Adding Fractions
In order to add fractions both the fractions must have the same denominator (the number on the bottom) and then you can simply add the numerator.
For example
3/5 + 1/5 = (1+3)/5 = 4/5
However not all fraction have the same denominator but we may still need to all them. To do this we make use of the fact that if you multiply the top and bottom of a fraction by the same number then it is still of the same value
for example
3/4 = (3 x 2) / (4 x 2) = 6/8
We can use this to add fractions as we can multiply the tops and bottoms of a fraction so that both the fractions we are adding have the same denominator (often called the lowest common denominator of LCD). This is can often be found by multiplying the denominators together.
eg)
3/4 + 2/3 = (3 x 3)/ (4 x 3) + (2 x 4)/(3 x 4) = 9/12 + 8/12
but in some examples you can then cancel these new fractions down to get simpler fractions with the same denominator
eg)
5/6 + 3/8 = (5×8)/(6×8) + (3×6)/(8×6) = 40/48 + 18/48
but both of these fractions can be cancelled down by dividing by 2 whilst keeping the denominator the same to get
20/24 + 9/24 = 29/24
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