Fractions, decimals, percentages

Foundation and Higher

The idea

A fraction, a decimal and a percentage can name the same amount: $\tfrac{3}{8} = 0.375 = 37.5\%$ . Percent means out of $100$ .

Fraction to decimal: divide the top by the bottom.
Decimal to percentage: multiply by $100$ .
To compare or order, change them all into one form, usually decimals.

Watch out $0.04$ is $4\%$ , not $40\%$ : move the point two places.

See it worked

Worked exampleNon-calculator2 marks

Work out 7/8 of 64.

$64/8$
To find a fraction of an amount, divide by the denominator and multiply by the numerator.
64 $\div$ 8 $\times$ 7 = 56.

Answer $56$

Your turn

Question 1Non-calculator5 marks

Answer each part without a calculator.

(a) Write $0.04$ as a percentage.

(b) Write $35\%$ as a fraction in its simplest form.

Question 2Non-calculator2 marks

Write 7/16 as a decimal.

Question 3Non-calculator5 marks

At a school, $\frac{3}{8}$ of the students walk to school and $45\%$ take the bus. The remaining $70$ students cycle.

(a) Work out the number of students at the school.

(b) $\frac{2}{5}$ of the students who take the bus are in Year 11. What percentage of all the students at the school are Year 11 students who take the bus?

In past papers

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