The four fraction rules
| Operation | Rule | Example |
|---|---|---|
| Add | Use a common denominator, then add the numerators | 2/3 + 3/4 = 8/12 + 9/12 = 17/12 |
| Subtract | Use a common denominator, then subtract the numerators | 3/4 − 2/3 = 9/12 − 8/12 = 1/12 |
| Multiply | Multiply the tops and multiply the bottoms | 2/3 × 3/4 = 6/12 = 1/2 |
| Divide | Multiply by the reciprocal of the second fraction | 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9 |
Worked example: 2/3 + 3/4. The lowest common denominator of 3 and 4 is 12, so 2/3 = 8/12 and 3/4 = 9/12. Adding gives 17/12, which is the mixed number 1 5/12 or about 1.4167.
Simplifying a fraction
Divide the numerator and denominator by their greatest common divisor (GCD). For 6/12 the GCD is 6, so 6/12 = 1/2. The calculator always simplifies its answer and uses the lowest common denominator when adding and subtracting, which keeps the numbers small.
Mixed numbers
To work with a mixed number, first turn it into an improper fraction: multiply the whole number by the denominator and add the numerator. 2 1/4 = (2 × 4 + 1)/4 = 9/4. The calculator does this for you and shows the answer both ways.
Pro-tip: before multiplying, cancel any common factors between a top and a bottom number. In 4/9 × 3/8, cancel 4 with 8 and 3 with 9 to get 1/3 × 1/2 = 1/6 without large numbers.
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator, rewrite each fraction with it, then add the numerators. 2/3 + 3/4 = 8/12 + 9/12 = 17/12.
How do I divide fractions?
Flip the second fraction and multiply. 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number result is the whole part and the remainder goes over the original denominator: 17/12 = 1 5/12.
How do I turn a fraction into a decimal?
Divide the numerator by the denominator. 17 ÷ 12 = 1.41666…, which rounds to 1.4167.