Download Simplifying Fractions - Maxwelltown High School

Simplifying Fractions
To simplify a fraction you must divide the top and bottom numbers by the highest number that can divide
both numbers exactly. The highest number that will divide both the top and bottom number exactly is
called the greatest common factor.
Before we start to simplify fractions we must be able to find factors. Factors are whole numbers you
multiply together to get another number so the factors of 15 would be 1, 3, 5, 15
! 1! ×!15! =!15
! 3! ×!15! =!15
the factors can be found by reading the numbers from each side of the multiplication sign.
Practise finding factors by finding the factors of 6, 9, 12, 20 and 30 by filling in the blanks.
! 1! ×! 6! = ! 6
! 1 !× !9 != !9
! 1! ×!12! = !12
! 1! ×! _! = !20
! _! ×!30! = !30
! _! ×! 3! = ! 6
! _ !× !_ != !9
! 2! ×! _! = !12
! 2! ×!10! = !20
! 2! ×! _! = !30
! _! ×! _! = !12
! _! ×! _! = !20
! _! ×! _! = !30
! 5! ×! _! = !30
You should have noticed each number has one and itself as a factor, a number that only has itself and one
as a factor is called a prime number.
The factors of 12 are 1, 2, 3, 4, 6 and 12
The factors of 30 are 1, 2, 3, 5, 6, 10 and 30
1, 2, 3 and 6 are common to both lists so these are common factors to 12 and 30.
The largest common number is 6 so 6 would be the greatest common factor of 12 and 30.
We are now ready to start simplifying fractions.
Simplify
12
30
The highest common factor of 12 and 30 is 6 so
12 ÷6 2
=
30 ÷6 5
Now try and simplify each of the following by filling in the blanks
6
8
10
15
9
21
15
36
6÷ _ _
=
8÷ _ _
10 ÷ _ _
=
15 ÷ _ _
9÷ _ _
=
21 ÷ _ _
15 ÷ _ _
=
36 ÷ _ _
Points to note
Simplifying or reducing a fraction means to make the fraction as simple as possible.
Factors are the numbers you multiply together to get another number.
A factor is a common factor when it is a factor of two or more numbers.
The greatest common factor or highest common factor is the largest of the common factors of
two or more numbers.
A number that only has two factors, one and itself is called a prime number.