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fraction

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​

  1. Enter the first fraction — Format: numerator/denominator (3/4) or whole numerator/denominator for mixed (1 3/4). Negative fractions are allowed (-3/4).
  2. Pick the operation — Add, subtract, multiply, or divide. Each operation uses the standard fraction rules and handles unlike denominators automatically.
  3. Enter the second fraction — Same format as the first. The calculator updates as you type.
  4. 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

Input: 2 1/3 × 3/4

Output: 7/4 = 1 3/4 = 1.75

Input: 5/6 − 1/4

Output: 7/12 ≈ 0.583

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.

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.

Try it now​

The full fraction runs in your browser at https://ztools.zaions.com/fraction — no signup, no upload, no data leaves your device.

Open the tool ↗

Last updated: 2026-05-05 · Author: Ahsan Mahmood · Edit this page on GitHub