Working with fractions
Equivalent fractions and simplifying
Multiplying or dividing the top and the bottom by the same number gives an equal fraction: 3/4 = 6/8 = 15/20.
To simplify, divide both by their highest common factor: 18/24 = 3/4 (÷ 6). A fraction is in its simplest form when the top and bottom have no common factor but 1.
To compare or order fractions, write them over a common denominator: 2/3 = 8/12 and 3/4 = 9/12, so 3/4 is bigger.
Adding and subtracting
You can only add fractions with the same denominator.
Change them first.
- 2/3 + 1/4
- common denominator 12: 8/12 + 3/12
- = 11/12
Never add the bottoms: 2/3 + 1/4 is not 3/7. With mixed numbers, change them to improper fractions first, especially when subtracting: 4 1/6 − 1 3/4 = 25/6 − 7/4 = 50/12 − 21/12 = 29/12 = 2 5/12.
A fraction of an amount
Divide by the bottom, multiply by the top.
3/5 of 45 km: 45 ÷ 5 = 9, then 9 × 3 = 27 km.
To write 18 out of 48 as a fraction, put the part over the whole and simplify: 18/48 = 3/8.
Check with the fraction calculator
Enter 2/3 + 1/4 and compare the steps with the working above. Then try 4 1/6 − 1 3/4 and see how it changes the mixed numbers into improper fractions first.
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