## What you need to know

**Division**

The two division methods we will see are **long division** and **short division**. Using short division enables you to then understand how long division and the bus stop method works.

**Example: **Use long and short division to work out 288 \div 9.

For **long division**, draw a rotated L-shape with the number we’re dividing (the **dividend**) on the inside, and the number we’re dividing by (the **divisor**) on the outside.

Now, see how many times the divisor, 9, goes into the first digit of the dividend, 2. 9 goes into 2 zero times, so we write a zero on top of the line above the 2. Then, we multiply this value by the divisor, 9\times 0=0, and write the answer below the two (see: left).

Next, we subtract the number below the 2 (zero) from 2 and write the answer underneath the zero. After that, we move onto the second digit of the dividend, 8, and bring it down to sit next to the result of this subtraction (see: right).

We’ve now seen all the steps involved, we just have to repeat them as many times as necessary until the division is complete. So, now we ask how many times our divisor, 9, goes into 28. The answer is 3, so we write a 3 above the top grey line, in line with the second digit of the dividend. Next, we multiply this 3 by the divisor to get 27 and write the 27 underneath 28. Next up, we subtract 27 from 28 to get 1, write the 1 underneath, bring the next digit of the dividend down and repeat this whole process. Once your divisor has 3 digits, then you just have to one final subtraction to determine the remainder. As you’ll see on the left, this gives us the answer: 288 \div 9 = 32 with no remainder.

For **short division**, we begin with exactly the same setup. From there, we ask how many times 9 goes into 2 and write the answer, zero, above the line, as before. Then, we write the remainder of this division, 2, in the gap just before the next digit of the dividend (see: right). Then, we ask how many times the divisor goes into the number formed by that remainder and the next digit, which here is 28. So, 9 goes into 28 three times with a remainder of 1, meaning we write a 3 above the line and a 1 in the gap before the third digit of the dividend. This process is exactly the same and repeats until we get to the end of the number (see: left).

If the divisor doesn’t fit perfectly into the divided, you can either stop once you get to the end and take the final remainder to be the remainder of the whole division, or you can put in a decimal point and keep going until you’re satisfied with how many decimal points you have.

As with multiplication, try both these methods and see which one is better for you.

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### Example Questions

1) Work out 315 \div 14.

Here we’re going to use the short division method, but the long division method is completely fine too (as long as you get the answer right). So, we draw our sideways L-shape with 315 on the inside and 14 on the outside.

14 goes into 3 zero times, so we write a zero above the line and a small 3 – the remainder – in between the 3 and the 1 from 315. Then, we see how many times 14 goes into 31, writing the result above the line and the remainder just before the next digit of the dividend. Repeat this process until you get the complete answer, which looks like

If you stopped at the decimal point and wrote the answer “22 remainder 7”, then this is correct for this question, but you should practice finding the whole answer, even when decimals are involved.

2) Calculate 225 \div 15

Using the same method as question 1 we get.

Answer = 15

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#### Multiplying and Dividing Q1

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