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.

Did you find the examples above tough to understand? Did you not understand them at all? Please take a look at this figure!

Divide using partial quotients

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