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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