Percentages

Understanding Percentages

A percentage is a way of expressing a number as a part of 100. The word "percent" comes from Latin and means "per hundred." So, when you see something like $45\%$, it simply means 45 out of 100.

The Percent Symbol (%)

The symbol % stands for "percent," and it represents a fraction with a denominator of 100. So, we can write: $$45\% = \frac{45}{100} = 0.45$$

 

Why Do We Use Percentages?

Percentages make it easy to compare different amounts on the same scale. For example, comparing scores on a test:

• Alice scored $80\%$
• Bob scored $90\%$

It’s clear from the percentages who scored higher, no matter how many questions were on the test

 

Percentages of an Amount

When we calculate a percentage of an amount, we’re finding what part of that amount matches the given percentage. For example, finding $25\%$ of $\pounds 200$ means finding how much $\pounds 200$ would be if we only took $25\%$ of it.

The Formula

To find a percentage of an amount, you can use this simple formula: $$\text{Percentage of an amount} = \left(\frac{\text{percentage}}{100}\right) \times \text{amount}$$

Breaking It Down

1. Turn the percentage into a decimal by dividing by 100.
2. Multiply the decimal by the amount you’re calculating the percentage of.

 

Example:

Find $30\%$ of $\pounds 150$

Solution:

1. Write $30\%$ as a decimal: $$\frac{30}{100} = 0.3$$
2. Multiply by the amount, $\pounds 150$: $$0.3 \times 150 = 45$$

Answer: $\pounds 45$