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Addition
To add/subtract fractions we must recall how to find the Lowest
Common Multiple of at least 2 numbers.
Let’s take 6 and 8 as our examples:
I can show you 2 separate methods:
(1)
Simpler Method
Multiples of 6 are
6
12
18
24
30
36
42
48
54 …..
Multiples of 8 are
8
16
24
32
40
48
56
64
72 ….
The Common Multiples are 24, 48 and … and the LOWEST Common Multiple is 24.
(2)
More complicated method
Write out the prime factors for each of the numbers, keeping each prime separate.
6
8
=
=
2
2
x
x
3
2
x
2
LCM =
2
x
2
x
2
x
3
=
24
Just multiply every prime that is in each column.
Our fraction we shall add is
1 1

6 8
That is the value we must get each of denominators or bottom numbers.
Now to get the 6 to 24 we must multiply by 4, so I’ll multiply both top and bottom by 4.
1 4 x1
4


;
6 4 x6 24
likewise for the fraction with a 8, I’ll need to multiply by 3.
1 3x1 3


.
8 3x8 24
Now I can put it altogether
1 1 4
3
7
 


6 8 24 24 24
Subtraction
1 1
 .
9 12
You have a go at finding the Lowest Common Multiples for both
9 and 12.
Let’s have a go at
Using either method I found the answer to be 36. Therefore,
4 x1 3x1
4
3 43 1





4 x9 3x12 36 36
36
36
Multiplying Fractions
In essence ‘multiply the tops and multiply the bottoms’!
3 2 3x2 6
x 

8 7 8 x7 56
It is important at this stage, to get every mark that you can in your exams, to SIMPLIFY the
answer. That means CANCEL down or find the common factors.
We could find the Highest Common Factor of 6 and 56 here, which would be 2. So,
6
3

. Many people, noting that both numbers are even, would divide BOTH numbers by 2
56 28
until one of the numbers is prime.
A trick here, to make your work easier and get you quickly to the big marks, is to see if you
swap the numerator OR denominators around (NOT BOTH), whether any of the numbers can
easily divide. Let me show you here:
3 5 5 3
3
x  x , this calculation has not changed at all in total value; however, what is ?
8 6 8 6
6
5 3 5 1 5 x1 5
x  x 

and no need to cancel at the end! Full Marks.
8 6 8 2 8 x 2 16
Division of Fractions
We don’t divide fractions! No. Never. We use a trick.
Watch this..
3 5

8 6
Step 1. Change the sign to multiply
3 5
x
8 6
Step 2. Flip (Find the reciprocal) the second fraction
3 6
x
8 5
Step 3. Multiply as normal
3 6 3x6 18
9
x 


(no primes here but I am unable to cancel down any further)
8 5 8 x5 40 20
{I could have spotted that trick with multiples here}
3 6 6 3 3 3 3 x3 9
x  x  x 

, swapping the numerators and spotting that 6  3 made
8
4
8 5 8 5 4 5 4 x5 20
the final answer much easier and guaranteed me full marks.