{9}{2}+\left(\frac{-4}{5}\right)=\frac{4}{5}+\left(\frac{-4}{5}\right)+\frac{9}{2}\quad$ [by commutative property of addition]
$=0+\frac{9}{2}$
$[\because x+(-x)=0$, for all $x$ being a rational number$]$
$=\frac{9}{2}\quad$ [by additive identity]

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Question 91 Mark

Give an example to show that subtraction is not associative for rational numbers.

Answer

For rational numbers $\frac{5}{4}, \frac{3}{4}$ and $\frac{1}{4}$, we see that
$\frac{5}{4}-\left(\frac{3}{4}-\frac{1}{4}\right)=\frac{5}{4}-\frac{2}{4}=\frac{3}{4}$ and $\left(\frac{5}{4}-\frac{3}{4}\right)-\frac{1}{4}=\frac{2}{4}-\frac{1}{4}=\frac{1}{4}$
Thus, $\quad \frac{5}{4}-\left(\frac{3}{4}-\frac{1}{4}\right) \neq\left(\frac{5}{4}-\frac{3}{4}\right)-\frac{1}{4}$
So, we can say that subtraction is not associative for rational numbers.

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Question 101 Mark

What is the sum of additive identity of whole numbers and rational numbers?

Answer

The additive identity of whole numbers is 0 and the additive identity of rational numbers is also 0.
Thus, the sum of additive identity of whole numbers and rational numbers is 0.

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Question 111 Mark

Name the property under addition used in the following expression
$5+[(-5)+7]-[5+(-5)]+7$

Answer

Associative property.

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Question 121 Mark

For two integers p and q, $\frac{\text{p}}{\text{q}}$ is a rational number, then write condition for q, $\frac{\text{p}}{\text{q}}$ to be a rational number.

Answer

$\text{q}$ will be a non-zero integer i.e. $\text{q} \neq 0$ is the condition for being $\frac{\text{p}}{\text{q}}$ a rational number.

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Question 131 Mark

For which operations, closure property for integers does not hold?

Answer

Integers are not closed under division.
$\because 3$ and 4 are integers but $3+4=\frac{3}{4}$ is not an integers.

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