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Percentages and percentage change
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Economists describe the world in percentages: price rises, growth rates, unemployment rates and interest rates. This starter makes sure the KS3 maths is secure.
Percentage of a total
Percentage = part ÷ whole × 100
If 1.5 million of a 30 million labour force are unemployed, the unemployment rate is 1.5 ÷ 30 × 100 = 5%.
If 1.5 million of a 30 million labour force are unemployed, the unemployment rate is 1.5 ÷ 30 × 100 = 5%.
Percentage change
Percentage change = (new − old) ÷ old × 100
A price rises from £2.00 to £2.30: (2.30 − 2.00) ÷ 2.00 × 100 = 15%.
A negative answer means a fall.
A price rises from £2.00 to £2.30: (2.30 − 2.00) ÷ 2.00 × 100 = 15%.
A negative answer means a fall.
Percent or percentage points?
If an interest rate rises from 2% to 3%, it has risen by 1 percentage point.
But as a percentage change it has risen by (3 − 2) ÷ 2 × 100 = 50%.
Use 'percentage points' when you subtract one percentage from another.
But as a percentage change it has risen by (3 − 2) ÷ 2 × 100 = 50%.
Use 'percentage points' when you subtract one percentage from another.
A country's output rises from $400 billion to $412 billion. What is the percentage change?
- New − old = 412 − 400 = 12
- 12 ÷ 400 × 100 = 3
Answer: 3% increase
Percentage = part ÷ whole × 100. Percentage change = (new − old) ÷ old × 100, dividing by the old value. Subtracting two percentages gives a change in percentage points.
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