# 3.3 Division

Division is probably the most awkward of the four arithmetic operations. Since you may have a calculator, you do not need to be able to carry out complicated divisions by hand, but you do need to carry out simple divisions in order to check your calculator calculations. Division is the reverse process of multiplication. The quantity 12 ÷ 3 tells us how many times 3 goes into 12. Since 4 × 3 = 12, 12 ÷ 3 = 4.

## Example 13

Small candles are sold in boxes of 40. How many boxes do you need in order to have 1000 candles?

### Answer

To solve the problem, you need to know how many times 40 goes into 1000.

There are several ways to do this. One is to divide 1000 by 40:

So its value is unchanged if top and bottom are multiplied or divided by the same number.

Here, notice that top and bottom are both divisible by 10.

So you need 25 boxes of candles.

Alternatively, you might say 1 box gives 40, so 10 boxes give 400, 20 boxes give 800, 5 boxes give 200, so 25 boxes give 1000.