Fraction Calculator - Add, Subtract & Simplify

Calculation

Simplify fractions and add, subtract, multiply, or divide them, with the working shown for each answer. Convert to decimals, mixed numbers, and back.

Select mode

Enter values

View your result

Use mixed numbers (optional)

Fraction results here are exact on the numbers you entered, at any size the fields take; a decimal longer than 15 digits becomes its nearest fraction. The risk is a mistyped fraction rather than a calculation error, and a typo carries straight through to the answer. Double-check what you typed before using it for homework or a recipe.

Formulas and sources

Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.

Fraction to decimal

Fraction to Decimal mode

Dec = N ÷ D
N
the numerator, with the whole part folded in when Use Mixed Numbers is on
D
the denominator, not zero
Dec
the decimal, shown to at most 10 places

A repeating decimal is cut at 10 places with no mark: 1/3 shows as 0.3333333333.

Source: Uses the definition in the Common Core State Standards for Mathematics, 5.NF.B.3 [1]: a/b = a ÷ b.

Decimal to fraction

Decimal to Fraction mode

N/D = Convert decimal to simplest fraction
N
the numerator
D
the denominator

A typed decimal of up to 15 digits is written over its power of ten and reduced, so 0.62 is 62/100, then 31/50. Where a simpler fraction lies within 0.0001 it is shown as "close to". A longer decimal, or one typed with an exponent, gets the nearest fraction instead.

Source: Uses the rule in the Common Core State Standards, 4.NF.C.6 and 4.NF.A.1 [1]. The nearest fraction comes from continued fractions [2]; its tolerances are CalcTrail’s own.

Simplify

Simplify mode

N/D ÷ GCD = Simplified fraction
N
the numerator
D
the denominator, not zero
GCD
the greatest common divisor of N and D, by Euclid’s algorithm

Decimal terms are first scaled to whole numbers by the same power of ten, so 2.5/5 reads as 25/50 and gives 1/2. The sign goes on the numerator.

Source: Uses the equivalent-fractions rule of the Common Core State Standards, 4.NF.A.1 [1], and Euclid’s algorithm as NIST defines it [3].

Add fractions

Add mode

A/B + C/D = ((A × D) + (C × B)) / (B × D)
A/B
the first fraction
C/D
the second fraction

The common denominator is the product of the two, B × D, as the standard prints it; the result is then reduced. A least common denominator gives the same value.

Source: Uses the formula in the Common Core State Standards for Mathematics, 5.NF.A.1 [1]: a/b + c/d = (ad + bc)/bd.

Subtract fractions

Subtract mode

A/B - C/D = ((A × D) - (C × B)) / (B × D)
A/B
the fraction subtracted from
C/D
the fraction taken away

Source: Uses the rule in the Common Core State Standards, 5.NF.A.1 [1], which covers adding and subtracting, with a minus in place of the plus.

Multiply fractions

Multiply mode

A/B × C/D = (A × C) / (B × D)
A/B
the first fraction
C/D
the second fraction

Source: Uses the formula in the Common Core State Standards for Mathematics, 5.NF.B.4.a [1]: (a/b) × (c/d) = ac/bd.

Divide fractions

Divide mode

A/B ÷ C/D = (A × D) / (B × C)
A/B
the fraction divided
C/D
the divisor; C must not be zero

Source: Uses the formula in the Common Core State Standards for Mathematics, 6.NS.A.1 [1]: (a/b) ÷ (c/d) = ad/bc.

Exact arithmetic and mixed numbers

Every mode

Every term is read digit for digit from what you typed and the arithmetic is done on whole numbers of any length, so the answer is exact at every size the fields take. For example, 1/999999999999 + 1/999999999998 is 1999999999997/999999999997000000000002. A mixed number w n/d is read as (w × d + n)/d; Use Mixed Numbers changes how a result is written, never its value.

Source: CalcTrail’s own implementation of the rules above; no publisher.

Figures beside the result

Every mode

Each result also shows its decimal or fraction, the percentage, a bar and a ring, and a grid when the denominator is 20 or less. A result of exactly 0 shows no decimal line.

Source: CalcTrail’s own figures; no publisher.

Sources

  1. National Governors Association Center for Best Practices and Council of Chief State School Officers. Common Core State Standards for Mathematics, standards 4.NF.A.1, 4.NF.C.6, 5.NF.A.1, 5.NF.B.3, 5.NF.B.4.a and 6.NS.A.1. 2010.
  2. National Institute of Standards and Technology. NIST Digital Library of Mathematical Functions, §1.12(ii), eq. 1.12.5. Release 1.2.8, September 15, 2026.
  3. National Institute of Standards and Technology. Dictionary of Algorithms and Data Structures: Euclid’s algorithm. Entry modified March 2, 2015.

What this calculator does not cover

  • Two fractions at a time, and basic conversions. It does not solve fraction word problems or algebraic fraction expressions; for percentage math, see the Percentage Calculator.
  • It does not compare or order fractions, and it writes no repeating-decimal notation.
  • Decimal to Fraction is exact only for a plain decimal of up to 15 digits; past that it gives the nearest fraction.

Sources checked on .

Help

Quick Start Guide

  1. Select mode: Choose what you want to do (Convert to Decimal, Convert to Fraction, Simplify, or an Operations mode like Add/Subtract/Multiply/Divide).
  2. Enter values: Type numerator and denominator for fractions, or a decimal for conversion.
  3. View your result: See the converted, simplified, or calculated result update automatically as you type.
  4. Use mixed numbers (optional): Toggle to show results as mixed numbers (e.g., 1 1/2) instead of an improper fraction.
  5. Copy your result: Copy the fraction or decimal to your clipboard.
  6. Export your results: Save calculations to JSON, CSV, or PDF.

Frequently Asked Questions

Select the 'Fraction to Decimal' operation, enter the numerator and denominator, and the calculator shows the decimal equivalent. For example, 3/4 = 0.75. The result updates automatically as you type. The result also shows the fraction as a percentage, so converting a fraction to a percent is the same step: 3/4 is 0.75 and 75%.

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