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Fraction arithmetic
Fractions follow four simple rules. Learn which rule goes with which operation and they stop being scary.
Adding and subtracting
You can only add pieces that are the same size. So make the denominators match first.
13 + 14 = 412 + 312 = 712
13 + 14 = 412 + 312 = 712
Multiplying
Multiply the tops, multiply the bottoms, then simplify.
23 × 35 = 615 = 25
23 × 35 = 615 = 25
Dividing
Keep the first fraction, change ÷ to ×, flip the second fraction.
34 ÷ 12 = 34 × 21 = 64 = 32
34 ÷ 12 = 34 × 21 = 64 = 32
Mixed numbers
Turn mixed numbers into improper fractions first.
2 13 = 73 because 2 × 3 + 1 = 7
2 13 = 73 because 2 × 3 + 1 = 7
Work out 2 13 + 1 34
- Make them improper: 73 + 74
- Common denominator 12: 2812 + 2112
- Add the tops: 4912
- As a mixed number: 49 ÷ 12 = 4 remainder 1, so 4 112
Answer: 4 112
Add or subtract: same denominator first. Multiply: straight across. Divide: flip the second fraction and multiply. Mixed numbers become improper fractions first.
The interactive lesson includes the diagrams for this topic.
Check you have got it
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