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Long Division Method. How to carry out long division. Numeracy math help.

Updated on September 15, 2011

Long division is a similar method to short division. The only difference being is that you put more working out down underneath the division. If you are not to good dividing and taking numbers away in your head then long division will stop you making a lot of simple mental errors. The easiest way to learn long division is to go through some examples (see below).

Although the long division can be used to divide most numbers it tends to be only used to divide whole numbers larger than 10. The long division method can also be used to divide polynomials.

Example 1

Work out 6365 ÷ 20

First set your division out by putting 6365 underneath a “turned around L shape” and the divisor (20) on the left hand side.

Now 6 ÷ 20 can’t be done, so work out 63 divide by 20. Since 3 × 20 = 60, put the 3 on the top line and write 60 underneath 63. Next take 63 from 60 to give a remainder of 3 and bring the number down from top (6) and put it next to the 3 to make 36.

Now work out 36 ÷ 20. Since 1 × 20 = 20, put the 1 on the top line and write 20 underneath the 36. Next take 36 from 20 to give a remainder of 16 and bring down the next number from the top (5) and put it next to the 16 to make 165.

Finally work out 165 ÷ 20. Since 8 × 20 = 160, put the 8 on the top line and write 160 underneath the 165. Next take 160 from 165 to give a remainder of 5. Since there are no more numbers to divide then remainder 5 can be put on the top line as well.

Therefore, 6365 ÷ 20 = 318 r5

Example 2

Work out 9748 ÷ 17

First set your division out by putting 9748 underneath a “turned around L shape” and the divisor (17) on the left hand side.

Firstly work out 97 divide by 17. Since 5 × 17 = 85, put the 5 on the top line and write 85 underneath 97. Next take 85 from 97 to give a remainder of 12 and bring the number down from top (4) and put it next to the 12 to make 124.

Now work out 124 ÷ 17. Since 7 × 17 = 119, put the 7 on the top line and write 119 underneath the 124. Next take 119 from 124 to give a remainder of 5 and bring down the next number from the top (8) and put it next to the 5 to make 58.

Finally work out 58 ÷ 17. Since 3 × 17 = 51, put the 3 on the top line and write 51 underneath the 58. Next take 51 from 58 to give a remainder of 7. Since there are no more numbers to divide then remainder 7 can be put on the top line as well.

Therefore, 9748 ÷ 17 = 573 r7

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