How to do Long Division Step by Step for Kid?

Long division is a versatile method for handling complex divisions without using a calculator. It is the preferred method when dividing by a number with two or more digits, particularly if the division is not exact. It can be used to calculate a remainder or give an answer to a paticular number of decimal places.

In order to demonstrate the method we'll work through the solution to 2738 ÷ 70.

Step 1

Long division works from left to right. Since 70 is a 2-digit number, it will not go into 2, the first digit of 2738, and so successive digits are added until a number greater than 70 is found. In this case 2 digits are added to make 273. Note the other digits in the original number have been turned grey to emphasise this and grey zeroes have been placed above to show where division was not possible with fewer digits.

The closest we can get to 273 without exceeding it is 210 which is 3 × 70. These values have been added to the division, highlighted in red.

			0	0	3
	70		2	7	3	8
			2	1	0

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 210 from 273. This gives us 63. Bring down the 8 to make a new target of 638.

					3
	70		2	7	3	8
			2	1	0
				6	3	8

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

Step 3

With a target of 638, the closest we can get is 630 by multiplying 70 by 9. Write 9 in the next column of the answer, and 630 below the 638 as shown.

					3	9
	70		2	7	3	8
			2	1	0
				6	3	8
				6	3	0

Step 4

Finally, subtract 630 from 638 giving 8. Since there are no other digits to bring down, 8 is therefore also the remainder for the whole sum.

So 2738 ÷ 70 = 39 rem 8

					3	9
	70		2	7	3	8
			2	1	0
				6	3	8
				6	3	0
						8

Solution: 2738 ÷ 70 = 39 r 8

Step 1 Long division works from left to right. Since 47 is a 2-digit number, it will not go into 4, the first digit of 46423, and so successive digits are added until a number greater than 47 is found. In this case 2 digits are added to make 464. Note the other digits in the original number have been turned grey to emphasise this and grey zeroes have been placed above to show where division was not possible with fewer digits. The closest we can get to 464 without exceeding it is 423 which is 9 × 47. These values have been added to the division, highlighted in red.

0 0 9  rem 34 47 4 6 4 2 3 4 2 3

47 × table 1 × 47 = 47 2 × 47 = 94 3 × 47 = 141 4 × 47 = 188 5 × 47 = 235 6 × 47 = 282 7 × 47 = 329 8 × 47 = 376 9 × 47 = 423

Step 2 Next, work out the remainder by subtracting 423 from 464. This gives us 41. Bring down the 2 to make a new target of 412.	9  rem 34 47 4 6 4 2 3 4 2 3 4 1 2
47 × table 1 × 47 = 47 2 × 47 = 94 3 × 47 = 141 4 × 47 = 188 5 × 47 = 235 6 × 47 = 282 7 × 47 = 329 8 × 47 = 376 9 × 47 = 423

Step 3 With a target of 412, the closest we can get is 376 by multiplying 47 by 8. Write 8 in the next column of the answer, and 376 below the 412 as shown.	9 8  rem 34 47 4 6 4 2 3 4 2 3 4 1 2 3 7 6
47 × table 1 × 47 = 47 2 × 47 = 94 3 × 47 = 141 4 × 47 = 188 5 × 47 = 235 6 × 47 = 282 7 × 47 = 329 8 × 47 = 376 9 × 47 = 423

Step 4 Next, work out the remainder by subtracting 376 from 412. This gives us 36. Bring down the 3 to make a new target of 363.	9 8  rem 34 47 4 6 4 2 3 4 2 3 4 1 2 3 7 6 3 6 3
47 × table 1 × 47 = 47 2 × 47 = 94 3 × 47 = 141 4 × 47 = 188 5 × 47 = 235 6 × 47 = 282 7 × 47 = 329 8 × 47 = 376 9 × 47 = 423

Step 5 With a target of 363, the closest we can get is 329 by multiplying 47 by 7. Write 7 in the next column of the answer, and 329 below the 363 as shown.	9 8 7  rem 34 47 4 6 4 2 3 4 2 3 4 1 2 3 7 6 3 6 3 3 2 9
47 × table 1 × 47 = 47 2 × 47 = 94 3 × 47 = 141 4 × 47 = 188 5 × 47 = 235 6 × 47 = 282 7 × 47 = 329 8 × 47 = 376 9 × 47 = 423

Step 6 Finally, subtract 329 from 363 giving 34. Since there are no other digits to bring down, 34 is therefore also the remainder for the whole sum. So 46423 ÷ 47 = 987 rem 34	9 8 7  rem 34 47 4 6 4 2 3 4 2 3 4 1 2 3 7 6 3 6 3 3 2 9 3 4
47 × table 1 × 47 = 47 2 × 47 = 94 3 × 47 = 141 4 × 47 = 188 5 × 47 = 235 6 × 47 = 282 7 × 47 = 329 8 × 47 = 376 9 × 47 = 423

[Read More...]