Math calculator

Fraction Calculator, Add, Subtract, Multiply & Divide with Steps

Add, subtract, multiply, and divide fractions with step-by-step solutions. Automatically simplifies results and converts to mixed numbers.

Published by · Reviewed against primary-source formulas

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Result (Fraction)

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Decimal Equivalent

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Step-by-Step Solution

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How CalcMesh works with fractions

We add, subtract, multiply and divide fractions over a common denominator and then reduce the result to lowest terms using the greatest common divisor, the procedure standard in arithmetic.

We also convert between improper fractions, mixed numbers and decimals; the reduction algorithm we use is described in our methodology.

How Fractions Work

Parts of a Fraction

A fraction has two parts: the numerator (top number, representing parts you have) and the denominator (bottom number, representing total equal parts).

Addition & Subtraction

You need a common denominator to add or subtract fractions. Multiply each fraction so they share the same bottom number, then add or subtract the top numbers.

Multiplication

Multiply numerators together and denominators together. This is the simplest fraction operation: a/b × c/d = (a×c) / (b×d).

Division

Flip the second fraction (take its reciprocal) and multiply: a/b ÷ c/d = a/b × d/c.

Simplifying Fractions

Find the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divide both by it. For example:

  • 12/18: GCD(12, 18) = 6 → 2/3
  • 8/20: GCD(8, 20) = 4 → 2/5
  • 15/25: GCD(15, 25) = 5 → 3/5

Converting to Decimals

Divide the numerator by the denominator. Some fractions give exact decimals (1/4 = 0.25), while others repeat (1/3 = 0.333...).

Methodology & Assumptions

This calculator implements standard formulas drawn from primary-source authorities. Values are point-in-time estimates; consult a licensed professional for high-stakes decisions. See the per-input definitions and source citations below.

How this works

Computations are deterministic and run client-side, no inputs leave your browser. Formulas are derived from standard published formulas for the calculator's domain (mortgage, taxes, energy, conversions, etc.). When the underlying agency publishes updated rates or thresholds we refresh defaults and update the page's lastmod timestamp.

Frequently Asked Questions

How do you add fractions with different denominators?
To add fractions with different denominators, first find a common denominator by multiplying the two denominators together (or finding the least common multiple). Then convert each fraction so they share that denominator, add the numerators, and simplify the result. For example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
How do you simplify a fraction?
To simplify (or reduce) a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 8/12: the GCD of 8 and 12 is 4, so 8/12 = (8÷4)/(12÷4) = 2/3.
What is the difference between fractions and decimals?
Fractions represent a part of a whole as a ratio of two integers (like 3/4), while decimals represent the same value using place values after a decimal point (like 0.75). To convert a fraction to a decimal, divide the numerator by the denominator. Some fractions produce repeating decimals (like 1/3 = 0.333...).
How do you multiply and divide fractions?
To multiply fractions, multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/4 = 6/12 = 1/2. To divide fractions, flip the second fraction (reciprocal) and multiply. For example, 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.

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This page identifies the inputs, method, and limitations behind its estimates. Calculator outputs are not professional advice and should be checked against the relevant primary source for a consequential decision. This calculator's formula and defaults are drawn from standard published sources for its domain, no figure is typed in by an editor. See our editorial standards & corrections policy, the methodology behind these numbers, or report a data error.

Inputs, defaults, and authoritative sources
Input Default Source / authority
All inputs Domain-typical defaults Editorial methodology, CalcMesh 2026