Question

Simplify each of the following by using suitable property. Also name the property $\left[\right(\frac{1}{2})\times (\frac{1}{4}\left)\right]+\left[\right(\frac{1}{2})\times 6]$.

Answer 1

Given that to simplify :$\left[\right(\frac{1}{2})\times (\frac{1}{4}\left)\right]+\left[\right(\frac{1}{2})\times 6]$

The given set of rational numbers is according to the rule of distributive law over addition.

The distributive property states, if $a,b$ and $c$ are three rational numbers, then;

$ax(b+c)=(axb)+(axc)$

Let us take$\frac{1}{2}$ as common.

So,

$=\frac{1}{2}[\frac{1}{4}+6]$

$=\frac{1}{2}\left[\frac{(1+24)}{4}\right]$

$=\frac{1}{2}\left[\frac{25}{4}\right]$

$=\frac{25}{8}$

Therefore, $\left[\right(\frac{1}{2})\times (\frac{1}{4}\left)\right]+\left[\right(\frac{1}{2})\times 6]$$=\frac{25}{8}$.