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Percentages

Sale prices, interest, test scores, tips: percentages are the everyday maths you meet most often. Get comfortable with three moves here and you can handle nearly all of them.

MYP 4Standard MathsNumberCriteria A · D~9 min read

Written by Fayek Jawad Haider · MYP student

Percentage of an amount

"Per cent" means "out of 100", so a percentage is just a fraction with a denominator of 100. \(15\%\) means \(\frac{15}{100} = 0.15\). To find a percentage of an amount, turn the percentage into a decimal and multiply.

\[ \text{percentage of an amount} = \frac{\text{percentage}}{100} \times \text{amount} \]
Worked example

Find \(15\%\) of \(240\).

1
Write the percentage as a decimal: \(15\% = \frac{15}{100} = 0.15\).
2
Multiply by the amount: \(0.15 \times 240 = 36\).
\(15\%\) of \(240\) is \(36\)

A no-calculator route

Build tricky percentages from easy ones. \(10\%\) of \(240\) is \(24\) (just divide by 10), and \(5\%\) is half of that, \(12\). So \(15\% = 24 + 12 = 36\). Same answer, no calculator needed.

Percentage change

When a quantity goes up or down, percentage change measures the size of that shift relative to where it started. The golden rule: you always divide by the original amount.

\[ \text{percentage change} = \frac{\text{change}}{\text{original}} \times 100\% \]
Worked example

A ticket rises in price from \(\pounds 40\) to \(\pounds 50\). Find the percentage increase.

1
Find the change: \(50 - 40 = 10\).
2
Divide by the original (the starting price, \(40\)) and multiply by 100: \(\frac{10}{40} \times 100\% = 25\%\).
A \(25\%\) increase

Divide by the original, not the new value

Dividing the \(10\) change by the new price \(50\) gives \(20\%\), which is wrong. Percentage change is always measured against where you started from.

Increase and decrease with a multiplier

To change an amount by a percentage in one step, use a multiplier. Start from \(100\%\) (the whole amount), then add or subtract the percentage and turn the result into a decimal.

  • Increase by \(12\%\): \(100\% + 12\% = 112\% \rightarrow\) multiply by \(1.12\).
  • Decrease by \(20\%\): \(100\% - 20\% = 80\% \rightarrow\) multiply by \(0.80\).
Worked example

A coat costs \(\pounds 80\). Increase its price by \(12\%\).

1
Find the multiplier: an increase of \(12\%\) means \(112\%\), so multiply by \(1.12\).
2
\(80 \times 1.12 = 89.6\).
The new price is \(\pounds 89.60\)

Where this is assessed

Percentages run through Criterion A (choosing and using the right method) and Criterion D (applying maths to real money and measurement problems). The multiplier method is prized because it does an increase or decrease in a single, clean calculation.

Check yourself

1. Find \(35\%\) of \(60\). +

Write as a decimal and multiply: \(0.35 \times 60 = \mathbf{21}\).

2. A coat is reduced from \(\pounds 45\) to \(\pounds 36\). Find the percentage decrease. +

Change \(= 45 - 36 = 9\). Divide by the original and multiply by 100: \(\frac{9}{45} \times 100\% = \mathbf{20\%}\).

3. Increase \(150\) by \(8\%\) using a multiplier. +

An \(8\%\) increase means \(108\%\), so the multiplier is \(1.08\). Then \(150 \times 1.08 = \mathbf{162}\).

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