Properties of Rational Numbers

Write the rational number that does not have any reciprocal.

Fill in the blanks:

$\frac{-16}{7}+\_\_\_\_\_=\frac{-16}{7}$

The property involved in the following example is _____ property in multiplication:

$\frac{5}{2}\times \frac{3}{7}=\frac{15}{14}$

Write the numbers whose multiplicative inverses are the numbers themselves.

Complete the following table.

Can you find the reciprocal of $\text{'}0\text{'}$(zero)? Is there any rational number such that when it is multiplied by $\text{'}0\text{'}$ gives $\text{'}1\text{'}$?

$\_\_\_\_\_\times 0=1$ and $0\times \_\_\_\_\_=1$

If a property holds good with respect to addition for rational numbers, whether it holds good for integers? And for whole number? Which one hold good and which doesn't hold good?

If $36$ trousers of equal sizes can be stitched with $64$ meters of cloth. The length of the cloth required for each trouser is $\mathrm{K} \mathrm{meters}$? Find $\mathrm{K}$. (express the answer in improper fraction)

What number should $\frac{-33}{16}$ be divided by to get $-\frac{11}{4}$?

The cost of  $7\frac{2}{3}$ meters of cloth is $₹ 12\frac{3}{4}$. The cost per metre is$₹ K$. Find $K$. (express the answer upto two decimal places)

If $\frac{2}{5}$ of a number exceeds $\frac{1}{7}$ of the same number by $36$. Find the number.

Divide the sum of $-\frac{13}{5}$ and $\frac{12}{7}$ by the product of $-\frac{13}{7}$ and $-\frac{1}{2}$.

Find $\left(x+y\right)÷\left(x-y\right)$ if  $x=\frac{1}{4}$ and $y=\frac{3}{2}$.

Find $\left(x+y\right)÷\left(x-y\right)$ if $x=\frac{5}{2}$ and $y=\frac{-3}{4}$

The area of a rectangular park which is $18\frac{3}{5}\mathrm{m}$ long and $8\frac{2}{3}\mathrm{m}$ broad is $\mathrm{K} {\mathrm{m}}^2$. Find $K$. (express the answer in improper fraction)

Write the reciprocal of negative rational number.

The sum of two rational numbers is $8$. If one of the numbers is $\frac{-5}{6}$ find the other.

What numbers to be added to$\frac{-5}{8}$ so as to get $\frac{-3}{2}$?

Subtract $-7$ from  $\frac{-4}{7}$.

Subtract $\frac{-32}{13}$ from $2$.