# Divide using partial quotients

Divide using partial quotients is closely related to divide using repeated subtraction.

## Examples showing how to divide using partial quotients

In the lesson about divide using repeated subtraction, we divided 28 by 5 and we came up with the following.

____
5   ) 28
-5                  1
________
23
-5                  1
_________
18
-5                  1
__________
13
-5                  1
__________
8
-5                  1
__________
3

Notice that 5 is subtracted five times. Subtracting 5 five times is the same as subtracting 25. Therefore, instead of subtracting 5 five times, you can just subtract 25 once.

When you do it like that, you are just subtracting greater multiples of the divisor. Notice that we call 5 partial quotient. Although in this problem, there is only one partial quotient, you will in practice get more than 1 partial quotient as example #2 below shows.

____
5   ) 28                                             Partial quotients
-25                  5 × 5                              5
_________
3

Since 3 is less than 5, 3 is the remainder. Thus the answer is 5 r3

Example #2.

Use partial quotients to divide 496 by 4

Step 1

Subtract greater multiples of the divisor. Notice that if we were using repeated subtraction, we would have to subtract 4 one hundred times! Now you see why it is good to divide using partial quotients.

Step 2

Subtract lesser multiples of the divisor.

Step 3

Add the partial quotients. All the steps are shown below.

_______
4   ) 496                                                 Partial quotients
-400                  100 × 4                             100
________
96
-80                    20 × 4                                20

________
16
-16                     4 × 4                                  4

________
0

After adding the partial quotients, the answer is 100 + 20 + 4 = 124

496 ÷ 4 = 124

Example #3.

Use partial quotients to divide 786 by 7

_______
7   ) 786                                                 Partial quotients
-700                  100 × 7                             100
________
86
-70                    10 × 7                               10

________
16
-14                     2 × 7                                  2

________
2

After adding the partial quotients, we get is 100 + 10 + 2 = 112

We also have a leftover or a remainder of 2.

Therefore, using partial quotients, 786 divided by 7 is 112 r2

The meaning of 112 r2 is a quotient of 112 with a remainder of 2.

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