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And Then There Were Three

You've started to understand long division and dividing two-digit numbers. Let's do a few examples with two- and three-digit numbers. If you can do these, you can divide any numbers under one thousand.

Example:
84 ÷ 6 = ?
Step 1: Does 6 go into 8? Yes, one time. (Write the 1 in your quotient.)
Step 2: 6 x 1 = 6
Step 3: 8 - 6 = 2 That value of 2 is your remainder. (Write the 1 in your quotient.)
Step 4: Bring the 4 down from the dividend to create 24.
Step 5: Does 6 go into 24? Yes, four times. (Write the 4 in your quotient)
Step 6: 6 x 4 = 24
Step 7: 24 - 24 = 0
Since the difference is 0 and there are no more values in the dividend, you are done.
84 ÷ 6 = 14
- or -

14 6 ) 84 - 6     24 - 24   0

Example:
648 ÷ 4 = ?

Does 4 go into 6? Yes, one time. Write 1 in your quotient.
4 x 1 = 4
6 - 4 = 2
Bring down the 4 to make 24.
Does 4 go into 24? Yes, six times. Write 6 in your quotient.
4 x 6 = 24
24 - 24 = 0 (Keep going since there are still numbers in the dividend.)
Bring down the 8 to make 8.
Does 4 go into 8? Yes, two times. Write 2 in your quotient.
4 x 2 = 8
8 - 8 = 0 (No remainder and no more numbers in the dividend.)
648 ÷ 4 = 162
- or -

162 4 ) 648 - 4       24   - 24     8 - 8   0

Two in the Divisor

Let's try an example with a three-digit dividend and a two-digit divisor. You will go through all of the same steps, but you will need to work with two-digit numbers and think about how many times they will go into the values of the dividend. You might even find that these go faster than you expect. We'll go easy on you.

Example:
156 ÷ 12 = ?

Does 12 go into 1? No. Look to the next digit in the dividend.
Does 12 go into 15? Yes, one time. Write a 1 in your quotient.
12 x 1 = 12
15 - 12 = 3
Bring down the 6 to make 36.
Does 12 go into 36? Yes, three times. Write 3 in your quotient.
12 x 3 = 36
36 - 36 = 0 (No remainder and no more numbers in the dividend.)
156 ÷ 12 = 13
- or -

13 12 ) 156 - 12     36 - 36   0

One With a Remainder

We've been giving you easy examples. Let's finish up with a problem that has a remainder. You will get a remainder when your final subtraction does not end in 0. Whatever is left will be the remainder.

Example:
217 ÷ 14 = ?

Does 14 go into 21? Yes, one time. Write 1 in your quotient.
14 x 1 = 14
21 - 14 = 7
Bring down the 7 from the dividend to make 77.
Does 14 go into 77? Yes, five times. Write 5 in your quotient.
14 x 5 = 70
77 - 70 = 7
Since there are no more values in the dividend to bring down, you're left with a value of 7. That 7 is your remainder.
So...
217 ÷ 14 = 15 r 7
- or -

15r7 14 ) 217     - 14       77     - 70       7

We're going to stop here with three-digit numbers, but it would be good for you to practice with larger values. We know that they will be on your tests, so practicing long division will only help your grades go up. Good luck!

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