Question

Question 5
$-\frac{3}{8}+\frac{1}{7}=\frac{1}{7}+\left(\frac{-3}{8}\right)$ is an example to show that
(a) addition of rational numbers is commutative.
(b) rational numbers are closed under addition.
(c) addition of rational number is associative.
(d) rational numbers are distributive under addition

Answer 1

Given, $-\frac{3}{8}+\frac{1}{7}=\frac{1}{7}+\left(\frac{-3}{8}\right)$
Let two rational numbers, $a=\frac{-3}{8},b=\frac{1}{7}$
$\therefore a+b=\frac{-3}{8}+\frac{1}{7}=\frac{-21+8}{56}=\frac{-13}{56}$
and $b+a=\frac{1}{7}+\frac{-3}{8}=\frac{8-21}{56}=\frac{-13}{56}$
Clearly, a + b = b + a
So, addition is commutative for rational numbers. Hence, the correct answer is option (a).