FRACTION PROBLEMS TYPE I TYPE II “Find a fractional part of a quantity” The QUESTION contains a fraction Example: Find 2/3 of £36 TYPE II “Express one quantity as a fraction of another” The ANSWER will be a fraction Example: Express £24 as a fraction of £36

TYPE I FRACTIONS (Finding One Part) In this type of problem, you’re always given the fraction. Example 1: Find 1/4 of £60 £60 £15 £15 £15 £15 Finding just one quarter of £60, means dividing the £60 by 4. 1/4 of £60 = £60 ÷ 4 = = £15

TYPE I FRACTIONS (Finding More Than One Part) Example 2: Find 2/5 of 30 people To find two fifths of 30, the traditional method is first to find one fifth 30 6 6 6 6 6 1/5 of 30 = 30 ÷ 5 = 6 people so 2/5 of 30 = 2 × 6 = 12 people 12 If the look of fractions puts you off, it might help to write fractions in words: 1 fifth of 30 = 30 ÷ 5 = 6 people so 2 fifths of 30 = 2 × 6 = 12 people

TYPE I FRACTIONS (Doing this ‘sum’ in a different order) In maths, “of” means “multiply” so the ‘sum’ to find 2 fifths of 30 people was: 2/5 × 30 We just did the ‘sum’ 30 ÷5 ×2 = 12 but you can rearrange this: 30 ×2 ÷5 = 12 2 ×30 ÷5 = 12 2 ÷5 ×30 = 12 Some of these are easier to work out on paper than others, but you can test that they all give the same answer using a calculator.

TYPE I FRACTIONS (Doing this ‘sum’ in a different order) The important thing is: In each case we have always MULTIPLIED by the top number of the fraction ×2 and DIVIDED by the bottom number ÷5

TYPE I FRACTIONS (Doing this ‘sum’ in a different order) 30 ÷5 ×2 = 12 30 ×2 ÷5 = 12 2 ×30 ÷5 = 12 2 ÷5 ×30 = 12 Multiply by  2 Divide by  5 × 30