Setting Up a Problem
Division problems may use one of three symbols. The first is the one you see in the image to the right. The second is the / and the third is a long solid dash dividing the two numbers–what most people know as a fraction.
The easiest way to complete a division problem is by creating a house. The divisor goes on the outside of the house. Draw a straight up-and-down line as the first part of the house.
Place the dividend on the inside of the straight line. Draw a line over the top of the dividend. The quotient goes on top of the dividend.
The number to the left of the symbol or above the solid dash is the dividend. The number to the right of the symbol or below the solid dash is the divisor. For the rest of this article, all problems examples will use the / symbol.
A few rules help make the steps to divide easier. First, you can never divide by zero. If zero is your divisor, the problem has no answer. Any number divided by one is the number. For instance, 8 / 1 is 8. Any number divided by itself is 1. For instance, 8 / 8 is 1.
Learn your multiplication rules and tables before learning division. Multiplication is the key to understanding division.
When you first see a division problem, it is important to set it up correctly. There are three terms important to understanding a division problem:
1) Dividend – The number you are trying to divide another number into is the dividend
2) Divisor – The divisor is the number you are dividing by.
3) Quotient – The answer is called the quotient.
The steps to divide are as follows:
- Determine the first digit or set of digits your divisor will go into at least once.
- Determine the maximum number of times your divisor will go into the said digit or digits.
- Place the answer over the corresponding digit. For multiple digits, place it over the last digit.
- Multiply the answer from above by your dividend.
- Place the result under your dividend starting from the left most digit.
- Subtract the result from your dividend. Only subtract the digits that line up. For instance, if you have a five digit dividend, but the result is only two digits, only subtract using the first two digits of your dividend.
- Bring down the next digit of your dividend beside the result.
- Repeat the process using the new set of digits. Each time, bring down the next digit of your dividend.
Steps to Divide In Detail
Once your problem is set up, it's time to start dividing. Using multiplication, determine the number of times your divisor will go into the first portion of your dividend.
Example: 840 / 8
Check the first digit of your dividend. Can your divisor go into the first digit at least once? It does not have to divide into it equally. In this case, 8 will divide into 8. Using the house set up, place a 1 over the 8 in 840.
Multiply your divisor by the first part of your quotient. Place the answer under the 8 in 840. Subtract your result. In this case, the result is 0.
Bring down the next available digit of your dividend. This would leave you with 04, but you only need to keep the 4.
Determine if 8 will divide into 4. Since it will not, place a 0 over the 4. Multiply 0 by 8 and place the resulting 0 under the 4. Subtract to get the result of 4.
Bring down your next digit. You should now have 40. Determine if 8 will go into 40. Since 40 is larger than 8, the answer is yes. Use your multiplication rules and tables to determine the maximum number of times 8 goes into 40. The answer is 5.
Place 5 over the 0 of 840. Multiply 5 by 8 and place the answer under the 40. Subtract 40 from 40. The result is 0. Your final quotient will be 105.
When you have run out of digits and your final subtraction result is not zero, you must either start using decimal places, which adds zeros to your number or place the remaining result as a remainder. For instance, if the example above had been 845 / 8, you would have subtracted 40 from 45, resulting in a remainder of 5. To state this result, use the remainder symbol R. The quotient would be 105 R 5.
Resources and Practice Activity Sheets
MCA, Division Steps
DoubleDivision.org, Teaching Long Division
Cool Math 4 Kids, How to Do Long Division
Wisc-Online, Long Division Step By Step
Practice Activity Sheets
Image Credits: Wikimedia Commons / Kudo-Kun