Step-by-Step

When you divide by a two-digit divisor, you follow the same basic steps as when you divide by a one-digit divisor. Let’s go through an example.

Divide 762 by 22.

Seven hundred sixty two divided by twenty two.

Click through the slides to see the process of how this division problem is worked out.

Slide: 1 / 5

Start Here…

With a larger divisor, you will need to consider the digits in both the ones and tens places of your dividend.

Think: How many equal groups of 22 can be made from 76?
22 does not go evenly into 76, however, the closest you can get is making 3 groups:
3 x 22 = 66.

Seven hundred sixty two divided by twenty two; three is in the quotient.

Record the 3 in the quotient above the 6. Make sure it is above the 6, not the 7. Always make sure to line up your quotients appropriately on top of the dividend.
Since you divided the 76, not just the 7, the 3 goes above the last digit to the right that was divided, which in this case is 6.

Next…

Now that you’ve made 3 equal groups of 22, with 3 x 22 = 66, it is time to subtract.

Subtract 66 from the 76.

Seven hundred sixty two divided by twenty two minus sixty six equals ten; three is in the quotient.

It might seem odd to have a difference as high as 10 after subtraction. Keep in mind though that as long as the difference is less than the divisor, you are doing the correct steps to solve.

10 is less than the divisor of 22, which means, so far, the division problem is being solved correctly.

Note that if the difference is higher than the divisor, check your previous division. If the difference is too high, you will have to make another group and add that to your quotient.

Then…

Now it is time to bring down the next digit.
Bring down the 2, and begin the steps again.
This time you are dividing 102 by 22.
If needed, ask yourself, “how many groups of 22 can be made from 102?”

Seven hundred sixty two divided by twenty two minus sixty six equals one hundred two; three is in the quotient.

It turns out 4 groups of 22 can be made to fit into 102 without going over: 22 x 4 = 88. This will be illustrated more in detail in the next slide.

Keep going…

Follow the same steps to complete the problem.

Seven hundred sixty two divided by twenty two minus sixty six equals one hundred two minus eighty eight equals fourteen; thirty four remainder fourteen is the quotient.

Since the difference is 14, and there are no more digits to bring down, the division problem is almost done. The remainder is 14. This is what is left over when dividing 762 by 22. This remainder of 14 might seem high, but it is less than the divisor of 22. You could not make another group of 22 from this number, so this remainder is correct.

Check your work…

Use multiplication (and addition if you have a remainder) to check your work.
First, multiply the divisor, 22, by the quotient obtained, 34.

Thirty four times twenty two equals sixty eight plus six hundred eighty; the sum is seven hundred forty eight

This gives you a product of 748.
Next is to add the remainder, 14, to the product, 748.

Seven hundred forty eight plus fourteen; the sum is seven hundred sixty two.

After multiplying and adding, since the solution is the dividend, the quotient (with remainder) of 748 R14 is correct.

Should you ever have a remainder that is larger than your divisor?

Learning Coach — Two-Digit Number Division

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