worldofcalcsFraction Calculator
34 + 56 = 1912 = 1 712
Common denominator 12: 19/12 before simplifying. Decimal: 1.583333
Adding, subtracting, multiplying and dividing fractions
This calculator works out a + b, a − b, a × b or a ÷ b for two fractions, simplifies the answer, shows it as a mixed number and a decimal, and shows the common denominator used for adding and subtracting. Negative numbers are allowed.
Fraction rules
a/b ± c/d = (a × d′ ± c × b′) ÷ LCD · a/b × c/d = ac/bd · a/b ÷ c/d = ad/bc
To add or subtract, rewrite both fractions over the lowest common denominator (the LCM of b and d), then add or subtract the numerators. To multiply, multiply tops and bottoms. To divide, multiply by the reciprocal of the second fraction. Finally divide top and bottom by their HCF to simplify.
Tips
- Simplify early: cancelling common factors before multiplying keeps the numbers small.
- A fraction is in its simplest form when the HCF of the numerator and denominator is 1.
- To compare fractions, put them over a common denominator or convert them to decimals.
- A mixed number such as 1 7/12 means 1 + 7/12, which is 19/12 as an improper fraction.
Worked example
- 3/4 + 5/6
- LCD of 4 and 6 is 12: 3/4 = 9/12 and 5/6 = 10/12
- 9/12 + 10/12 = 19/12
- As a mixed number: 1 7/12; as a decimal: 1.583333
- 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9
Common fractions as decimals and percentages
Handy conversions to remember.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 | 33.33% |
| 2/3 | 0.6667 | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% |
Recurring decimals are rounded to four places.