Question

What is closure property???

Answer 1

Answer:

1. Closure property

    If two rational numbers are added together, the result is always a rational number.

For example:-

✔ Addition of rational numbers $\rm\dfrac{3}{4} \: and \: \dfrac{5}{6}$

= $\rm\dfrac{3}{4}+\dfrac{5}{6}=\dfrac{9}{12}+\dfrac{10}{12}=\dfrac{9+10}{12}=\dfrac{19}{12}$, which is a rational number

✔ Addition of rational numbers $\rm\dfrac{-3}{8} \: and \: \dfrac{5}{12}$

= $\dfrac{-3}{8}+\dfrac{5}{12}=\dfrac{-9}{24}+\dfrac{10}{24}=\dfrac{-9+10}{24}=\dfrac{1}{24}$, which is a rational number

Thus according to the closure property, if $\rm\dfrac{a}{b} \: and \: \dfrac{c}{d}$ are two rational        numbers, then their addition $\rm[\dfrac{a+c}{b+d}]$ is also a rational number.

                ✔ We say, set of rational numbers is closed for addition