What is maths division? Explained
Math division is breaking a number into equal parts and determining how many equal parts can be made. For example, dividing 15 by three means splitting 15 into three equal groups of 5.
The division is represented by the symbol ‘÷’ or sometimes ‘/’.
When dividing numbers, the number being divided is called the dividend.
The number which shows how many groups the dividend will be divided into is called a divisor.
And finally, the number that you end up with is called the quotient. See the example below:
10 ÷ 5 = 2
10 is the dividend;
5 is the divisor.
2 is the quotient
Kids will start learning about division as early as Year 1. This is because division is one of the four fundamental maths operations, so it plays a vital role in maths education. The other operations are addition, subtraction, and multiplication.
Throughout the years, children will practice using mental and written methods to complete this operation. They’ll also practice dividing whole numbers, fractions, and decimals and learn to achieve a division with a remainder.
They may also understand how division is essential and valuable in real life. For example, if they are playing a game and need equal numbers of people in groups to form teams.
Let’s have a look at some examples of dividing different types of numbers, including dividing:
- whole numbers;
- fractions by whole numbers;
- decimals.
Then, we’ll go into the different short and long-division methods, which children will need to know by the end of KS2.
Maths: Division of whole numbers
Whole numbers are any positive numbers that don’t have a decimal or fractional part. 1, 2, 15, 500, and 1546 are all whole numbers as they meet these criteria.
As children learn multiplication tables, they’ll practice dividing whole numbers. This is because all numbers part of the times tables is whole numbers!
They will also learn that division is the inverse operation to multiplication –in maths, division and multiplication do the opposite jobs to each other.
For example, if we divide 56 by 7, we get 8, which are all whole numbers.
56 ÷ 7 = 8
Children can learn to test their division skills by checking their answers with multiplication. Using the example above:
7 × 8 = 56
This is why children must know their timetables by heart. It helps them to learn and understand the relationships between different numbers. This comes in handy both in their future maths lessons and everyday life (for example, they may need to understand division to share things between groups of people).
Maths: Division of fractions by whole numbers
Children will learn to divide fractions by whole numbers in Year 5. That’s also one of the curricula aims for that school year, so it’s essential to master completing these calculations.
Let’s take the example below and look at what steps kids need to follow to find the answer.
First, let’s revise: fractions have a numerator (the top number) and denominator (the bottom number). In the fraction above, 2 is the numerator, and 3 is the denominator.
Now, what you need to remember when dividing a fraction by a whole number is that you must multiply the fraction’s denominator by the whole number. Look at the example below.
In this case, you can remember that division is the opposite of multiplication, so multiply the denominator by the whole number.
In the example below, you can complete one more step – simplifying the fraction to its simplest form.
Maths: Division of decimals
In Year 5, children will also learn how to divide decimal numbers.
The most important rule for dividing decimals is to make the divisor a whole number. This can be done by multiplying the divisor by 10, although each time you multiply the divisor, you must also multiply the dividend.
Don’t worry; we’ll show you how this is done in practice with the example below.
How to divide whole numbers by decimals:
3 divided by .04
(dividend) divided by (divisor)
- Multiply the divisor by 10:
.04 × 10 = .4
- This still isn’t a whole number, so we’ll do it once more:
.4 × 10 = 4
- Now we want to do the same thing to the dividend:
3 × 10 = 30
- Because we multiplied the divisor by ten twice, we’ll do the same to the dividend:
30 × 10 = 300
- Now three divided by .04 has turned into:
300 divided by 4
How to divide decimals by decimals:
We want to do the same thing we did above, making sure that a divisor is a whole number:
5.2 divided by .8
.8 × ten is 8
5.2 × ten is 52
52 divided by 8
52 divided by eight is the same as 5.2/.8 and is easier to work out.
What if the dividend isn’t a whole number?
Let’s say you’re given this problem:
3.35 divided by .3
.3 × 10 = 3
3.35 × 10 = 46.5
A divisor is now a whole number, and the dividend isn’t. In this case, we remove the .5 from the dividend and then add it to the answer at the end:
33.5 divided by 3
turns into
33 divided by 3
the answer to this is 11
Now we take that .5 and add it to the answer:
33.5 divided by 3 = 11.5
