How to do double digit long division step by step?
More books about long division for kids
How to do Long Division with Remainders?
When we are given a long division to do it will not always work out to a whole number. Sometimes there will be numbers left over. These are known as
remainders. Taking an example similar to that on the
Long Division page it becomes more clear: 435 ÷ 25.
If you feel happy with the process on the Long Division
 | 4 ÷ 25 = 0 remainder 4 | The first number of the dividend is divided by the divisor. |
 |
| The whole number result is placed at the top. Any remainders are ignored at this point. |
 | 25 × 0 = 0 | The answer from the first operation is multiplied by the divisor. The result is placed under the number divided into. |
 | 4 – 0 = 4 | Now we take away the bottom number from the top number. |
 |
| Bring down the next number of the dividend. |
 | 43 ÷ 25 = 1 remainder 18 | Divide this number by the divisor. |
 |
| The whole number result is placed at the top. Any remainders are ignored at this point. |
 | 25 × 1 = 25 | The answer from the above operation is multiplied by the divisor. The result is placed under the last number divided into. |
 | 43 – 25 = 18 | Now we take away the bottom number from the top number. |
 |
| Bring down the next number of the dividend. |
 | 185 ÷ 25 = 7 remainder 10 | Divide this number by the divisor. |
 |
| The whole number result is placed at the top. Any remainders are ignored at this point. |
 | 25 × 7 = 175 | The answer from the above operation is multiplied by the divisor. The result is placed under the number divided into. |
 | 185 – 175 = 10 | Now we take away the bottom number from the top number. |
|
| There is still 10 left over but no more numbers to bring down. |
 |
| With a long division with remainders the answer is expressed as 17 remainder 10 as shown in the diagram |
How to explain long division to children?
Solution for 531219 ÷ 579 - with remainder
Step 1Long division works from left to right. Since 579 will not go into 5, a grey 0 has been placed over the 5 and we combine the first two digits to make 53. In this case, 53 is still too small. A further 0 is added above 3 and a third digit is added to make 531. Note the other digits in the original number have been turned grey to emphasise this. The closest we can get to 531 without exceeding it is 5211 which is 9 × 579. These values have been added to the division, highlighted in red. |
| | | 0 | 0 | 0 | 9 |
|
| rem 276 |
| 579 |  | 5 | 3 | 1 | 2 | 1 | 9 | |
| | | 5 | 2 | 1 | 1 |  |  | |
|
| 579 × table |
| 1 × 579 = | 579 |
| 2 × 579 = | 1158 |
| 3 × 579 = | 1737 |
| 4 × 579 = | 2316 |
| 5 × 579 = | 2895 |
| 6 × 579 = | 3474 |
| 7 × 579 = | 4053 |
| 8 × 579 = | 4632 |
| 9 × 579 = | 5211 |
|
Step 2Next, work out the remainder by subtracting 5211 from 5312. This gives us 101. Bring down the 1 to make a new target of 1011. |
| | | | | | 9 |
|
| rem 276 |
| 579 | | 5 | 3 | 1 | 2 | 1 | 9 | |
| | | 5 | 2 | 1 | 1 | | | |
| | | | 1 | 0 | 1 | 1 | | |
|
| 579 × table |
| 1 × 579 = | 579 |
| 2 × 579 = | 1158 |
| 3 × 579 = | 1737 |
| 4 × 579 = | 2316 |
| 5 × 579 = | 2895 |
| 6 × 579 = | 3474 |
| 7 × 579 = | 4053 |
| 8 × 579 = | 4632 |
| 9 × 579 = | 5211 |
|
Step 3With a target of 1011, the closest we can get is 579 by multiplying 579 by 1. Write the 579 below the 1011 as shown. |
| | | | | | 9 | 1 |
| rem 276 |
| 579 | | 5 | 3 | 1 | 2 | 1 | 9 | |
| | | 5 | 2 | 1 | 1 | | | |
| | | | 1 | 0 | 1 | 1 | | |
| | | | | 5 | 7 | 9 | | |
|
| 579 × table |
| 1 × 579 = | 579 |
| 2 × 579 = | 1158 |
| 3 × 579 = | 1737 |
| 4 × 579 = | 2316 |
| 5 × 579 = | 2895 |
| 6 × 579 = | 3474 |
| 7 × 579 = | 4053 |
| 8 × 579 = | 4632 |
| 9 × 579 = | 5211 |
|
Step 4Next, work out the remainder by subtracting 579 from 1011. This gives us 432. Bring down the 9 to make a new target of 4329. |
| | | | | | 9 | 1 |
| rem 276 |
| 579 | | 5 | 3 | 1 | 2 | 1 | 9 | |
| | | 5 | 2 | 1 | 1 | | | |
| | | | 1 | 0 | 1 | 1 | | |
| | | | | 5 | 7 | 9 | | |
| | | | | 4 | 3 | 2 | 9 | |
|
| 579 × table |
| 1 × 579 = | 579 |
| 2 × 579 = | 1158 |
| 3 × 579 = | 1737 |
| 4 × 579 = | 2316 |
| 5 × 579 = | 2895 |
| 6 × 579 = | 3474 |
| 7 × 579 = | 4053 |
| 8 × 579 = | 4632 |
| 9 × 579 = | 5211 |
|
Step 5With a target of 4329, the closest we can get is 4053 by multiplying 579 by 7. Write the 4053 below the 4329 as shown. |
| | | | | | 9 | 1 | 7 | rem 276 |
| 579 | | 5 | 3 | 1 | 2 | 1 | 9 | |
| | | 5 | 2 | 1 | 1 | | | |
| | | | 1 | 0 | 1 | 1 | | |
| | | | | 5 | 7 | 9 | | |
| | | | | 4 | 3 | 2 | 9 | |
| | | | | 4 | 0 | 5 | 3 | |
|
| 579 × table |
| 1 × 579 = | 579 |
| 2 × 579 = | 1158 |
| 3 × 579 = | 1737 |
| 4 × 579 = | 2316 |
| 5 × 579 = | 2895 |
| 6 × 579 = | 3474 |
| 7 × 579 = | 4053 |
| 8 × 579 = | 4632 |
| 9 × 579 = | 5211 |
|
Step 6Finally, subtract 4053 from 4329 giving 276. Since there are no other digits to bring down, 276 is therefore also the remainder for the whole sum.
So 531219 ÷ 579 = 917 rem 276 |
| | | | | | 9 | 1 | 7 | rem 276 |
| 579 | | 5 | 3 | 1 | 2 | 1 | 9 | |
| | | 5 | 2 | 1 | 1 | | | |
| | | | 1 | 0 | 1 | 1 | | |
| | | | | 5 | 7 | 9 | | |
| | | | | 4 | 3 | 2 | 9 | |
| | | | | 4 | 0 | 5 | 3 | |
| | | | | | 2 | 7 | 6 | |
|
| 579 × table |
| 1 × 579 = | 579 |
| 2 × 579 = | 1158 |
| 3 × 579 = | 1737 |
| 4 × 579 = | 2316 |
| 5 × 579 = | 2895 |
| 6 × 579 = | 3474 |
| 7 × 579 = | 4053 |
| 8 × 579 = | 4632 |
| 9 × 579 = | 5211 |
|
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