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Fractions Toolkit
Number
Three routes to the same answer
- Dividing by the denominator and then multiplying by the numerator keeps every number whole for as long as possible
- For 3/8 of 56: 56 ÷ 8 = 7, then 7 × 3 = 21
- Converting the fraction to a decimal and multiplying suits fractions with a short decimal form
- For 3/4 of 26: 0.75 × 26 = 19.5
- Writing the amount over a denominator of 1 turns the problem into a fraction multiplication
- For 2/9 of 45: 2/9 × 45/1 = 90/9 = 10
- The word "of" between a fraction and a quantity always means multiply
Shading a fraction of a shape
- Shading works the same way: count the parts, divide by the denominator, then shade as many groups as the numerator asks for
- To shade 5/7 of a grid of 21 squares, 21 ÷ 7 = 3, and 3 × 5 = 15 squares are shaded
- Which particular squares are shaded does not matter, though grouping them together makes the fraction easier to read
- Where the shape is not already divided, cut it into the number of equal parts the denominator names first
Worked example
Finding a fraction of a quantity
A theatre has successfully sold 5/6 of its 342 seats. Work out how many seats were sold.
Solution:
- Divide by the denominator first, since 342 divides exactly by 6
- 342 ÷ 6 = 57, so one sixth is 57 seats
- Multiply by the numerator: 57 × 5 = 285
- 285 seats were sold