Question

The numerical expression '$\left(\frac{3}{8}\right)+\left(\frac{-5}{7}\right)=\left(\frac{-19}{56}\right)$' shows that:

• A. rational numbers are closed under addition
• B. rational numbers are not closed under addition
• C. rational numbers are closed under multiplication
• D. addition of rational numbers is not commutative

Answer 1

The correct option is A

rational numbers are closed under addition

Verifying the given expression:

Evaluating the L.H.S.

$\begin{array}{rcl}& & \frac{3}{8}+\left(\frac{-5}{7}\right)=\frac{3\times 7+8\left(-5\right)}{56}\\ & =& \frac{21-40}{56}\\ & =& \frac{-19}{56}\\ & & \end{array}$

Here, L.H.S.=R.H.S.,

‘$\frac{3}{8}$' and '$\frac{-5}{7}$‘ are rational numbers, and on adding these we get ’$\frac{-19}{56}$', which is also a rational number.

On adding two rational numbers we got a rational number.

This implies that, rational numbers are closed under addition.

Therefore, option A is correct.