Calculate with fractions
To multiply two fractions together, simply multiply the numerators (top bits), and then the denominators (bottom bits), separately.
e.g. 3/2 x 4/5 = 12/10
To divide two fractions, first take the reciprocal of the second fraction (flip it) then turn the divide sign into a multiply sign.
e.g. 3/2 ÷ 4/5 = 3/2 x 5/4 = 15/8
Addition and Subtraction (Same Denominator)
To add or subtract two fractions if the denominators are the same, just add or subtract the numerators, and put them over the same denominator. Think of it as saying “If I start with 2 sevenths, and I add 3 sevenths to that, how many sevenths do I get by the end?”
e.g. 2/7 + 3/7 = 5/7
2/7 – 3/7 = -1/7
Addition (Different Denominators)
When adding fractions which have different denominators we must firstly find a common denominator, this will make it easier for the addition to take place.
Example: 1/3 + 1/6
So, we can multiply 1/3 by 2/2 to give use 2/6 (as we know 1/3 is equal to 2/6 so we are still working with the same number even if it seems to look different). Now all we have to do is add our new fraction 2/6 to our original fraction 1/6 which equals = 3/6.
We can simplify this fraction even further by dividing our answer by 3/3 since both our numerator and denominator are divisible by 3:
which leaves us with 1/2, which is are final answer.
Look at another example below where we need to make sure that the numerators are the same:
2/3 + 2/9
Must now find the common denominator
2/3 x 3/3 = 6/9
Now we can add our new fraction to our original fraction
6/9 + 2/9 = 8/9
Our final answer is 8/9
Subtraction (Different Denominators)
We must follow the same rule of finding the common denominator when we subtract fractions which have different denominators, but this time rather than adding the fractions together we must obviously subtract them.
1/2 – 5/12 = ?
Must find common denominators…
1/2 x 6/6 = 6/12
5/12 x 1/1 = 5/12
Now we can subtract them
6/12 – 5/12 = 1/12
So 1/12 is our final answer
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