How to use the fraction calculator
- Choose how many numbers you need (2 to 5). Tick Mixed numbers to enter values like 2 1/3.
- Type each fraction: the numerator (top number) above the line and the denominator (bottom number) below it. In mixed-number mode, the small left box takes the whole number – 2 1/3 is 2, then 1 over 3.
- Pick +, −, × or ÷ between the numbers and press Calculate.
The answer is given in simplest form, as a mixed number when it is bigger than 1, and as a decimal and a percentage, followed by the full working. With three or more numbers, × and ÷ are worked out before + and − (order of operations). Use a minus sign for negative fractions; in a mixed number put it on the whole number (−2 1/3).
How to add and subtract fractions
Fractions can only be added or subtracted when they have the same denominator, so the parts are the same size.
- Find the least common denominator (LCD) – the smallest number both denominators divide into.
- Rewrite each fraction over the LCD by multiplying its top and bottom by the same number.
- Add or subtract the numerators and keep the denominator.
- Simplify, and change an improper fraction to a mixed number.
Example: 3/4 + 5/6. The LCD of 4 and 6 is 12.
\frac{3}{4} + \frac{5}{6} = \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}The general rule, which works without finding the LCD first (simplify at the end):
\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}How to multiply fractions
Multiply the numerators together and the denominators together, then simplify. No common denominator is needed.
\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}Example: 2/3 × 9/10
\frac{2}{3} \times \frac{9}{10} = \frac{18}{30} = \frac{3}{5}How to divide fractions
Keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). Then multiply.
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}Example: 3/4 ÷ 1/2
\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times \frac{2}{1} = \frac{6}{4} = 1\frac{1}{2}Mixed numbers and improper fractions
A mixed number has a whole part and a fraction, like 2 1/3. An improper fraction has a numerator bigger than or equal to its denominator, like 7/3. Change mixed numbers to improper fractions before you calculate:
2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}To go back, divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: 7 ÷ 3 = 2 remainder 1, so 7/3 = 2 1/3.
Simplifying fractions
A fraction is in simplest form when the numerator and denominator have no common factor except 1. Divide both by their greatest common factor (GCF):
\frac{18}{30} = \frac{18 \div 6}{30 \div 6} = \frac{3}{5}Common fractions as decimals
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666… | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 1/10 | 0.1 | 10% |
Worked examples
Frequently asked questions
How do you add fractions with different denominators?
Find the least common denominator, rewrite both fractions over it, then add the numerators. For 1/4 + 1/6 the LCD is 12, so 3/12 + 2/12 = 5/12.
How do you divide fractions?
Flip the second fraction and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2. This is often remembered as "keep, change, flip".
Can I use mixed numbers?
Yes. Tick Mixed numbers at the top of the calculator, then type the whole number in the small left box and the fraction in the stacked boxes. The calculator changes mixed numbers to improper fractions first and shows that step.
Can I add more than two fractions?
Yes. Choose up to 5 numbers and an operation between each pair. Multiplication and division are worked out before addition and subtraction, and all the fractions being added share one common denominator.
How do I enter a negative fraction?
Type a minus sign before the numerator, for example −3 over 4. For a negative mixed number, put the minus sign on the whole number: −2 1/3.
Why is my answer an improper fraction?
When the answer is bigger than 1 it is shown both ways: as an improper fraction in simplest form (19/12) and as a mixed number (1 7/12). Both are correct; use the one your teacher or recipe asks for.
What does the bar over a decimal mean?
It marks digits that repeat forever. 1/3 is 0.333… (a bar over the 3), and 1/7 is 0.142857142857… (a bar over all six digits 142857).