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.

According to the National Institute of Standards and Technology and the American Statistical Association, more than 1,000 published arithmetic, statistics, and unit-conversion reference identities appear in textbooks and standards that CalcMesh math tools implement directly. The CalcMesh registry listed 53 calculators across 9 categories as of August 2026. See our methodology for derivation standards and refresh cadence.

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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...).

Worked example, 3/4 + 5/6

Labelled rational-arithmetic scenario:

  • LCD of 4 and 6 is 12 → 9/12 + 10/12 = 19/12.
  • Mixed form: 19/12 = 1 7/12; decimal ≈ 1.5833.
  • Product 3/4 × 5/6 = 15/24 → reduce by 3 → 5/8.
  • Division 3/4 ÷ 5/6 = 3/4 × 6/5 = 9/10.

After you run the numbers

What to do with the results

  • Always reduce by the GCD after operating so equivalent fractions compare cleanly.
  • LCD for add/subtract; multiply numerators/denominators for products; invert the divisor to divide.
  • Mixed numbers are convenience display, the improper fraction is the algebraic form.
  • Zero denominators are undefined; the tool should refuse them rather than invent a value.

Methodology & Assumptions

This fraction tool reduces and combines rationals with cross-product and GCD cancellation on the numerators and denominators you enter. Exact arithmetic is used until a float display is unavoidable; see the assumptions table.

How this divisor node runs

GCD/LCM and fraction tools use Euclidean and cross-product identities. Results are exact for integer inputs within JS safe-integer range. Published domain formulas govern the identities; when an agency updates rates or thresholds we refresh defaults and the page lastmod.

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.

This page identifies the inputs, method, and limitations behind its estimates. CalcMesh does not publish lender, insurer, provider, or plan fee schedules. Any monetary output is calculated from the inputs shown on the page, not a current quote. Compare a fee, rate, or term with the governing agreement or disclosure before a consequential decision. Calculator outputs are not professional advice. Fraction arithmetic here uses the numerators and denominators you enter—reduction steps are computed, not pasted from a reference sheet. See our editorial standards & corrections policy, the methodology behind these numbers, or report a data error.

Catalog graph

Cross the mesh from Fraction Calculator

Rational-arithmetic neighbours rank first; cooking and mortgage bridges follow when recipe scaling or payment fractions share the same denominator logic.

Inputs, defaults, and authoritative sources
Input Default Source / authority
Numerators & denominators Non-zero denominators Rational cross-product + GCD reduction