How to explain long division to children?

How to explain long division to children?

Solution for 531219 ÷ 579 - with remainder

Step 1 Long division works from left to right. Since 579 will not go into 5, a grey 0 has been placed over the 5 and we combine the first two digits to make 53. In this case, 53 is still too small. A further 0 is added above 3 and a third digit is added to make 531. Note the other digits in the original number have been turned grey to emphasise this. The closest we can get to 531 without exceeding it is 5211 which is 9 × 579. These values have been added to the division, highlighted in red.

0 0 0 9  rem 276 579 5 3 1 2 1 9 5 2 1 1

579 × table 1 × 579 = 579 2 × 579 = 1158 3 × 579 = 1737 4 × 579 = 2316 5 × 579 = 2895 6 × 579 = 3474 7 × 579 = 4053 8 × 579 = 4632 9 × 579 = 5211

Step 2 Next, work out the remainder by subtracting 5211 from 5312. This gives us 101. Bring down the 1 to make a new target of 1011.	9  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1
579 × table 1 × 579 = 579 2 × 579 = 1158 3 × 579 = 1737 4 × 579 = 2316 5 × 579 = 2895 6 × 579 = 3474 7 × 579 = 4053 8 × 579 = 4632 9 × 579 = 5211

Step 3 With a target of 1011, the closest we can get is 579 by multiplying 579 by 1. Write the 579 below the 1011 as shown.	9 1  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9
579 × table 1 × 579 = 579 2 × 579 = 1158 3 × 579 = 1737 4 × 579 = 2316 5 × 579 = 2895 6 × 579 = 3474 7 × 579 = 4053 8 × 579 = 4632 9 × 579 = 5211

Step 4 Next, work out the remainder by subtracting 579 from 1011. This gives us 432. Bring down the 9 to make a new target of 4329.	9 1  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9 4 3 2 9
579 × table 1 × 579 = 579 2 × 579 = 1158 3 × 579 = 1737 4 × 579 = 2316 5 × 579 = 2895 6 × 579 = 3474 7 × 579 = 4053 8 × 579 = 4632 9 × 579 = 5211

Step 5 With a target of 4329, the closest we can get is 4053 by multiplying 579 by 7. Write the 4053 below the 4329 as shown.	9 1 7  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9 4 3 2 9 4 0 5 3
579 × table 1 × 579 = 579 2 × 579 = 1158 3 × 579 = 1737 4 × 579 = 2316 5 × 579 = 2895 6 × 579 = 3474 7 × 579 = 4053 8 × 579 = 4632 9 × 579 = 5211

Step 6 Finally, subtract 4053 from 4329 giving 276. Since there are no other digits to bring down, 276 is therefore also the remainder for the whole sum. So 531219 ÷ 579 = 917 rem 276	9 1 7  rem 276 579 5 3 1 2 1 9 5 2 1 1 1 0 1 1 5 7 9 4 3 2 9 4 0 5 3 2 7 6
579 × table 1 × 579 = 579 2 × 579 = 1158 3 × 579 = 1737 4 × 579 = 2316 5 × 579 = 2895 6 × 579 = 3474 7 × 579 = 4053 8 × 579 = 4632 9 × 579 = 5211