You know from the last section that multiplication is repeated addition, similarly division can be thought of as repeated subtraction. For example, 20 divided by 4 is 5 (20 ÷ 4 = 5). The answer is 5 because 5 is the number of times you subtract 4 from 20 to arrive at zero:
This also leads to the realisation that division is the opposite or undoes multiplication. If you add 4, five times to zero (repeated addition or multiplication) then you will arrive back at 20.
And just as with the other operators, there are words that tell us you need to divide.
Here are some examples that you may recognise:
- How many times does 8 go into 72?
- How can you share 72 items equally among eight people?
- How many lots of five are there in 20?
Unlike multiplication when there is only one symbol that says multiply, division has a whole family of notation! If you want to divide 72 by 8 this can be written in the following ways:
72 ÷ 8, or , or 72/8 or
Not all division problems will result in a nice whole number answer and you may have a number left over. This number is known as the remainder. The common notation is to show this using the letter R.
Now, you’re going to look at division on paper, just as you did with multiplication.
You set up division on paper using the final notation from our list. Starting from the left, in this case, divide into each number in turn, writing the result above the number you have divided into. In this case if you can’t divide into a number move to the next and divide into both.
Before the next activity you might like to watch this video showing you how to carry out long division.
Now have a go at the next activity. If you wish you canagain.
Activity _unit3.3.1 Activity 4 Division
On a piece of paper, perform the following operations by hand.
(a) 4968 ÷ 24
The solution is 207.
(b) 4035 ÷ 15
The solution is 269.
When looking at subtraction and addition you thought about whether it mattered in what order these were carried out. You found that for addition the answer is the same whatever the order but this is not the case for subtraction. What about multiplication and division? You’ll find out in the next section.