Fraction Calculator — Add, Subtract, Multiply, Divide & Simplify (Free)
Calculate with fractions: add, subtract, multiply, divide, simplify, and convert to decimal. Mixed numbers supported. Free, instant.
About Fraction Calculator
A fraction calculator performs the four arithmetic operations on fractions and mixed numbers, simplifies the result to lowest terms, and converts between fractions and decimals — showing each step of the work so the math is auditable. The ZTools Fraction Calculator handles proper fractions (3/4), improper fractions (7/4), and mixed numbers (1 3/4); supports add, subtract, multiply, and divide; auto-simplifies via the greatest common divisor; and renders the worked equation step-by-step for homework checks and teaching.
Use cases
- Math homework — fractions chapter. Students enter problems like 3/4 + 5/6, see the answer 19/12 (or 1 7/12 mixed), AND read the work: common denominator → 9/12 + 10/12 → 19/12 → 1 7/12.
- Cooking and recipe scaling. Doubling a recipe with 3/4 cup of flour: enter 3/4 × 2 → 6/4 → 1 1/2 cups. Halving a recipe with 1/3 tsp salt: 1/3 × 1/2 = 1/6 tsp.
- Construction and woodworking measurements. Subtract 7/16" from 2 1/4" to plan a cut: 2 4/16 − 7/16 = 1 13/16". The calculator handles imperial fractions natively.
- Music theory time signatures and rhythm math. Add note values: a half note (1/2) plus a quarter note (1/4) plus an eighth note (1/8) = 7/8. Useful when checking that a measure adds up.
How it works
- Enter the first fraction. Format: numerator/denominator (3/4) or whole numerator/denominator for mixed (1 3/4). Negative fractions are allowed (-3/4).
- Pick the operation. Add, subtract, multiply, or divide. Each operation uses the standard fraction rules and handles unlike denominators automatically.
- Enter the second fraction. Same format as the first. The calculator updates as you type.
- Read the result and the work. Final answer in both improper-fraction and mixed-number form, plus a decimal equivalent. The step-by-step worked solution is below the answer.
Examples
Input: 3/4 + 5/6
Output: 19/12 = 1 7/12 ≈ 1.583
LCD = 12. 9/12 + 10/12 = 19/12.
Input: 2 1/3 × 3/4
Output: 7/4 = 1 3/4 = 1.75
Convert mixed to improper: 7/3. 7/3 × 3/4 = 21/12 = 7/4.
Input: 5/6 − 1/4
Output: 7/12 ≈ 0.583
LCD = 12. 10/12 − 3/12 = 7/12.
Frequently asked questions
How do I add fractions with different denominators?
Find the least common denominator (LCD), convert each fraction to use it, then add the numerators. 3/4 + 1/6 → LCD 12 → 9/12 + 2/12 = 11/12. The calculator does this automatically and shows each step.
What's the difference between an improper fraction and a mixed number?
An improper fraction has a numerator ≥ denominator (7/4). A mixed number combines a whole and a proper fraction (1 3/4). They're the same value in different forms; the calculator shows both.
How do I simplify a fraction to lowest terms?
Divide both numerator and denominator by their greatest common divisor (GCD). 12/16 → GCD is 4 → 3/4. The calculator simplifies automatically; you can also use the GCD/LCM tool to find the GCD by hand.
Why is multiplying fractions easier than adding them?
Multiplication doesn't need a common denominator — just multiply numerators and denominators directly: 2/3 × 3/4 = 6/12 = 1/2. Addition requires the extra step of finding the LCD.
Can it handle negative fractions?
Yes — prefix the fraction with a minus sign (-3/4 + 1/2 = -1/4). The calculator follows standard sign rules.
Pro tips
- For fast LCD finding: if one denominator divides the other (e.g., 1/2 and 1/8), the larger is the LCD.
- When multiplying, simplify before multiplying — cancel common factors to keep numbers small (e.g., 2/3 × 6/5 → 2/1 × 2/5 = 4/5).
- Convert to decimal with a calculator only after simplifying — rounding early loses precision.
- For repeating decimals (1/3 = 0.333…), keep the fraction form for exact arithmetic.
Reviewed by Ahsan Mahmood · Last updated 2026-05-05 · Part of ZTools.
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