Divide using partial quotients

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

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 fives times is the same as subtracting 25. Therefore, instead of subtracting 5 five times, you can just subtract 25 once.

When you do that, you are just subtracting greater multiples of the divisor.

                  ____  
            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







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