How to Do Short Division

Co-authored by David Jia

Last Updated: October 24, 2024 Fact Checked

Short division is similar to long division, but it involves less written work and more mental arithmetic. The general method for both short and long division is the same, but in short division, you write down less of your work, doing the simple subtraction and multiplication mentally.^{[1]
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Research source} To understand short division, you must have mastered the basic skills of subtraction and multiplication. Short division is ideal when the divisor, the number that you're dividing into another number, is less than 10.

Part 1

Part 1 of 2:

Doing Short Division

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1
Write the problem. To write the problem correctly, place the divisor, the number that you're dividing into another number, outside the long division bar. Place the dividend, the number that you'll be dividing by the divisor, inside the long division bar. The quotient, or your result, will go on top of the division bar. Remember that for short division to work, your divisor has to be less than 10.^{[2]
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- For example: In 847/5, 5 is the divisor, so write it outside the division bar. 847 is the dividend, so place it inside the division bar.
- The quotient is blank because you haven't started dividing yet.
2
Divide the first number of the dividend by the divisor. When you divide, you are stating how many times one number can fit into another number. For example, 2 can fit into 6 three times (2 + 2 + 2 =6). Continuing with our example, 5 goes into 8 just one time, but it doesn’t evenly divide into 8. We have 3 left over. Write the number 1, the first number of the quotient, on top of the division bar. This leftover number is called the remainder.
- If you were using long division, you would write out 8 minus 5 equals 3 and then bring down the 4 from the dividend. Short division simplifies this written process.
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3
Write the remainder next to the first number of the dividend. Write a small 3 to the top right of the number 8. This will remind you that there was a remainder of 3 when you divided 8 by 5. The next number you will divide into is the combination of the remainder and the second number.^{[3]
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- In our example, the next number is 34.
4
Divide the number formed by the first remainder and the second number in the dividend by the divisor. The remainder is 3 and the second number of the dividend is 4, so the new number you'll be working with is 34.^{[4]
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- Now, divide 34 by 5. 5 goes into 34 six times (5 x 6 =30) with a remainder of 4.
- Write your quotient, 6, on the division bar to the right of the 1.
- Again, keep in mind you are doing most of the math mentally.
5
Write the second remainder above the second number in the dividend and divide. Just as you did the first time, simply write a small 4 above and to the right of the number 4. The next number you will be dividing by is 47.^{[5]
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- Now, divide 47 by 5. 5 goes into 47 nine times (5 x 9 = 45) with a remainder of 2.
- Write your quotient, 9, on the division bar to the right of the 6.
Write "r 2" to the right of the quotient on the division bar. The final answer of 847/5 is 169 with a remainder 2. or 169.4.

Part 2

Part 2 of 2:

Dividing in Special Cases

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1
Recognize that the divisor may not go into the first number of the dividend. In some cases, the divisor will be larger than the first number of the dividend and you will not be able to divide. In this case, you will divide into the first two numbers of the dividend.^{[6]
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- For example, 567/7. In this case, 7 doesn’t go into 5, but it does go into 56 eight times. When solving this problem, write the first number of the quotient over the 6 instead of the 5 and continue solving. The final answer is 81.
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Add a zero in the quotient if the divisor does not go into the dividend. This is similar to the first special case, except this time, you will put a zero in the middle of the quotient. If you encounter a problem like this, simply write a zero in the quotient, and try dividing with the next two numbers in the dividend until the number can be divided.^{[7]
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- For example, 3208/8, 8 goes into 32 four times, but does not go into 0. You would add a 0 and then divide into the next number. 8 goes into 8 one time, therefore, the solution would be 401.
3
Practice with some more examples. The best way to understand short division is practicing with many different types of problems.^{[8]
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Research source} Below are a few more examples for you to try out.
- Divide 748 by 2. How many times can 2 go into 7? Three with a remainder of 1. Write 1 next to the 4. How many times can 2 go into 14? Seven times, evenly. Two goes into 8 four times, evenly; therefore, the final answer is 374.
- Divide 368 by 8. Eight doesn’t fit into 3, but it does divide into 36. Eight fits into 36 four times with a remainder of 4 (8 x 4 = 32, 36 - 32 = 4). Write the 4 next to the 9. Eight can go into 48 six times, evenly; therefore, the final answer is 46.
- Divide 1228 by 4. Four doesn’t fit into 1, but it does fit into 12 three times, evenly. Four does not fit into 2, so you must add a zero in the quotient and divide four into 28. Four fits into 28 seven times; therefore, the final answer is 307.

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What if your divisor divides exactly into the dividend?

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You just don't have a remainder. For example, 27 divided by 9 is simply 3.

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How to do long division?

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The same basic way, except that you write down all of your steps. See How to Do Long Division.

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How do I do short division when the dividend is a longer number than the divisor?

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If the question is 362 divided by 56, first you put a decimal point above the "6" in the dividend where the quotient would be. Then add more zeros to 56 until you can fit the divisor inside the number. Then divide. When you answer, there should be a decimal in your quotient.

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Tips

Check your answer. One way to check is to multiply the quotient by the divisor and add the remainder if there is one.

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Remember that division is just the opposite of multiplication. Know your multiplication tables: what numbers do you need to multiply to get to the division problem at hand?

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