Simple Division Algorithm

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 3128 = 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