Math help - Division
When did you last do long division? Probably when you were at school. However there is a more informal method which is based on our mental process when we do division in our head. It is called chunking, and is the method now taught in schools.
Chunking
Let us try 597 ÷ 22.
We use repeated multiplication with numbers that we are confident with such as 10 and 5. We know that 10 x 22 = 220 so we will start by deducting 220 from 597.
597 |
÷ |
22 |
||
10 |
220 |
- | ||
377 |
We still have more than 220 left over so we will repeat this step.
377 |
||||
10 | 220 |
- | ||
157 |
We now have 157 left over. We know that 5 x 22 = 110 so we will now deduct that.
157 |
||||
5 |
110 |
- | ||
47 |
We now have 47 left over. We know that 2 x 22 = 44. So we do the final step.
47 |
||||
2 |
44 |
- | ||
27 |
r3 |
Short Division
Short division is the method often used for dividing by a single-digit number. Let's first look at the sharing process. For example let us share 65p between 5 children.
We can give each child one 10p coin. We then exchange the remaining 10p coin for ten 1p coins, giving us 15 1p coins to share out. Thus each child gets one 10p and three 1p coins. It is the process of exchanging a ten for ten ones, or a hundred for 10 tens, that is used in short division.
If we divide 65 by 5 using short division we firstly divide 6 ( tens) by 5 to get 1 remainder 1(ten). We then exchange it for 10 units and add them to the 5 to make 15 units. 15 divided by 5 is 3 and so the answer is 13.
Let us divide 235 by 6. Firstly we find that the 2 (hundreds) cannot be divided by 6 and so we exchange them for 20 tens. We add these to the 3 tens to make 23 tens. 23 divided by six is 3 remainder 5(tens). We convert these to 50 units and add them to the 5 to make 55. 55 divided by 6 is 9 remainder 1. Thus the answer is 39 remainder 1.