Q12. - Algebra 1

Question

Example 1  Evaluate each expression. Name the property used in each step.

12. $\left[3÷\left(2\cdot 1\right)\right]\frac{\mathbf{2}}{\mathbf{3}}$

Step-by-Step Solution

Answer

The value of the expression is 1.

Step 1 – Write the formulae used

Inverse property of multiplication:

$a\cdot \frac{1}{a}=\frac{1}{a}\cdot a=1$

Identity property of multiplication:

$a\cdot 1=a\cdot 1=a$

Step 2 – Write the given information

The expression given is

$\left[3÷\left(2\cdot 1\right)\right]\frac{2}{3}$

Step 3 - DESCRIPTION OF STEP

To solve the given expression first solve the operation inside the small bracket, then solve the square bracket, and then proceed to simplify further as:

$\begin{array}{c}\left[3÷\left(2\cdot 1\right)\right]\frac{2}{3}=\left[3÷\left(2\right)\right]\frac{2}{3}\text{ identity property}\\ =\left[\frac{3}{2}\right]\frac{2}{3}\\ =\frac{3}{2}\cdot \frac{2}{3}\\ =1\text{ inverse property}\end{array}$

Thus, $\left[3÷\left(2\cdot 1\right)\right]\frac{2}{3}=1$