Fraction Calculator
Add, subtract, multiply and divide fractions and mixed numbers, then see the answer in lowest terms with the steps.
Results are provided as is, for general information. Check anything important before relying on it. See the Terms of Use.
About this tool
Add, subtract, multiply or divide two fractions, mixed numbers or decimals and get the answer in lowest terms, as a mixed number, an exact decimal and a percentage. Each answer lists its steps: the least common denominator for addition and subtraction, the reciprocal for division, and the greatest common divisor used to simplify. Simplify & convert reduces a single fraction, or turns a decimal, repeating decimal or percentage into an exact fraction. Arithmetic uses whole-number numerators and denominators, so there is no floating-point rounding: 0.(3) + 0.(6) is exactly 1.
How it works
a/b ± c/d = (a × L/b ± c × L/d) / L, L = LCD(b, d) a/b × c/d = (a × c) / (b × d) a/b ÷ c/d = a/b × d/c (c ≠ 0) w n/d = (w × d + n) / d Simplify: divide numerator and denominator by GCD
Addition and subtraction rewrite both fractions over the least common denominator (LCD) before combining numerators. Multiplication multiplies straight across, and division multiplies by the reciprocal. Every answer is then divided through by the greatest common divisor (GCD) of its numerator and denominator, so it is in lowest terms. Mixed numbers become improper fractions first.
| Question | Working | Answer |
|---|---|---|
| What is 1/3 + 1/4? | LCD 12: 4/12 + 3/12 | 7/12 |
| What is 1 1/2 + 2 3/4? | 3/2 + 11/4 = 6/4 + 11/4 | 17/4 = 4 1/4 |
| What is 3/4 − 1/6? | LCD 12: 9/12 − 2/12 | 7/12 |
| What is 2/3 ÷ 4/5? | 2/3 × 5/4 = 10/12, GCD 2 | 5/6 |
| Simplify 18/24 | GCD(18, 24) = 6; 18 ÷ 6 = 3, 24 ÷ 6 = 4 | 3/4 |
| What is 0.375 as a fraction? | 375/1000, GCD 125 | 3/8 |
| What is 0.333… (repeating) as a fraction? | Entered as 0.(3): 3/9, GCD 3 | 1/3 |
| What is 5 3/8 + 2 11/16 inches? | 43/8 + 43/16 = 86/16 + 43/16 | 129/16 = 8 1/16 inches |
When to use it
Questions
How do you add fractions with different denominators?
Rewrite both fractions over their least common denominator, add the numerators, then simplify. For 1/3 + 1/4 the least common denominator is 12, so 1/3 = 4/12 and 1/4 = 3/12, and 4/12 + 3/12 = 7/12. Subtraction works the same way with the numerators subtracted.
How do you divide fractions?
Multiply by the reciprocal of the second fraction. 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12, which simplifies to 5/6. Dividing by zero is undefined, so the tool shows an error instead of an answer.
How do I enter a mixed number?
Type the whole number, a space, then the fraction: 2 3/4. A minus sign applies to the whole mixed number, so -1 1/2 means −(1 + 1/2), which is -3/2. Improper answers are shown both as a fraction and as a mixed number, for example 17/4 and 4 1/4.
How do I convert a decimal to a fraction?
Use Simplify & convert. A decimal with n digits after the point is that number over 10^n, then reduced: 0.375 = 375/1000 = 3/8. For a repeating decimal, put the repeating digits in parentheses: 0.(3) is 1/3 and 0.1(6) is 1/6. You can also enter a percentage such as 37.5%.
What do the parentheses in the decimal result mean?
They mark digits that repeat forever. 1/6 is 0.1(6), meaning 0.1666…, and 1/7 is 0.(142857). A rounded value to six decimal places is shown alongside. When the repeating block is longer than 100 digits, the first 100 digits are shown and marked as cut short.
Can I add fractional inch measurements?
Yes. Enter them as mixed numbers: 5 3/8 + 2 11/16 = 129/16, which is 8 1/16 inches. To convert a metric length into a ruler fraction first, use the centimeters to inches converter.