Fraction Calculator
It adds, subtracts, multiplies and divides two fractions, then reduces the answer to lowest terms and shows it as a mixed number and a decimal.
3/4 + 2/3
17/12
Simplified
17/12
Before simplifying
17/12
Mixed number
1 5/12
Decimal
1.416667
Percentage
141.67%
Reciprocal
12/17
What it calculates
It adds, subtracts, multiplies and divides two fractions, then reduces the answer to lowest terms and shows it as a mixed number and a decimal.
Why it matters
Fractions turn up in recipes, measurements and schoolwork, and the arithmetic is easy to get wrong — especially the rule that dividing means multiplying by the reciprocal.
Who it's for
Students and parents helping with homework, cooks scaling recipes, and anyone working in imperial measurements.
Formula
- a/b
- First fraction
- c/d
- Second fraction
- GCD
- Greatest common divisor, used to simplify
Worked example
3/4 ÷ 2/3
- 1Dividing means multiplying by the reciprocal
- 23/4 × 3/2 = 9/8
- 39 and 8 share no factor, so it is already simplified
9/8 = 1 1/8 = 1.125
How the fraction calculator works
Addition and subtraction need a common denominator, so both fractions are scaled to b × d before the numerators combine. Multiplication multiplies straight across. Division flips the second fraction and multiplies. Every result is then divided by the greatest common divisor of numerator and denominator to reach lowest terms.
Addition and subtraction need a common denominator, so both fractions are scaled to b × d before the numerators combine. Multiplication goes straight across, and division flips the second fraction first.
Every answer is then divided by the greatest common divisor of its numerator and denominator, which is what puts it in lowest terms.
Common mistakes
- Adding numerators and denominators separately — 1/2 + 1/3 is 5/6, not 2/5.
- Forgetting to flip the second fraction when dividing.
- Leaving an answer unsimplified, which is usually marked wrong.
Tips and best practice
- To compare two fractions quickly, cross-multiply: 3/4 beats 5/7 because 3×7 > 5×4.
- Simplify before multiplying to keep the numbers small.
Frequently asked questions
How do you add fractions with different denominators?
Convert both to a common denominator, add the numerators, then simplify. 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.
How do you divide fractions?
Multiply by the reciprocal of the second fraction: 3/4 ÷ 2/3 becomes 3/4 × 3/2 = 9/8.
What is a mixed number?
A whole number plus a proper fraction. 9/8 is 1 1/8 — one whole and one eighth left over.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 12/18 the GCD is 6, giving 2/3.
What happens if the denominator is zero?
The fraction is undefined — division by zero has no value. The calculator flags it rather than showing infinity.
Related calculators
Methodology & trust
- Formula source
- Standard rational-number arithmetic with GCD reduction.
- Last updated
- 2026-07-28
- Privacy
- Every calculation runs in your browser. No inputs are sent to a server or stored.
- Accessibility
- Keyboard navigable, labeled inputs and WCAG AA color contrast.