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Maths

Long multiplication and division

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# Long division

As with long multiplication, you do not have to use the traditional method here. The two methods are:

1. Traditional method
2. Repeated subtraction (chunking)

Remember, you must show sufficient workings out to get the marks.

## Traditional method

This is a similar method to 'short' division, but, rather than writing the remainder at the top each time, we work it out underneath.

To calculate 748 divided by 51,

First, set the sum out as shown:

We work out 74 divided by 51, and write the answer (1) above the 4.

1 × 51 = 51, so we write this underneath 74.

Subtract 51 from 74 to get the remainder (23).

We now bring down the next digit (8) and write it on the end of the 23.

We now work out 238 divided by 51, and write the answer (4) above the 8. You use estimation skills here: 51 is roughly 50 and 4 × 50 = 200. You can work out 51 × 4 = 204 separately.

We write 204 underneath the 238 and subtract to find the remainder. There are no more digits to bring down, so we have our answer:

So the answer is 14 remainder 34.

Question

A farmer has 630 eggs. They are to be placed in trays. Each tray holds 48 eggs. How many trays can be filled?

Answer

The answer is 13 trays, with 6 eggs left over.

You need to divide 63 by 48; subtract to get 15; then divide 150 by 48, and then subtract to get 6.

If your answer was incorrect, perhaps you need to practise subtraction, or estimation? Here is a worked solution. Compare it with yours to see where you went wrong.

## Repeated subtraction

In this method, to calculate 748 divided by 51, we keep subtracting multiples of 51 until we cannot take any more away. We keep a note of how many lots of 51 we have taken away. This gives us our final answer.

To make life easier, we can begin by working out two easy sums. These should both be easy enough to do in your head:

• 10 × 51 = 510
• 2 × 51 = 102

We have 748, so we are able to subtract 510 from this. Notice that we write 10 × 51 on the side.

10 × 51 ]

We are left with 238, so we cannot subtract 510 again. But we can subtract 102. Notice we write 2 x 51 on the side.

2 × 51 ]

This leaves us with 136, so we can subtract another 102, writing 2 × 51 on the side:

2 × 51 ]

This leaves 34. We cannot subtract any more lots of 51, so we have reached the end. The numbers we wrote at the side were 10, 2 and 2. Add these together to get 14. So our answer is: 14 remainder 34.

Question

A farmer has 630 eggs. They are to be placed in trays. Each tray holds 48 eggs. How many trays can be filled?

Answer

The answer is 13 trays, with 6 eggs left over.

You subtract 10 × 48, 2 × 48 and 1 × 48.

If your answer was incorrect, you may need to practise subtraction, or multiplying by 10 and 2.

Here is a worked solution. Compare it with yours to see where you went wrong:

solution of 630 divided by 48

10 + 2 + 1 = 13  ∴   630 ÷ 48 = 13 remainder 6

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