How to teach long division with remainders?

 

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Division, Ages 7-12 (Workbook w/Music CD) 

 

Solution for 76999 ÷ 123 - with remainder

Step 1 Long division works from left to right. Since 123 will not go into 7, a grey 0 has been placed over the 7 and we combine the first two digits to make 76. In this case, 76 is still too small. A further 0 is added above 6 and a third digit is added to make 769. Note the other digits in the original number have been turned grey to emphasise this. The closest we can get to 769 without exceeding it is 738 which is 6 × 123. These values have been added to the division, highlighted in red.

0 0 6  rem 1 123 7 6 9 9 9 7 3 8

123 × table 1 × 123 = 123 2 × 123 = 246 3 × 123 = 369 4 × 123 = 492 5 × 123 = 615 6 × 123 = 738 7 × 123 = 861 8 × 123 = 984 9 × 123 = 1107

Step 2 Next, work out the remainder by subtracting 738 from 769. This gives us 31. Bring down the 9 to make a new target of 319.	6  rem 1 123 7 6 9 9 9 7 3 8 3 1 9
123 × table 1 × 123 = 123 2 × 123 = 246 3 × 123 = 369 4 × 123 = 492 5 × 123 = 615 6 × 123 = 738 7 × 123 = 861 8 × 123 = 984 9 × 123 = 1107

Step 3 With a target of 319, the closest we can get is 246 by multiplying 123 by 2. Write the 246 below the 319 as shown.	6 2  rem 1 123 7 6 9 9 9 7 3 8 3 1 9 2 4 6
123 × table 1 × 123 = 123 2 × 123 = 246 3 × 123 = 369 4 × 123 = 492 5 × 123 = 615 6 × 123 = 738 7 × 123 = 861 8 × 123 = 984 9 × 123 = 1107

Step 4 Next, work out the remainder by subtracting 246 from 319. This gives us 73. Bring down the 9 to make a new target of 739.	6 2  rem 1 123 7 6 9 9 9 7 3 8 3 1 9 2 4 6 7 3 9
123 × table 1 × 123 = 123 2 × 123 = 246 3 × 123 = 369 4 × 123 = 492 5 × 123 = 615 6 × 123 = 738 7 × 123 = 861 8 × 123 = 984 9 × 123 = 1107

Step 5 With a target of 739, the closest we can get is 738 by multiplying 123 by 6. Write the 738 below the 739 as shown.	6 2 6  rem 1 123 7 6 9 9 9 7 3 8 3 1 9 2 4 6 7 3 9 7 3 8
123 × table 1 × 123 = 123 2 × 123 = 246 3 × 123 = 369 4 × 123 = 492 5 × 123 = 615 6 × 123 = 738 7 × 123 = 861 8 × 123 = 984 9 × 123 = 1107

Step 6 Finally, subtract 738 from 739 giving 1. Since there are no other digits to bring down, 1 is therefore also the remainder for the whole sum. So 76999 ÷ 123 = 626 rem 1	6 2 6  rem 1 123 7 6 9 9 9 7 3 8 3 1 9 2 4 6 7 3 9 7 3 8 1
123 × table 1 × 123 = 123 2 × 123 = 246 3 × 123 = 369 4 × 123 = 492 5 × 123 = 615 6 × 123 = 738 7 × 123 = 861 8 × 123 = 984 9 × 123 = 1107