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Skillswise Factsheet
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N1/L1.5

*NEW* Division using repeated subtraction

One way of dividing is to think of it as repeated subtraction.

For example, look at the question 20 ÷ 5
    Subtract  5             20 - 5 = 15
    Subtract 5 again   15 - 5 = 10
    Subtract 5 again   10 - 5 = 5
    Subtract 5 again     5 - 5 = 0

Count the total number of times you subtracted 5. In this question it was 4 times. As the final number after all the subtractions is 0, the 5 divides into 20 exactly with no remainder.
    20 ÷ 5 = 4

Here's another example, 25 ÷ 6
    Subtract  6             25 - 6 = 19
    Subtract 6 again   19 - 6 = 13
    Subtract 6 again   13 - 6 = 7
    Subtract 6 again     7 - 6 = 1

You can't subtract another 6 as there is only 1 left, which is less than the divisor 6. This is the remainder. 6 was subtracted 4 times, but you have a remainder, 1.
    25 ÷ 6 = 4 remainder 1
 

Using multiples with repeated subtraction

You can also combine this method with using multiples, such as multiples of 10, as a shortcut.

For example, 400 ÷ 8
As 400 is divisible exactly by 10 you can subtract 80 instead of 8.
    Subtract 80 (i.e. 10 x 8)  400 - 80 = 320
    Subtract 80 (i.e. 10 x 8)  320 - 80 = 240
    Subtract 80 (i.e. 10 x 8)  240 - 80 = 160
    Subtract 80 (i.e. 10 x 8)  160 - 80 = 80
    Subtract 80 (i.e. 10 x 8)    80 - 80 = 80

Add the total number of 8s subtracted which is 10 + 10 + 10 + 10 + 10 to get the answer 50 with no remainder.
    400 ÷ 8 = 50


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