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Making decimal calculations easier

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Decimals

Making decimal calculations easier

A hard-looking decimal sum usually has an easier one hiding inside it. Three tricks find it.

There is an easier sum hiding insideuse place value0.06 × 3500= 6 × 3500 ÷ 100= 6 × 35 = 210swap for a round number8.2 × 9= 8.2 × 10 − 8.2= 82 − 8.2 = 73.8shrink the divisor12.56 ÷ 40= 1.256 ÷ 4= 0.314× and ÷ can be done in any order — so do the easy one first
Multiplying by 10 is easy, so make × 9 into × 10 − 1.

Trick 1 — use the place value

Rewrite the decimal as a whole number divided by a power of 10, then reorder. 0.06 × 3500 0.06 = 6/100 = 6 ÷ 100 So 0.06 × 3500 = 6 ÷ 100 × 3500 = 6 × 3500 ÷ 100 = 6 × 35 = 210 You can do the × and ÷ in any order — so do the easy one first.

Trick 2 — swap for a round number

Multiplying by 9 is fiddly; multiplying by 10 is not. 8.2 × 9 = 8.2 × (10 − 1) = 8.2 × 10 − 8.2 × 1 = 82 − 8.2 = 73.8 The same works for × 11 as × (10 + 1), or × 19 as × (20 − 1).

Trick 3 — simplify the fraction first

Dividing by 40 is awkward. Dividing by 4 is easy. 12.56 ÷ 40 = 12.56/40 Divide top and bottom by 10: = 1.256/4 = 0.314 You have turned one hard division into one easy one.

Worked examples

0.06 × 3500 using place value

  1. 0.06 = 6 ÷ 100.
  2. So it is 6 × 3500 ÷ 100.
  3. Do the easy division first: 3500 ÷ 100 = 35.
  4. 6 × 35 = 210.

Answer: 210

8.2 × 9 as × (10 − 1)

  1. 8.2 × 10 = 82.
  2. Subtract one lot of 8.2.
  3. 82 − 8.2 = 73.8.

Answer: 73.8

12.56 ÷ 40 by simplifying

  1. Write it as 12.56/40.
  2. Divide top and bottom by 10: 1.256/4.
  3. 1.256 ÷ 4 = 0.314.

Answer: 0.314

5.9 × 9

  1. 5.9 × 10 = 59.
  2. 59 − 5.9 = 53.1.

Answer: 53.1

Why you can reorder × and ÷

  1. Multiplication and division can be done in any order.
  2. So do whichever is easier first.

Answer: Pick the easy step first

7.4 × 11 as × (10 + 1)

  1. 7.4 × 10 = 74.
  2. Add one more 7.4.

Answer: 81.4

Where you see this in real life

  • Working out 9 lots of £8.20 in your head: ten lots is £82, take one lot off, £73.80.
  • Finding 0.06 of 3500 by turning it into 6 × 35 is the kind of shortcut that makes mental arithmetic possible.

Key words

Partitioning
splitting a number into easier parts
Equivalent fraction
a fraction of equal value written differently
Place value
what a digit is worth because of its position
Mental method
a way of calculating in your head
Reorder
change the order of steps without changing the answer
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