Question

Simplify $4\frac{1}{2}-\frac{1}{4}÷\frac{1}{5}+\frac{3}{5}$.

Answer 1

We can write mixed function as

$a\frac{b}{c}=\frac{a.c+b}{c}=a+\frac{b}{c}$

So,

$4\frac{1}{2}-\frac{1}{4}÷\frac{1}{5}+\frac{3}{5}$

$=4+\frac{1}{2}-\frac{1}{4}÷\frac{1}{5}+\frac{3}{5}$

From BODMAS principle

$=4+\frac{1}{2}+\{(-\frac{1}{4})÷\left(\frac{1}{5}\right)\}+\frac{3}{5}$

$=4+\frac{1}{2}+\left(\frac{-5}{4}\right)+\frac{3}{5}$

$=\{4+\frac{1}{2}+\frac{3}{5}\}+\left(\frac{-5}{4}\right)$

$=\left(\frac{40+5+6}{10}\right)+\left(\frac{-5}{4}\right)$

$=\frac{51}{10}-\frac{5}{4}$

$=\frac{\left(2\right)\left(51\right)-\left(5\right)\left(5\right)}{20}$

$=\frac{77}{20}$

$=3+\frac{17}{20}=3+\frac{17}{20}=3\frac{17}{20}$

So, $4\frac{1}{2}-\frac{1}{4}÷\frac{1}{5}+\frac{3}{5}=3\frac{17}{20}$