So, 534 ÷ 6 = 89

2. Factoring & cancelling

• This involves treating division as you would if you were asked to cancel fractions
• You can use the fact that with division, most non-calculator questions will have only number answers
• The only thing to be aware of is that this might not be the case if you’ve been asked to write a fraction as a mixed number (but if you are asked to do that it should be obvious from the question)

eg. 1008 ÷ 28

1008 ÷ 28 = 504 ÷ 14 = 252 ÷ 7 = 36

• You may have spotted the first two values (1008 and 28) are both divisible by 4 which is fine but if not, divide top and bottom by any number you can
• To do the last part (252 ÷ 7) you can use the short division method above

3. Intelligent repeated addition

• This is virtually identical to the version for multiplication – the process stops when the number dividing into is reachedeg 1674 ÷ 27This is the same as saying ? × 27 = 1674So we can build up in “chunks” of 27 until we get to 16741 × 27 = 2710 × 27 = 270

  20 × 27 = 54040 × 27 = 1080

  60 × 27 = 1620 … by using the last two results added together.Now you are close we can add on 27 one at a time again.61 × 27 = 1647

  62 × 27 = 1674So 1674 ÷ 27 = 62

4. Dividing by 10, 100, 1000, … (Powers of 10)

• This is a case of moving digits (or decimal points) or knocking off zeroseg. 380 ÷ 10 = 38

  45 ÷ 100 = 0.45

5. Dividing by 2, 4, 8, 16, 32, … (Powers of 2)

• This time it is a matter of repeatedly halvingeg. 280 ÷ 8 = 140 ÷ 4= 70 ÷ 2 = 35

  1504 ÷ 32 = 752 ÷ 16 = 376 ÷ 8 = 188 ÷ 4 = 94 ÷ 2 = 47