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Examples of Long Division

In this part, I have chosen to add some extra examples on the long division method. It might be useful to observe what happens when things don’t add up or when the residual value is too small. Enjoy these calculations.

Example 1

Calculate 42 ÷ 4 and 79 ÷ 3.

42 : 4 = 10.5 solved using long division.     79 : 3 = 26.3 solved using long division.

In the example to the right, you can see that I suddenly stop the calculation, although the residual value is 1. The reason I do so, is because I will continue to get 3’s at the decimal places in my answer when the residual value is 1. The rule on the previous page does indeed tell me to add 0. Then I have to answer what to multiply with, which is 3. Once again, I get 10 9 and I’m left with a residual value equal to 1.

Think About This

Can this division method be used when you have been given a fraction?

The answer is yes! Since the long division method and fractions are two different ways to write a division problem, you can use them interchangeably. If you’re struggling with a fraction, try the long division method, it always works.

Example 2

Calculate 623 ÷ 13 and 428 ÷ 5.

623 ÷ 13 = 47.92 solved using long division.     428 ÷ 5 = 85.6 solved using long division.

In the example to the left above, I have completed the calculation, even though there is a residual value of 4. In school problems, you’re told how many decimals to include before you stop the calculation. In this problem, I chose two decimals.

Example 3

Calculate 525 ÷ 3 and 1575 ÷ 15.

525 divided by 3 = 175 solved using long division     1575 divided by 15 = 105 solved using long division

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How to Do Long Division