Properties of Subtraction of Rational Numbers

Subtract the sum of $\frac{-5}{7}$ and $\frac{-8}{3}$ from the sum of $\frac{5}{2}$ and $\frac{-11}{12}$. Write the answer in mixed fraction.

What rational number should be subtracted from $-4\frac{3}{5}$ to get $-3\frac{1}{2}$? Express the result in mixed fraction.

What rational number should be added to $\frac{-5}{11}$ to get $\frac{-7}{8}$?

Sum of two rational numbers is $\frac{3}{5}$. If one of them is $\frac{-2}{7}$, find the other.

Subtract: $-3\frac{1}{5}$ from $-4\frac{7}{9}$. Express the result in mixed fraction.

Subtract: $\frac{-4}{9}$ from $3\frac{5}{8}$. Express the result in mixed fraction.

Subtract: $2\frac{3}{5}$ from $\frac{-3}{7}$. Express the result in mixed rational number.

$0$ is the identity element for subtraction of rational numbers.

Associative property does not hold for subtraction of rational numbers.

Commutative property holds for subtraction of rational numbers.

$0$ is the additive inverse of its own.

$\frac{-5}{7}$ is the additive inverse of $\frac{5}{7}$.

$\frac{2}{3}-\frac{4}{5}$ is not a rational number.

If $x=\frac{4}{9}, y=\frac{-7}{12}$ and $z=\frac{-2}{3}$, then verify that $x-(y-z)\ne (x-y)-z$.

If $x=\frac{-4}{7}$ and $y=\frac{2}{5}$, then verify that $x-y\ne y-x$.