Work Out Any Fraction in Seconds
Type in two fractions and this fraction calculator instantly adds, subtracts, multiplies, or divides them — showing the answer in its lowest terms (fully simplified). No pencil, no scratch paper, no wasted time.
It works for simple fractions like 1/2 + 1/4 and trickier ones like 7/12 − 5/8. Students, parents helping with homework, and anyone splitting a recipe or a bill will find it useful.
How to Use the Fraction Calculator
- Enter the numerator (top number) and denominator (bottom number) for your first fraction.
- Choose your operation: + add, − subtract, × multiply, or ÷ divide.
- Enter the numerator and denominator for your second fraction.
- Hit Calculate. The answer appears instantly, already reduced to lowest terms.
Snippet: The One-Line Rule for Fractions
The golden rule for adding and subtracting fractions: get a common denominator first, then add or subtract the numerators.
Example: 1/2 + 1/3
- Common denominator of 2 and 3 is 6.
- Rewrite: 1/2 = 3/6 | 1/3 = 2/6
- Add the numerators: 3 + 2 = 5
- Result: 5/6 (already in lowest terms)
For multiplication, multiply tops together and bottoms together. For division, flip the second fraction and multiply.
Worked Example: Step by Step
Let's say you need to subtract 3/4 − 2/5.
- Find the common denominator. The lowest common multiple (LCM) of 4 and 5 is 20.
- Convert both fractions. 3/4 = 15/20 | 2/5 = 8/20
- Subtract the numerators. 15 − 8 = 7
- Write the result. 7/20
- Simplify. 7 and 20 share no common factor other than 1, so 7/20 is already in lowest terms.
The calculator handles all five steps above in a fraction of a second.
How It Is Calculated
Here are the four formulas the calculator uses, written in plain terms:
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c) ← flip the second fraction, then multiplyAfter getting the result, the calculator divides both the top and bottom by their GCD (greatest common divisor — the largest number that divides both evenly). That gives you the simplified answer.
| Operation | Example | Result |
|---|---|---|
| Add | 1/3 + 1/6 | 1/2 |
| Subtract | 5/6 − 1/4 | 7/12 |
| Multiply | 2/3 × 3/4 | 1/2 |
| Divide | 3/5 ÷ 9/10 | 2/3 |
Different Ways People Ask the Same Question
You might be looking for one of these — they all use the same four operations:
- Adding fractions with different denominators — needs a common denominator first (the calculator does this automatically).
- Simplifying or reducing a fraction — enter the fraction as numerator/denominator and divide by 1/1; the result comes back simplified.
- Mixed numbers — convert to improper fractions first (e.g. 1½ = 3/2), then use the tool.
- Equivalent fractions — multiply both top and bottom by the same number; the value stays the same.
- Dividing fractions — also called "multiplying by the reciprocal." Flip the second fraction and multiply.
Quick Tips and Common Mistakes
- Never add denominators. 1/4 + 1/4 is 2/4 (= 1/2), not 1/8. The bottom stays the same when the denominators already match.
- Zero denominators are undefined. You cannot divide by zero — leave the denominator field at 1 or higher.
- Negative fractions: enter a minus sign in front of the numerator (e.g. −3/4) when the fraction is negative.
- Always simplify. 4/8 and 1/2 are the same number; the calculator always gives you the reduced form so you don't have to guess.
- Mixed numbers: convert 2¾ to 11/4 before entering it. Multiply the whole number (2) by the denominator (4) and add the numerator (3): 2×4+3 = 11.
Privacy note: All calculations happen directly in your browser. Nothing you type is sent to a server or stored anywhere.
Ready to crunch your numbers? Use the fraction calculator above — it's free, instant, and takes the guesswork out of any rational number arithmetic.