Question

Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=[-\frac{1}{4}\times \frac{2}{3}]+[-\frac{1}{4}\times \left(\frac{-4}{7}\right)]$
(b) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=[\frac{1}{4}\times \frac{2}{3}]-\left(\frac{-4}{7}\right)$
(c) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=\frac{2}{3}+(-\frac{1}{4})\times \frac{-4}{7}$
(d) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=\{\frac{2}{3}+\left(\frac{-4}{7}\right)\}-\frac{1}{4}$

Answer 1

We know that the distributive property of multiplication over addition for rational numbers can be expressed as $a\times (b+c)=ab+ac$, where a, b and c are rational numbers.
Here, $\frac{-1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=[\frac{-1}{4}\times \frac{2}{3}]+[\frac{-1}{4}\times \left(\frac{-4}{7}\right)]$ i.e option (a) is the example of distributive property of multiplication over addition for rational numbers.