Properties of Rational Numbers

Verify and name the property of the following:
$\frac{2}{7}\times \left(\frac{3}{4}-\frac{7}{8}\right)=\frac{2}{7}\times \frac{3}{4}-\frac{2}{7}\times \frac{7}{8}$

Use distributive property to solve the following:
$\frac{3}{5}\times \frac{-7}{8}+\frac{9}{15}\times \frac{7}{8}$

Find the missing number using the properties of the rational number in the following:
$\frac{7}{9}\times \left(\frac{4}{13}-\frac{1}{2}\right)=\frac{7}{9}\times \frac{4}{13}-$ _____ $\times \frac{7}{9}$.

Find the missing number using the properties of the rational number in the following:
$-\frac{4}{7}\times 2\frac{3}{4}=2\frac{3}{4}\times$ _____.

Verify and name the following property:

$\left(\frac{4}{7}+\frac{2}{3}\right)+\frac{3}{5}=\frac{4}{7}+\left(\frac{2}{3}+\frac{3}{5}\right)$

Write the additive and multiplicative inverse of $\frac{3}{7}$.

Find the product of the multiplicative inverse of $\frac{-9}{11}$ and $\frac{22}{3}$

Verify the property $a\times 0=0=0\times a$ for the given rational number.

$a=\frac{-8}{13}$

Verify the property $a\times 0=0=0\times a$ for the given rational number.

$a=\frac{-4}{7}$

Verify the property $a\times \left(b\times c\right)=\left(a\times b\right)\times c$ for the given rational number.

$a=\frac{-3}{5}; b=\frac{3}{7}; c=\frac{-5}{6}$

Verify the property $a\times \left(b\times c\right)=\left(a\times b\right)\times c$ for the given rational number.

$a=3\frac{1}{4}; b=\frac{-2}{13}; c=\frac{1}{2}$

Verify the property $a\times \left(b-c\right)=a\times b-a\times c$ for the given rational number.

$a=\frac{5}{15}; b=\frac{-8}{15}; c=\frac{4}{5}$

Verify the property $a\times \left(b-c\right)=a\times b-a\times c$ for the given rational number.

$a=\frac{-3}{5}; b=\frac{5}{9}; c=\frac{-10}{3}$

Check that $a÷b\ne b÷a$ for the given numbers.

$a=\frac{5}{8}, b=\frac{-5}{16}$

Check that $a÷b\ne b÷a$ for the given numbers.

$a=\frac{-5}{4}, b=\frac{-3}{4}$

Verify the commutative property of multiplication for the given pairs of rational number.

$\frac{-4}{5}$ and $\frac{10}{11}$

Verify the commutative property of multiplication for the given pairs of rational number.

$\frac{2}{11}$ and $\frac{3}{5}$

Verify the commutative property of multiplication for the given pairs of rational number.

$7$ and $\frac{-6}{7}$

Verify the commutative property of multiplication for the given pairs of rational number.

$-\frac{12}{13}$ and $-\frac{2}{3}$

Add $\frac{4}{7} \& \frac{-3}{5}$.