Question

Which of the following is an example of distributive property of multiplication over addition for rational numbers?

• A. $\frac{-1}{4}\times [\frac{2}{3}+(\frac{-4}{7}\left)\right]=$ $(\frac{-1}{4}\times \frac{2}{3})+(\frac{-1}{4}\times \frac{-4}{7})$
• B. $\frac{-1}{4}\times [\frac{2}{3}+(\frac{-4}{7}\left)\right]=$ $(\frac{-1}{4}\times \frac{2}{3})-\left(\frac{-4}{7}\right)$
• C. $\frac{-1}{4}\times [\frac{2}{3}+(\frac{-4}{7}\left)\right]=$ $(\frac{2}{3}\times \frac{-1}{4})\times \left(\frac{-4}{7}\right)$
• D. $\frac{-1}{4}\times [\frac{2}{3}+(\frac{-4}{7}\left)\right]=$ $\frac{2}{3}+\left(\frac{-4}{7}\right)-\frac{1}{4}$

Answer 1

The correct option is A $\frac{-1}{4}\times [\frac{2}{3}+(\frac{-4}{7}\left)\right]=$ $(\frac{-1}{4}\times \frac{2}{3})+(\frac{-1}{4}\times \frac{-4}{7})$

According to the distributive property of multiplication over addition, $\text{a}\times (\text{b}+\text{c})=(\text{a}\times \text{b})+(\text{a}\times \text{c})$

So, $\frac{-1}{4}\times [\frac{2}{3}+(\frac{-4}{7}\left)\right]=$ $(\frac{-1}{4}\times \frac{2}{3})+(\frac{-1}{4}\times \frac{-4}{7})$