How to explain long division to children?

Master Long Division Practice Workbook: Improve Your Math Fluency Series (Volume 8)

Long Division

The Long Division

Master Long Division Practice Workbook: Improve Your Math Fluency Series (Volume 8)

Basic Math and Pre-Algebra Workbook For Dummies

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

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

example 2:

Solution for 4870 ÷ 42 - with remainder

Step 1

Long division works from left to right. Since 42 will not go into 4, a grey 0 has been placed over the 4 and we combine the first two digits to make 48. Note the other digits in the original number have been turned grey to emphasise this.
The closest we can get to 48 without exceeding it is 42 which is 1 × 42. These values have been added to the division, highlighted in red.

			0	1			rem 40
	42		4	8	7	0
			4	2

You will notice that the division is set out carefully with the digits in vertical columns. This is very important when you work them out by hand.

Step 2

Next, work out the remainder by subtracting 42 from 48. This gives us 6. Bring down the 7 to make a new target of 67.

				1			rem 40
	42		4	8	7	0
			4	2
				6	7

The digit brought down and the new target have been highlighted in blue.

Step 3

With a target of 67, the closest we can get is 42 by multiplying 42 by 1. Write the 42 below the 67 as shown.

				1	1		rem 40
	42		4	8	7	0
			4	2
				6	7
				4	2

Step 4

Next, work out the remainder by subtracting 42 from 67. This gives us 25. Bring down the 0 to make a new target of 250.

				1	1		rem 40
	42		4	8	7	0
			4	2
				6	7
				4	2
				2	5	0

Step 5

With a target of 250, the closest we can get is 210 by multiplying 42 by 5. Write the 210 below the 250 as shown.

				1	1	5	rem 40
	42		4	8	7	0
			4	2
				6	7
				4	2
				2	5	0
				2	1	0

Step 6

Finally, subtract 210 from 250 giving 40. Since there are no other digits to bring down, 40 is therefore also the remainder for the whole sum.
So 4870 ÷ 42 = 115 rem 40

				1	1	5	rem 40
	42		4	8	7	0
			4	2
				6	7
				4	2
				2	5	0
				2	1	0
					4	0

Solution: 4870 ÷ 42 = 115 r 40