# Percentage

In this chapter, we will be discussing the below-mentioned topics in detail:

• Fractions, Ratio, Decimals and Percentage
• Convert a non-integer percentage to fraction/ decimal and vice versa
• Percentages greater than $100\%$ or less than $1\%$
• Percentage of quantities
• Percentage of a quantity
• Express one quantity as a percentage of another quantity
• Compare two quantities by percentage
• Percentage change

## Fractions, Ratio, Decimals and Percentage

Let’s understand this with the help of some examples:

Fractions Ratio Percentage Decimals
\begin{align} \frac{2}{5} \end{align} $\mathrm{2:5}$ \begin{align} \frac{2}{5} \times 100 = 40\% \end{align} \begin{align*} 40\% &= \frac{40}{100}\\ \\ &= 0.4 \end{align*}
\begin{align} 25\% &= \frac{25}{100}\\\\ &= \frac{1}{4} \end{align} $\mathrm{1:4}$ $\mathrm{25\%}$ $\mathrm{0.25}$
\begin{align} \frac{90}{100} = \frac{9}{10} \end{align} $9:10$ \begin{align} 0.9 \times 100\% = 90\% \end{align} $\mathrm{0.9}$

## Percentages Greater Than 100% or Less Than 1%

Let’s understand this with the help of some examples:

Question 1:

Without using a calculator, express each of the following percentages as a fraction.

1. $105\%$
2. $0.04\%$

Solution:

1.

\begin{align*} 105\% &= \frac{105}{100}\\ &= \frac{21}{20}\\ &= 1\frac{1}{20} \end{align*}

1.

\begin{align*} 0.04\% &= \frac{0.04 × 100}{100 × 100}\\ &= \frac{4}{10000}\\ &= \frac{1}{2500} \end{align*}

Question 2:

Without using a calculator, express each of the following percentages as a decimal.

1. $274\%$
2. $0.38\%$

Solution:

1.

\begin{align*} 274\% &= \frac{274}{100}\\ \\ &= 2.74 \\ \\ \end{align*}

1.

\begin{align*} 0.38\% &= \frac{0.38}{100}\\ \\ &= 0.0038\\ \end{align*}

## Percentage Of A Quantity

Let’s understand this with the help of some examples:

Question 3:

A box contains $60$ balls, of which $16$ are red.

1. If $40\%$ of the balls are green, find the number of green balls.
2. The rest of the balls in the box are yellow.

If $70\%$ of the yellow balls are removed, find the number of yellow balls left.

Solution:

1. Number of green balls\begin{align}\\[2ex] &= \frac{40}{100} \times 60\\[2ex] &=24 \text{ balls} \end{align}

OR
Number of green balls\begin{align}\\[2ex] &= 0.4 \times 60\\[2ex] &=24 \text{ balls} \end{align}

1. Number of yellow balls at first\begin{align}\\[2ex] &= 60 \;– 16 \;– 24\\[2ex] &=20 \end{align}
Number of yellow balls remaining\begin{align}\\[2ex] &= \frac{30}{100} \times 20\\[2ex] &=6 \text{ balls} \end{align}

OR
Number of yellow balls remaining\begin{align}\\[2ex] &= 0.3 \times 20\\[2ex] &=6 \text{ balls} \end{align} 

## Comparing Two Quantities By Percentage

Let’s understand this with the help of some examples:

Question 4:

Shop A sold $225$ out of $1000$ vinyl records in January. Shop B sold $400$ out of $1500$ vinyl records in the same month. Which shop had a higher proportion of sales in January?

Solution:

Percentage of sales by Shop A\begin{align}\\[2ex] &= \frac{225}{1000} \times 100\\[2ex] &=22.5\% \end{align}
Percentage of sales by Shop A\begin{align}\\[4ex] &= \frac{400}{1500} \times 100\\[2ex] &=26\frac{2}{3}\% \end{align}

Shop $B$ had a higher proportion of sales in January.

Continue Learning
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