Q53. - Algebra 1

Question

Evaluate the expression ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}$ if $a=8,b=4,c=16$.

Step-by-Step Solution

Answer

The value of the expression ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}$ is 0.

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed by division, multiplication, addition, and finally subtraction.

Step 2. Example of applying BODMAS rule.

The expression $5b-\frac{2a}{c}$ where $a=3,b=4,c=2$ can be written as

$\begin{array}{l}5b-\frac{2a}{c}=5\left(4\right)-\frac{2\left(3\right)}{2}\\ =(5\times 4)-\frac{(2\times 3)}{2}\\ =20-3\\ =17\end{array}$

Step 3. DESCRIPTION OF STEP.

Substituting $a=8,b=4\text{ and c}=16$ in ${\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}$

$\begin{array}{l}{\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}={\left(\frac{8}{4}\right)}^2-\frac{16}{8-4}\\ \text{Divide 8 by 4 in side the grouping}\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}={\left(2\right)}^2-\frac{16}{8-4}\end{array}$

$\begin{array}{l}\text{Evaluate the power }\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=4-\frac{16}{8-4}\end{array}$

$\begin{array}{l}\text{Subtract 4 from 8 in the denominator of second term}\\ {\left(\frac{a}{b}\right)}^2-\frac{c}{a-b}=4-\frac{16}{4}\end{array}$