What is division?
Division is the opposite of multiplication.
The symbol for division looks like this:
To divide something is to split it in to equal parts. If we divide 12 by 4 we need to split 12 in to 4 equal parts. Lets see how this works.
Imagine you have a birthday cake cut in to 12 slices.
If you have a total of 12 people at your birthday party you can all have 1 slice from the cake. So we can say 12 divided by 12 equals 1 (remember division is the opposite of multiplication so you can check this is correct: 12 x 1 = 12).
If there are 6 people at your party how much cake can you each have? Look at the diagram, the slices have been coloured to show how many each person gets.
12 slices of cake divided between 6 people means you can all have 2 slices. So we say 12 ÷ by 6 equals 2.
If there are just 4 of you, you can have three slices each. 12 divided in to 4 parts gives 3.
We would write it like this:
12 ÷ 4 = 3
Continuing our birthday cake example, you might be thinking it is all well and good, but what happens if there are 5 people at your party? How do you divide the birthday cake evenly? Everyone can have 2 slices, but not everyone can have three as this would mean there would need to be 18 slices of cake and there are only 12. So 12 won’t divide in to 5 whole parts exactly and this is where the remainder comes in.
Imagine how we would make the birthday party fair if there were 5 hungry people there all wanting cake. Well, everyone can have 2 slices of cake and the remaining 2 can be left over. The 2 slices left over are called the remainder. The remainder is just the name for the slices of cake left over that can’t be shared evenly between the guests.
So 12 ÷ 5 = 2 remainder 2.
You can check this makes sence by multiplying the numbers:
2 x 5 = 10
And 10 + the remaining 2 = 12
Use this method when you are dividing a single digit number in to a bigger number.
The method involves taking the single digit number, such as 8 or 4, and dividing it in to each digit in the big number, one digit at a time, starting at the left.
Lets’s work through a sum together.
Question: What is 624 ÷ 6?
Firstly we need to layout our division sum as below with the small number (6) at the front and the big number (624) inside the lines. I have labled the columns Units, Tens and Hundreds so you can see how the big number is sitting – don’t worry about labling the columns in your sums.
Now we can start dividing. We start with the digit furthest left in the big number, in this case it is a 6, and we divide the small number in to it. So we are dividing 6 by 6 which = 1. We write the answer above the line:
Next we move one digit to the right and divide again.
The next division in this example is 2 ÷ 6. This will not divide exactly and so the remainder is carried over to the next column. 2 ÷ 6 = 0 remainder 2. We write the remainder as a little number in the next column:
Next we move on to the last division in our sum. With the remainder from the previous division carried over the sum is now 24 ÷ 6, which equals 4:
And there we have our answer written on the top of the sum: 104!
Long division is for dividing two big numbers.
It is a bit of a pain to learn, but you must learn this method and then you won’t make any mistakes!
Let’s work through an example together to learn how to do it.
Question: What is 3538 ÷ 11?
We lay out our sum similar to in short division with the smaller number in front of the bigger one:
Now we divide the smaller number in to each number in the bigger number. With the first digit the big number will never divide in to it in this method as it has more than one digit:
So we carry over the 3 and divide 11 in to 35. When there is a remainder like in this case we write the answer on top, the answer multiplied by the small number underneath, and then subtract the two numbers to find our remainder, like this:
Now we have our remainder which is 2. We can now bring down the next digit in the big number to sit beside the remainder. And then we divide 11 in to this new number, 23:
This goes 2 times with a remainder of 1. The 2 is written on top and the remainder below. We repeat this method bringing down the next number to sit next to our remainder:
The final remainder is now left at the end of the sum when there are no more digits to bring down. We have our final answer, 321 remainder 7.