Q57. - Algebra 2

Question

Find the value of each expression.

 

$\mathbf{14}\left(\frac{\mathbf{1}}{\mathbf{4}}\right)\mathbf{-}\mathbf{12}\left(\frac{\mathbf{1}}{\mathbf{6}}\right)$

Step-by-Step Solution

Answer

The value of $14\left(\frac{1}{4}\right)-12\left(\frac{1}{6}\right)$ is $\frac{\mathbf{3}}{\mathbf{2}}$.

 

Step 1 – Description of step.

Divide 14 by 4.

 

$\frac{14}{4}=\frac{7}{2}$

Step 2 – Description of step.

Write $12$ as $2·6$ into $12\left(\frac{1}{6}\right)$.

$\left(2·6\right)·\frac{1}{6}$

Step 3 – Associative property of multiplication.

For any real numbers $p,q$ and $r$, $p·\left(q·r\right)=\left(p·q\right)·r$.

Step 4 – Apply associative property of multiplication.

Apply associative property of multiplication to the expression in step 1.

$2·\left(6·\frac{1}{6}\right)$

Step 5 - Inverse property.

For any real number $p$, if $p\ne 0$, then $p·\frac{1}{p}=1=\frac{1}{p}·p$.

Step 6 – Apply inverse property.

Apply inverse property to the expression in step 4 and simplify.

$2·1=2$

Step 7 – Description of step.

Subtract 2 from $\frac{7}{2}$ and simplify.

$\begin{array}{c}\frac{7}{2}-2=\frac{7-4}{2}\\ =\frac{3}{2}\end{array}$

Therefore, the value of $14\left(\frac{1}{4}\right)-12\left(\frac{1}{6}\right)$ is $\frac{3}{2}$.