Exercise

The product of a negative rational number with its multiplicative inverse is $-1$.

Do you agree? Give examples to support your answer.

Which property of multiplication is not involved in the following:

$32\times \frac{1}{4}=\left(8\times 4\right)\times \frac{1}{4}=8\times \left(4\times \frac{1}{4}\right)=8\times 1=8$

If $\frac{1}{3}$ of a number exceeds its $\frac{2}{7}$ by $1$, find the number.

Radha and Vijay, thought of a number each. When they multiplied their numbers, the answer they got was $1$. Which of these could be the pair(s) of numbers they thought?

$\frac{31}{41}$, when multiplied by $\text{'}x\text{'}$ gives the product as $1$. Which fraction does $x$ represent?

In the party , all the children were given candy bars . All the children got three candy bars each except the child sitting in the end . Sita got only $2$ candy bars . If only each child had been given two candy bars , there would have been eight candy bars remaining . How many candy bars were there altogether to begin with.

Rohan was practicing operations on rational numbers, but he is doubtful if all operations done using rational number will result in a rational numbers. He tried some examples but wanted to satisify himself that the operations on rational numbers are indeed closed, except for division by zero.

Prove that rational numbers are closed under addition.

Vinod is solving the sum, $\left(\frac{-2}{3}+\frac{3}{2}\right)\left(\frac{-2}{3}-\frac{3}{2}\right)$, his brother told him that ${\left(\frac{2}{3}\right)}^2-{\left(\frac{3}{2}\right)}^2$  gives the same answer as the sum Vinod is trying to solve.

Use distributive property of rational numbers to show that both expressions gives the same answer.