Traditional Division Examples

It’s interesting to see and think about the different methods and strategies you can use to complete a division problem. To begin, let’s review some examples of how to solve division expressions using traditional long division strategies.

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Consider the problem 762 ÷ 22.


Step 1	Check the largest place value in 762 to see if 22 can divide into it. Ask yourself if 22 can fit into 7. It cannot, so try to divide 22 into 76: To decide how many times 22 might go into 76, look at the digits in the largest place of 22 and 76 (which are 2 and 7). You know that 2 goes into 7 three times, so try 22 x 3 to see if it fits into 76: 22 x 3 = 66. This will fit into 76, so try it. When you subtract, you get 10. Since this is less than 22, you know that you can’t fit another 22 into 76. Write 3 in the quotient, above the 6, since you divided into 76. Always line up division appropriately.
Step 2	Next, bring down the 2 and see how many times 22 now goes into 102: 22 x 4 = 88. Subtract 102 − 88 to get 14; 14 is less than 22, so you can't fit any more 22s into 102. This means you should write 4 in the quotient and then write next to it the remainder of 14, R14.


Step 1	First, check the largest place value to see if 46 can divide into it. Does 46 fit into 9? No, it does not, so try to divide 96 by 46. To decide how many times 46 might go into 96, look at the digits that are in the largest place of 46 and 96, (which are 4 and 9). You know that 4 goes divides into 9 two times, so try 46 x 2 to see if it fits into 96: 46 x 2 = 92. So, 46 fits into 96 2 times. When you subtract 96 and 92, the difference is 4. Since 46 is greater than 4, you cannot fit another 46 into 96. Now, write 2 in the quotient, above the 6, since you divided into 96. Always make sure to line up the digits in the quotient.
Step 2	Now, bring down the 3 next to the 4. Now, 43 is smaller than 46, so 46 divides 43 zero times. This means that you should place a 0 in the quotient and subtract 43 – 0.
Step 3	Next, bring down the 4 next to the 43 and see how many times 46 divides into 434. Start with compatible numbers: 46 x 10 is 460; this is close to 434, but is more than 434, so let’s try 46 x 9: 46 x 9 = 414. This is less than 434. So, write a 9 in the quotient. Since the difference between 434 and 414 is less than 46, this will now be the remainder. Write R20 next to the 209 to finish.

What are the four steps in traditional long division?

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Traditional Division Examples

How do you solve this type of division problem?