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Fractions, decimals and the order of operations Cambridge IGCSE Mathematics revision

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In plain words

A fraction is a division waiting to happen: 3/4 means 3 ÷ 4. Fractions, decimals and percentages are three ways of writing the same amount. And when a calculation has several steps, there is an agreed order to do them in.

Three things to know

  1. To add or subtract fractions, give them the same denominator first. To multiply, multiply the tops and multiply the bottoms. To divide, flip the second fraction and multiply.
  2. Fraction to decimal: divide the top by the bottom. Decimal to percentage: multiply by 100.
  3. Order of operations (BIDMAS): Brackets, Indices, Division and Multiplication, Addition and Subtraction.

Worked example

Work out 2/3 + 3/4.

  1. A common denominator is 12: 2/3 = 8/12 and 3/4 = 9/12.
  2. 8/12 + 9/12 = 17/12.
  3. As a mixed number: 1 5/12.

Tips and tricks

  • Change mixed numbers into top-heavy fractions before multiplying or dividing.
  • In 3 + 4 × 2, the multiplication comes first: the answer is 11, not 14.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Fractions, decimals and the order of operations: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is 1/2 + 1/3?
    • 2/5
    • 5/6 (the answer)
    • 1/6
    • 2/6

    3/6 + 2/6.

  2. What is 3/8 as a decimal?
    • 0.38
    • 0.375 (the answer)
    • 0.83
    • 2.67

    3 ÷ 8.

  3. What is 2/3 × 3/5?
    • 5/8
    • 2/5 (the answer)
    • 10/9
    • 6/8

    6/15, which cancels to 2/5.

  4. What is 20 − 2 × 3²?
    • 324
    • 162
    • 2 (the answer)
    • 14

    3² = 9, then 2 × 9 = 18, then 20 − 18.

  5. What is 1/4 ÷ 1/2?
    • 1/8
    • 1/2 (the answer)
    • 2
    • 3/4

    1/4 × 2/1 = 2/4.

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