Related-Calculations Aqa Higher

Related calculations

What are related calculations?

• If you know the result of one calculation, you can use it to find the result of a similar, related calculation

• For example, because 3 × 2 = 6

  • We also know the following:

    • 2 × 3 = 6

    • 6 ÷ 2 = 3

    • 30 × 2 = 60

What are inverse operations?

• An inverse operation is an operation which undoes another

  • Adding and subtracting are inverses of one another

  • Multiplying and dividing are inverses of one another

• Inverse operations can be used to help find related calculations

• For example,

  • If we know that 3 × 5 = 15, then we also know that 15 ÷ 3 = 5 and 15 ÷ 5 = 3

  • If we know that 3² = 9, then we also know that = 3

What types of related calculations are there?

• For example, consider the calculation 12 × 13 = 156

• Using the fact that the order of multiplication does not matter (commutativity)

  • 13 × 12 = 156

  • The order of multiplication and addition does not matter

  • The order of division and subtraction does matter

• Using inverse operations

  • 156 ÷ 13 = 12

  • 156 ÷ 12 = 13

• Using multiples of ten

  • Ten times larger

    • 120 × 13 = 1560

  • Ten times smaller

    • 1.2 × 13 = 15.6

  • One value ten times larger, one value 1000 times smaller

    • Answer will therefore be 100 times smaller

    • 0.013 × 120 = 1.56

• Using a combination of multiples of ten and inverse operations

  • 15 600 ÷ 12

  • = 100 × 156 ÷ 12

  • = 100 × 13

  • = 130

• If you are dividing by a decimal, use a multiple of ten to change it to an integer first

  • Writing the calculation as a fraction can help

  • Consider 1560 ÷ 1.2

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