The document discusses how to reduce fractions to their simplest form by finding common factors between the numerator and denominator. It explains that to simplify a fraction, you divide both the numerator and denominator by any number that divides into both. Examples show reducing 3/6 to 1/2 and 6/10 to 3/5. It emphasizes the importance of reducing fractions all the way to their lowest form by finding the highest common factor.

1. Reducing Fractions
to their
Simplest Form
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2. Sometimes it is useful to reduce (or simplify) a fraction down, so that it is
easier to work with. To do this you have to look for a number that will divide
into both the number on the top of the fraction (the numerator) and the
number on the bottom of the fraction (the denominator).
This is called a common factor.

3. Sometimes it is useful to reduce (or simplify) a fraction down, so that it is
easier to work with. To do this you have to look for a number that will divide
into both the number on the top of the fraction (the numerator) and the
number on the bottom of the fraction (the denominator).
This is called a common factor.
For example, the fraction 3/6 has a common factor of 3:

4. Sometimes it is useful to reduce (or simplify) a fraction down, so that it is
easier to work with. To do this you have to look for a number that will divide
into both the number on the top of the fraction (the numerator) and the
number on the bottom of the fraction (the denominator).
This is called a common factor.
For example, the fraction 3/6 has a common factor of 3:
3
6
three
sixths
The numerator can be divided
by 3, as 3 ÷ 3 = 1

5. Sometimes it is useful to reduce (or simplify) a fraction down, so that it is
easier to work with. To do this you have to look for a number that will divide
into both the number on the top of the fraction (the numerator) and the
number on the bottom of the fraction (the denominator).
This is called a common factor.
For example, the fraction 3/6 has a common factor of 3:
3
6
three
sixths
The numerator can be divided
by 3, as 3 ÷ 3 = 1
And the denominator can be
divided by 3, as 6 ÷ 3 = 2

6. Sometimes it is useful to reduce (or simplify) a fraction down, so that it is
easier to work with. To do this you have to look for a number that will divide
into both the number on the top of the fraction (the numerator) and the
number on the bottom of the fraction (the denominator).
This is called a common factor.
For example, the fraction 3/6 has a common factor of 3:
3
6
three
sixths
The numerator can be divided
by 3, as 3 ÷ 3 = 1
And the denominator can be
divided by 3, as 6 ÷ 3 = 2
Therefore 3/6 is reduced to 1/2:

7. Sometimes it is useful to reduce (or simplify) a fraction down, so that it is
easier to work with. To do this you have to look for a number that will divide
into both the number on the top of the fraction (the numerator) and the
number on the bottom of the fraction (the denominator).
This is called a common factor.
For example, the fraction 3/6 has a common factor of 3:
The numerator can be divided
by 3, as 3 ÷ 3 = 1
3
6
three
sixths
And the denominator can be
divided by 3, as 6 ÷ 3 = 2
Therefore 3/6 is reduced to 1/2:
÷3
3
6
1
2
÷3

8. Similarly, the fraction 6/10 has a common factor of 2:

9. Similarly, the fraction 6/10 has a common factor of 2:
6
10
six
sixths
The numerator can be divided
by 2, as 6 ÷ 2 = 3

10. Similarly, the fraction 6/10 has a common factor of 2:
6
10
six
sixths
The numerator can be divided
by 2, as 6 ÷ 2 = 3
And the denominator can be
divided by 2, as 10 ÷ 2 = 5

11. Similarly, the fraction 6/10 has a common factor of 2:
6
10
six
sixths
The numerator can be divided
by 2, as 6 ÷ 2 = 3
And the denominator can be
divided by 2, as 10 ÷ 2 = 5
Therefore 6/10 is reduced to 3/5:

12. Similarly, the fraction 6/10 has a common factor of 2:
6
10
six
sixths
The numerator can be divided
by 2, as 6 ÷ 2 = 3
And the denominator can be
divided by 2, as 10 ÷ 2 = 5
Therefore 6/10 is reduced to 3/5:
÷2
6
10
3
5
÷2

13. When looking for a common factor, it is worth remembering the following:
Any even number (a number that ends in 0, 2, 4, 6 & 8) can be divided by 2

14. When looking for a common factor, it is worth remembering the following:
Any even number (a number that ends in 0, 2, 4, 6 & 8) can be divided by 2
A number that ends in 5 or 0 can be divided by 5

15. When looking for a common factor, it is worth remembering the following:
Any even number (a number that ends in 0, 2, 4, 6 & 8) can be divided by 2
A number that ends in 5 or 0 can be divided by 5
A number that ends in 0, can be divided by 10

16. When looking for a common factor, it is worth remembering the following:
Any even number (a number that ends in 0, 2, 4, 6 & 8) can be divided by 2
A number that ends in 5 or 0 can be divided by 5
A number that ends in 0, can be divided by 10
If you add the digits of a number together and they make 9 or a multiple of 9
(18, 27, 36 etc) the number can be divided by 9

17. The most common mistake when trying to simplify a
fraction, is that the fraction isn’t reduced to the lowest
form. This means that it can still be simplified further.

18. The most common mistake when trying to simplify a
fraction, is that the fraction isn’t reduced to the lowest
form. This means that it can still be simplified further.
Ideally, you need to find the highest common factor – the largest number
that will divide into both the numerator & the denominator – straight
away. However, this can be difficult to see sometimes, so you may have to
divide in stages.

19. The most common mistake when trying to simplify a
fraction, is that the fraction isn’t reduced to the lowest
form. This means that it can still be simplified further.
Ideally, you need to find the highest common factor – the largest number
that will divide into both the numerator & the denominator – straight
away. However, this can be difficult to see sometimes, so you may have to
divide in stages.
For example, when reducing 36/90 you may notice that both the
numerator and denominator are even and can therefore be divide by 2:

20. The most common mistake when trying to simplify a
fraction, is that the fraction isn’t reduced to the lowest
form. This means that it can still be simplified further.
Ideally, you need to find the highest common factor – the largest number
that will divide into both the numerator & the denominator – straight
away. However, this can be difficult to see sometimes, so you may have to
divide in stages.
For example, when reducing 36/90 you may notice that both the
numerator and denominator are even and can therefore be divide by 2:
÷2
36
90
18
45
÷2

21. 18/45 does though have a common factor of 3 and is reduced to 6/15:
÷3
18
45
6
15
÷3

22. 18/45 does though have a common factor of 3 and is reduced to 6/15:
÷3
18
45
6
15
÷3
6/15 does though also have a common factor of 3 and is reduced to 2/5:
÷3
6
15
2
5
÷3

23. 18/45 does though have a common factor of 3 and is reduced to 6/15:
÷3
18
45
6
15
÷3
6/15 does though also have a common factor of 3 and is reduced to 2/5:
÷3
6
15
2
5
÷3
2/5 has no common factors and can’t be simplified any further. It is said to be in
its lowest form.

24. 18/45 does though have a common factor of 3 and is reduced to 6/15:
÷3
18
45
6
15
÷3
6/15 does though also have a common factor of 3 and is reduced to 2/5:
÷3
6
15
2
5
÷3
2/5 has no common factors and can’t be simplified any further. It is said to be in
its lowest form.
It is important that you always check that you have reduced the fraction as much
as possible.
Good Luck!!

25. 18/45 does though have a common factor of 3 and is reduced to 6/15:
÷3
18
45
6
15
÷3
6/15 does though also have a common factor of 3 and is reduced to 2/5:
÷3
6
15
2
5
÷3
2/5 has no common factors and can’t be simplified any further. It is said to be in
its lowest form.
It is important that you always check that you have reduced the fraction as much
as possible.
Good Luck!!

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