How to teach long division without a calculator?In the olden days, knowing how to divide large numbers was important. Basic long division is still good to know, so the following examples will show you how to divide a one-digit divisor into another number, and then how to find a remainder.
Recall that the
divisor in a division problem is the number that you’re dividing by. When you’re doing long division, the size of the divisor is your main concern: Small divisors are easy to work with, and large ones are a royal pain. So here you’ll work with a nice, small, one-digit divisor. Suppose you want to find 860 5. Start off by writing the problem like this:
Unlike the other Big Four operations, long division moves from left to right. In this case, you start with the number in the hundreds column (8). To begin, ask how many times 5 goes into 8 — that is, what’s 8 5? The answer is 1 (with a little bit left over), so write 1 directly above the 8. Now multiply 1 5 to get 5, place the answer directly below the 8, and draw a line beneath it:
Subtract 8 – 5 to get 3. (Note: After you subtract, the result should always be smaller than the divisor. If not, you need to write a higher number above the division symbol.) Then bring down the 6 to make the new number 36:
These steps are one complete cycle, and to complete the problem you just need to repeat them. Now ask how many times 5 goes into 36 — that is, what’s 36 5? The answer is 7 (with a little left over). Write 7 just above the 6, and then multiply 7 5 to get 35; write the answer under 36:
Now subtract to get 36 – 35 = 1; bring down the 0 next to the 1 to make the new number 10:
Another cycle is complete, so begin the next cycle by asking how many times 5 goes into 10 — that is, 10 5. The answer this time is 2. Write down the 2 in the answer above the 0. Multiply to get 2 5 = 10, and write this answer below the 10:
Now subtract 10 – 10 = 0. Because you have no more numbers to bring down, you’re finished, and here’s the answer (that is, the quotient):
So 860 5 = 172.
This problem divides evenly, but many don’t. The following instructions tell you what to do when you run out of numbers to bring down.
Division is different from addition, subtraction, and multiplication in that having a remainder is possible. A remainder is simply a portion left over from the division.
The letter r indicates that the number that follows is the remainder.
For example, suppose you want to divide seven candy bars between two people without breaking any candy bars into pieces (too messy). So each person receives three candy bars, and one candy bar is left over. This problem shows you the following:
7 2 = 3 with a remainder of 1, or 3 r 1
In long division, the remainder is the number that’s left when you no longer have numbers to bring down. The following equation shows that 47 3 = 15 r 2:
Note that when you’re doing division with a small dividend and a larger divisor, you always get a quotient of 0 and a remainder of the number you started with:
1 2 = 0 r 1
14 23 = 0 r 14
2,000 2,001 = 0 r 2,000
How to do long division step by step?
Dividing a three digit number by a one digit number (for example 416 ÷ 7) involves several steps.
- Place the divisor before the division bracket and place the dividend (416) under it.
7)416
- Examine the first digit of the dividend(4). It is smaller than 7 so can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket.
5
7)416
- Multiply the 5 by 7 and place the result (35) below the 41 of the dividend.
5
7)416
35
- Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 6 from the 416 and place it to the right of the other 6.
5
7)416
35
66
- Divide 66 by 7 and place that answer above the division bracket to the right of the five.
59
7)416
35
66
- Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 66. Subtract 63 from 66 to give an answer of 3. The number 3 is called the remainder and indicates that there were three left over.
59 R 3
7)416
35
66
63
3
How to long division without remainder? How to divide a three digit number by a one digit number (e.g 413 ÷ 7)?- Place the divisor before the division bracket and place the dividend (413) under it.
7)413
- Examine the first digit of the dividend(4). It is smaller than 7 so it can't be divided by 7 to produce a whole number. Next take the first two digits of the dividend (41) and determine how many 7's it contains. In this case 41 holds five sevens (5*7=35) but not six (6*7=42). Place the 5 above the division bracket.
5
7)413
- Multiply the 5 by 7 and place the result (35) below the 41 of the dividend.
5
7)413
35
- Draw a line under the 35 and subtract it from 41 (41-35=6). Bring down the 3 from the 413 and place it to the right of the 6.
5
7)413
35
63
- Divide 63 by 7 and place that answer above the division bracket to the right of the five.
59
7)413
35
63
- Multiply the 9 of the quotient by the divisor (7) to get 63 and place this below the 63 under the dividend. Subtract 63 from 63 to give an answer of 0. This indicates that there is nothing left over and 7 can be evenly divided into 413 to produce a quotient of 59.
59
7)413
35
63
63
0
More books about long division for kidsHow 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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