Related Calculations (Edexcel IGCSE Maths)

Spec point — 1.8D

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 $\sqrt{9}$ = 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
  • = 1300

• 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
  • $\frac{1560}{1.2}=\frac{15600}{12}=\frac{156\times100}{12}=13\times100=1300$

Exam Hint Use estimation to check your answer is sensible.

Rounding numbers to one significant figure can help you estimate the correct order of magnitude.

E.g. If the answer should be closer to 20 or 2 or 200.

Worked Example Given that 43 × 16 = 688, find the answer to

(i) 688 ÷ 16

Answer:

Division is the inverse operation to multiplication

• If 16 × 43 = 688 then *

688 ÷ 16 = 43

Final answer: 43

(ii) 1.6 × 4300

Answer:

1.6 is 16 divided by 10

4300 is 43 multiplied by 100

(43 × 100) × (16 ÷ 10)

43 × 16 × 100 ÷ 10

43 × 16 × 10

We know that 43 × 16 = 688

688 × 10

Final answer: 6880

(iii) 68.8 ÷ 4.3

Answer:

Begin by writing as a fraction and changing the denominator to an integer

$\frac{68.8}{4.3}=\frac{688}{43}$

Division is the inverse operation to multiplication

If 43 × 16 = 688 then 688 ÷ 43 = 16

Final answer: 16

(iv) Explain how you can use estimation to check your answer for part (iii).

Answer:

Estimate 68.8 ÷ 4.3 by rounding each number to one significant figure

70 ÷ 4 = 17.5

This shows that 16 is likely to be correct, if we had an answer of 1.6 or 160 then we would know we are wrong

Final answer: We can estimate 68.8 ÷ 4.3 by carrying out the calculation 70 ÷ 4 = 17.5 and comparing our answer