Q52. - Algebra 1

Question

Evaluate the expression $\frac{3ab+c^2}{a}$ if $a=8,b=4,c=16$.

Step-by-Step Solution

Answer

The value of the expression $\frac{3ab+c^2}{a}$ is 44.

Step 1. Apply the BODMAS rule.

According to the BODMAS rule of simplification, at first, the bracket operation must be completed followed division, by 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 $\frac{3ab+c^2}{a}$

$\frac{3ab+c^2}{a}=\frac{3\cdot 8\cdot 4+{16}^2}{8}$

$\begin{array}{l}{\text{Evaluate the power 16}}^2\\ \frac{3ab+c^2}{a}=\frac{3\cdot 8\cdot 4+256}{8}\end{array}$

$\begin{array}{l}\text{Multiply 3,\hspace{0.17em}4\hspace{0.17em}\& 8 in the numerator}\\ \frac{3ab+c^2}{a}=\frac{96+256}{8}\end{array}$

$\begin{array}{l}\text{Add 96\hspace{0.17em}\& 256 in the numerator}\\ \frac{3ab+c^2}{a}=\frac{352}{8}\end{array}$

$\begin{array}{l}\text{Simplify }\\ \frac{3ab+c^2}{a}=44\end{array}$