Q47. - Algebra 1

Question

Evaluate the expression $25+\left[(16-3\cdot 5)+\frac{12+3}{5}\right]$.

Step-by-Step Solution

Answer

The value of the expression $25+\left[(16-3\cdot 5)+\frac{12+3}{5}\right]$ is 29.

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 $\frac{{(2+3)}^2}{5(4-3)}$ can be written as

$\begin{array}{l}\frac{{(2+3)}^2}{5(4-3)}=\frac{5^2}{5\left(1\right)}\\ =\frac{5\times 5}{5\times 1}\\ =\frac{25}{5}\\ =5\end{array}$

Step 3. DESCRIPTION OF STEP.

The given expression is $25+\left[(16-3\cdot 5)+\frac{12+3}{5}\right]$

$\begin{array}{l}\text{Multiply 3 \& 5 inside the bracket}\\ 25+\left[\left(16-3\cdot 5\right)+\frac{12+3}{5}\right]=25+\left[\left(16-15\right)+\frac{12+3}{5}\right]\\ \text{Subtracting 15 from 16}\\ 25+\left[\left(16-3\cdot 5\right)+\frac{12+3}{5}\right]=25+\left[1+\frac{12+3}{5}\right]\\ \text{Adding 12 and 3}\\ 25+\left[\left(16-3\cdot 5\right)+\frac{12+3}{5}\right]=25+\left[1+\frac{15}{5}\right]\\ \text{Divide 15 by 5}\\ 25+\left[\left(16-3\cdot 5\right)+\frac{12+3}{5}\right]=25+\left[1+3\right]\\ \text{Add 1 and 3}\\ 25+\left[\left(16-3\cdot 5\right)+\frac{12+3}{5}\right]=25+4\\ \text{On simplifying}\\ 25+\left[\left(16-3\cdot 5\right)+\frac{12+3}{5}\right]=29\end{array}$