1.4 Fractions, decimals, percentages and ratio
Fractions
Everything on fractions that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.
A worked example
Adding fractions · [2 marks]
Work out 4/9 + 5/6. Give your answer in its simplest form.
- M18/18 + 15/18
- A123/18 or 1 5/18
The exam skills (6)
Adding fractions
- Find a common denominator (a multiple of both bottoms).
- Change each fraction, multiplying top and bottom by the same number.
- Add the tops, keep the bottom, then simplify.
Watch out: Adding the bottoms: 1/2 + 2/3 is not 3/5.
Fraction of an amount
- Divide by the bottom number.
- Multiply by the top number.
- Include units.
Watch out: Multiplying by the bottom number instead of dividing.
Multiplying fractions
- Multiply the tops together.
- Multiply the bottoms together.
- Simplify (you can cancel first to keep numbers small).
Watch out: Finding a common denominator. You only need that for adding and subtracting.
Mixed numbers
- Change each mixed number into an improper (top-heavy) fraction.
- Multiply or divide (to divide, flip the second fraction and multiply).
- Change back to a mixed number and simplify.
Watch out: Multiplying the whole numbers and the fractions separately.
Fractions, decimals, percentages
- Fraction to decimal: divide the top by the bottom.
- Decimal to percentage: × 100.
- Learn the common ones: 1/8 = 0.125, 1/5 = 0.2, 3/4 = 0.75.
Watch out: Writing 1/8 as 0.8. Divide 1 by 8.
Fractions problem
- Work out what fraction is left after each step.
- The second fraction is OF WHAT IS LEFT, so multiply the fractions.
- Use the amount left to work back to the total.
Watch out: Taking the second fraction of the whole amount instead of what is left.
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