Question

Verify Closure property for subtraction of $\frac{-4}{5}$ and $\frac{1}{2}$.

Answer 1

Here the two rational numbers are $\frac{-4}{5}$and$\frac{1}{2}$
Let's verify they are closed under subtraction or not.
= $\frac{-4}{5}$ - $\frac{1}{2}$=$\frac{\left(-4\times 2\right)-\left(1\times 5\right)}{2\times 5}=\frac{-8-5}{10}$
= $\frac{-13}{10}$
Here $\frac{-13}{10}$ is in the form $\frac{p}{q}$, where p and q are integers and q not equal to 0

Now, lets reverse the order and check
$\frac{1}{2}$ - $\frac{-4}{5}$ = $\frac{\left(1\times 5\right)-\left(-4\times 2\right)}{2\times 5}=\frac{5+8}{10}$
= $\frac{13}{10}$
Here $\frac{13}{10}$ is in the form p/q, where p and q are integers and q not equal to 0
Hence the two rational numbers $\frac{-4}{5}$ and $\frac{1}{2}$ are verified under closure property of subtraction.