Question

Express the following percent as a fraction or mixed number in the simplest form.

120%

Short answer

The simplest form of 120% is $1\frac{1}{5}$.

Step-by-step solution

Step 1. Concept of Percentage.

The percent of a number is defined as the ratio of the number and 100.

Step 2. Find the percent of given numbers.

$120\%=\frac{120}{100} \left[\mathrm{Bydefinitionofpercent}\right]$

Step 3. Evaluate the expression.

Write Numerator and denominator in factored form and then cancel out the common factor.

$$\begin{gathered} 120\%=\frac{120}{100} \\ =\frac{2·2·3·10}{2·5·10} \left[\mathrm{divideN}\&\mathrm{Dbycommonfactor}10\right] \\ =\frac{2·2·3\frac{10}{10}}{2·5\frac{10}{10}} \\ =\frac{2·2·3·1}{2·5·1} \left[\mathrm{divideN}\&\mathrm{Dbycommonfactor}2\right] \\ =\frac{\frac{2}{2}·2·3}{\frac{2}{2}·5} \\ =\frac{1·2·3}{1·5} \\ =\frac{6}{5} \\ =1\frac{1}{5} \end{gathered}$$