Once you know the multiplication facts (such as 7 × 4 = 28), you can use these in reverse while performing divisions.
Simple example with explanation: 31 ÷ 7
- Look for 31 amongst multiples of 7, and find that 31 is just larger than 28 = 7 × 4
- So 31 ÷ 7 = 4 with a remainder.
- Since 31 – 28 = 3, the remainder is 3
- Therefore, 31 ÷ 7 = 4 remainder 3
- The remainder of 3 represents the part of 31 that we have not yet divided by 7. So as a fraction, 31 ÷ 7 = 4 3/7
- In a later section, you will memorize that 3/7 = 0.428571… Using this, we know that 31 ÷ 7 = 4.428571…
Simple example without explanation: 47 ÷ 9
- 47 ÷ 9 = 5 2/9
- From memory, 2/9 = 0.222222…
- 47 ÷ 9 = 5.222222…
Example with multiple stages: 458 ÷ 7
- Look first at the tens: 45
- 45 ÷ 7 = 6 remainder 3
- Therefore 450 ÷ 7 = 60 remainder 30, and 458 ÷ 7 = 60 remainder 38
- We can (and should) continue, to find some multiples of 7 inside 38
- 38 ÷ 7 = 5 remainder 3
- Therefore, 458 ÷ 7 = 65 remainder 3
- 458 ÷ 7 = 65.428571…