Properties of Rational Numbers

Using Appropriate properties find:

$\frac{2}{3}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

Verify :- $\frac{15}{4}\times \left(\frac{3}{7}+\frac{-12}{5}\right) = \left(\frac{-15}{4}\times \frac{3}{7}\right)+\left(\frac{-15}{4}\times \frac{-12}{5}\right)$.

Solve this by using distributive property $\frac{9}{13}$ multiplied by $3\frac{1}{5}$ then subtracted from $2\frac{1}{3}$.

Write the additive inverse of the following:

$\frac{4}{8}$

Verify that $a+b=b+a$, by taking $a=\frac{3}{4}, b=\frac{-2}{5}$

The multiplicative inverse of $\left(x+1\right)+\frac{1}{\left(x-1\right)}$ is 

The multiplicative inverse of $(x+1 )+ \frac{1}{(x-1)}$

$\left(a-\frac{1}{2}\right)\left(a-\frac{3}{2}\right)=?$

Find: $3\frac{7}{8}\times 7\frac{1}{2}-3\frac{7}{8}\times 2\frac{1}{2}$.

Multiplicative inverse of $-8$.

Simplify:

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

Using distributive law, simplify and express in form of improper fraction.

$5\frac{3}{4}\times \frac{3}{5}+5\frac{3}{4}\times \frac{2}{15}$

Simplify and answer in $\frac{p}{q}$ form: $\frac{3}{13}\times \frac{4}{5}-\frac{7}{5}-\frac{4}{5}\times \frac{5}{13}$

Solve using a suitable property. Also, name the property used.

$\frac{1}{3}\times \left(3+\frac{11}{13}\right)$.

Solve using a suitable property. Also, name the property used.

$\frac{2}{9}+\left(\frac{-1}{7}\right)+\frac{4}{9}+\left(\frac{-2}{7}\right)$.

Subtract the additive inverse of $\frac{7}{8}$ from the multiplicative inverse of $\frac{-5}{7}\times \frac{14}{3}$.

Name the property used to solve the following:

$\frac{9}{10}\times 1=\frac{9}{10}$

$x$ and $y$ are two rational numbers. Then which of the following statements are true about $x$ and $y$.

$x+y$ is a rational number

$x-y$ is a rational number

$xy$ is a rational number

$\frac{x}{y}$ is a rational number

Which of the following statement is false?

$\frac{c}{d}$  is called the reciprocal or multiplicative inverse of another non-zero rational number $\frac{a}{b}$, if $\frac{a}{b}\times \frac{c}{d}=$