Question

Verify the closure property of addition of -7/8+3/5

Answer 1

The closure property of addition of rational numbers states that the sum of two rational numbers will also be a rational number.

In other words, if  $\frac{a}{b}$ and $\frac{c}{d}$ are two rational numbers, then their sum $(\frac{a}{b} + \frac{c}{d} )$ is also a rational number.

Here,

$\frac{a}{b} = \frac{-7}{8}$

$\frac{c}{d} = \frac{3}{5}$

Then,

$\frac{a}{b} + \frac{c}{d} = \frac{-7}{8} + \frac{3}{5}$

          $= \frac{-7*5}{8*5} + \frac{3*8}{5*8}$

          $= \frac{-35}{40} + \frac{24}{40}$

          $= \frac{-35+24}{40}$

          $= \frac{-11}{40}$, which is also a rational number.

Hence verified.