Fraction Calculator

Complete fraction toolkit

Six exact fraction tools on one page

Choose the form that matches your question. Every calculator stays visible, keeps its own inputs, and shows the exact result with real calculation steps.

Approved exact calculationFormula 1.0.0. Integer strings stay exact through BigInt arithmetic; repeating decimals are detected from remainder cycles.

Fraction arithmetic

Fraction Calculator

Add, subtract, multiply, or divide two fractions and reduce the exact answer.

First fraction

NumeratorSigned whole-number numerator.

DenominatorSigned whole-number denominator; not zero.

OperationChoose addition, subtraction, multiplication, or division.

Second fraction

NumeratorSigned whole-number numerator.

DenominatorSigned whole-number denominator; not zero.

Answer23/30

Mixed-number form: 23/30
Decimal: 0.7(6)

a/b ± c/d = (ad ± bc)/bd

How it was calculated7 exact steps · View the full solution

Start with the entered fractions5/12 + 7/20
Check and reduce each input5/12 is already in lowest terms. 7/20 is already in lowest terms.
Find the least common denominatorgcd(12, 20) = 4; LCM = (12 ÷ 4) × 20 = 60
Rewrite both fractions with the least common denominator5/12 × 5/5 = 25/60; 7/20 × 3/3 = 21/60
Add the numerators25/60 + 21/60 = 46/60
Reduce the result to lowest termsgcd(46, 60) = 2; (46 ÷ 2)/(60 ÷ 2) = 23/30
Write the exact answer and decimal formExact fraction: 23/30; Decimal: 0.7(6)

Reduce to lowest terms

Simplify Fractions Calculator

Simplify an ordinary fraction or mixed number and see its improper form and GCD.

Whole numbers and fractions

Mixed Number Calculator

Use signed mixed numbers, proper or improper fractions, or whole numbers.

First mixed numberExamples: 1 1/2, -3/5, or 4.

OperationChoose addition, subtraction, multiplication, or division.

Second mixed numberExamples: 2 2/3, 5/8, or 4.

Answer4

Exact fraction: 4/1
Decimal: 4

w n/d = (wd + n)/d before the selected operation

How it was calculated7 exact steps · View the full solution

Start with the entered mixed numbers1 1/2 × 2 2/3
Convert the first mixed number to an improper fraction1 1/2 = (1 × 2 + 1)/2 = 3/2
Convert the second mixed number to an improper fraction2 2/3 = (2 × 3 + 2)/3 = 8/3
Cancel common factors before multiplyinggcd(3, 3) = 3; gcd(8, 2) = 2
Rewrite the fractions after cancellation3/2 × 8/3 = 1/1 × 4/1
Multiply the remaining numerators and denominators(1 × 4) / (1 × 1) = 4/1
Write the exact answer and decimal formExact fraction: 4/1; Whole or mixed-number form: 4; Decimal: 4

Exact finite-decimal conversion

Decimal to Fraction Calculator

Convert the characters you enter directly to a reduced fraction without floating-point rounding.

Terminating or repeating decimal

Fraction to Decimal Calculator

Divide exactly and identify a repeating block with parentheses when one exists.

Exact large-integer arithmetic

Big Number Fraction Calculator

Use long numerators or denominators without sending them through JavaScript Number.

First fraction

NumeratorSigned whole-number numerator.

DenominatorSigned whole-number denominator; not zero.

OperationChoose addition, subtraction, multiplication, or division.

Second fraction

NumeratorSigned whole-number numerator.

DenominatorSigned whole-number denominator; not zero.

Answer1/4

Mixed-number form: 1/4
Decimal: 0.25

up to 240 digits per integer · exact BigInt cross-products and GCD

How it was calculated6 exact steps · View the full solution

Start with the entered fractions123456789012345678901234567891/987654321098765432109876543211 × 987654321098765432109876543211/493827156049382715604938271564
Check and reduce each input123456789012345678901234567891/987654321098765432109876543211 is already in lowest terms. 987654321098765432109876543211/493827156049382715604938271564 is already in lowest terms.
Cancel common factors before multiplyinggcd(123456789012345678901234567891, 493827156049382715604938271564) = 123456789012345678901234567891; gcd(987654321098765432109876543211, 987654321098765432109876543211) = 987654321098765432109876543211
Rewrite the fractions after cancellation123456789012345678901234567891/987654321098765432109876543211 × 987654321098765432109876543211/493827156049382715604938271564 = 1/1 × 1/4
Multiply the remaining numerators and denominators(1 × 1) / (1 × 4) = 1/4
Write the exact answer and decimal formExact fraction: 1/4; Decimal: 0.25

Exact fraction kitchen

Scale a recipe while keeping fractional quantities exact

Fractions preserve a part-to-whole relationship that a prematurely rounded decimal can blur. A recipe provides a practical audit trail: normalize mixed numbers, choose the operation, use compatible denominators where needed, and simplify only after the value is secure.

Step-by-step guide · Exact fraction kitchen

The flour example exposes every structural fraction step

Equivalent form: a/b = ka/kb for nonzero k and b
Unlike-denominator sum: Rewrite both terms over a common denominator
Division rule: Multiply by the reciprocal of a nonzero divisor

Normalize mixed notation
Convert a mixed number by multiplying the whole part by the denominator and adding the numerator: 1 3/4 = (1×4+3)/4 = 7/4. Keep the original unit attached.
Build equivalent twelfths
Because 12 is divisible by both 4 and 3, multiply 7/4 by 3/3 and 2/3 by 4/4. Multiplying numerator and denominator by the same nonzero number changes the notation, not the value.
Add and reduce at the end
Combine 21/12 + 8/12 as 29/12. Since 29 and 12 share no factor above 1, the improper fraction is already reduced; 2 5/12 is its mixed-number display.

Scale a recipe while keeping fractional quantities exact: Fractions preserve a part-to-whole relationship that a prematurely rounded decimal can blur. A recipe provides a practical audit trail: normalize mixed numbers, choose the operation, use compatible denominators where needed, and simplify only after the value is secure.

Recipe scaling separates measured amounts from serving ratios

Imagine a bread formula that uses 1 3/4 cups of whole-grain flour and 2/3 cup of rye flour per batch. To find the combined flour, first rewrite 1 3/4 as the improper fraction 7/4. The denominators 4 and 3 describe different-sized pieces, so adding the numerators directly would be meaningless. The least common denominator is 12: 7/4 becomes 21/12 and 2/3 becomes 8/12. Their sum is 29/12, or 2 5/12 cups.

That exact total can then be scaled. For 1 1/2 batches, multiply 29/12 by 3/2 to get 87/24, reduce to 29/8, and write 3 5/8 cups. This is a multiplication of quantities, not the same job as comparing ingredient proportions. Use the mixed-number calculator for another recipe expressed in whole-and-fraction form; when an unknown scale factor must satisfy an equation, use the equation solver.

The flour example exposes every structural fraction step

Normalize mixed notation
Convert a mixed number by multiplying the whole part by the denominator and adding the numerator: 1 3/4 = (1×4+3)/4 = 7/4. Keep the original unit attached.
Build equivalent twelfths
Because 12 is divisible by both 4 and 3, multiply 7/4 by 3/3 and 2/3 by 4/4. Multiplying numerator and denominator by the same nonzero number changes the notation, not the value.
Add and reduce at the end
Combine 21/12 + 8/12 as 29/12. Since 29 and 12 share no factor above 1, the improper fraction is already reduced; 2 5/12 is its mixed-number display.

Different fraction operations require different denominator logic

Addition and subtraction need common-sized pieces

A common denominator is essential before numerators can be combined. The smallest convenient denominator is tied to the least common multiple calculator, although any valid common multiple preserves the sum.

Multiplication does not need an LCD

Multiply across numerator and denominator, canceling common nonzero factors when useful. Creating a common denominator first adds work without improving correctness.

Division changes to reciprocal multiplication

For a/b ÷ c/d, require c/d to be nonzero, then calculate a/b × d/c. In a kitchen interpretation, dividing total flour by flour per loaf estimates the number of loaf-equivalents.

Exact fraction output still needs a real-world measurement policy

A zero denominator is undefined. It is not an extremely large fraction and should never be replaced silently with zero or infinity.
Reducing 18/24 to 3/4 preserves value; it does not preserve the original measurement resolution. If 18 of 24 counted items matters, retain that context alongside the simplified fraction.
Kitchen tools have finite markings. An exact answer such as 3 5/8 cups may need conversion to tablespoons or a mass measurement rather than casual decimal rounding.
For whole-number simplification, the greatest common factor calculator explains why numerator and denominator can be divided by the same largest shared factor.

Important limitations

Finite decimal input does not accept exponent or repeating-decimal notation. Exact fraction and mixed-number outputs are authoritative within the stated input bound; nonterminating decimal previews stop after 48 digits when no short repeat cycle has appeared. The calculator does not solve symbolic algebraic fractions.

This formula passed its registered engineering tests and is published under an explicit site-owner policy authorization. No independent expert, QA, editorial, legal, or third-party review is claimed. Verify consequential results with a qualified professional.

Exact fraction kitchen

Scale a recipe while keeping fractional quantities exact

Step-by-step guide · Exact fraction kitchen

The flour example exposes every structural fraction step

Equivalent form: a/b = ka/kb for nonzero k and b
Unlike-denominator sum: Rewrite both terms over a common denominator
Division rule: Multiply by the reciprocal of a nonzero divisor

Normalize mixed notation
Convert a mixed number by multiplying the whole part by the denominator and adding the numerator: 1 3/4 = (1×4+3)/4 = 7/4. Keep the original unit attached.
Build equivalent twelfths
Because 12 is divisible by both 4 and 3, multiply 7/4 by 3/3 and 2/3 by 4/4. Multiplying numerator and denominator by the same nonzero number changes the notation, not the value.
Add and reduce at the end
Combine 21/12 + 8/12 as 29/12. Since 29 and 12 share no factor above 1, the improper fraction is already reduced; 2 5/12 is its mixed-number display.

Recipe scaling separates measured amounts from serving ratios

The flour example exposes every structural fraction step

Normalize mixed notation
Convert a mixed number by multiplying the whole part by the denominator and adding the numerator: 1 3/4 = (1×4+3)/4 = 7/4. Keep the original unit attached.
Build equivalent twelfths
Because 12 is divisible by both 4 and 3, multiply 7/4 by 3/3 and 2/3 by 4/4. Multiplying numerator and denominator by the same nonzero number changes the notation, not the value.
Add and reduce at the end
Combine 21/12 + 8/12 as 29/12. Since 29 and 12 share no factor above 1, the improper fraction is already reduced; 2 5/12 is its mixed-number display.

Different fraction operations require different denominator logic

Addition and subtraction need common-sized pieces

Multiplication does not need an LCD

Multiply across numerator and denominator, canceling common nonzero factors when useful. Creating a common denominator first adds work without improving correctness.

Division changes to reciprocal multiplication

For a/b ÷ c/d, require c/d to be nonzero, then calculate a/b × d/c. In a kitchen interpretation, dividing total flour by flour per loaf estimates the number of loaf-equivalents.

Exact fraction output still needs a real-world measurement policy

A zero denominator is undefined. It is not an extremely large fraction and should never be replaced silently with zero or infinity.
Reducing 18/24 to 3/4 preserves value; it does not preserve the original measurement resolution. If 18 of 24 counted items matters, retain that context alongside the simplified fraction.
Kitchen tools have finite markings. An exact answer such as 3 5/8 cups may need conversion to tablespoons or a mass measurement rather than casual decimal rounding.
For whole-number simplification, the greatest common factor calculator explains why numerator and denominator can be divided by the same largest shared factor.

Normalize mixed notation

Build equivalent twelfths

Add and reduce at the end

Recipe scaling separates measured amounts from serving ratios

The flour example exposes every structural fraction step

Different fraction operations require different denominator logic

Addition and subtraction need common-sized pieces

Multiplication does not need an LCD

Division changes to reciprocal multiplication

Exact fraction output still needs a real-world measurement policy

Important limitations

Normalize mixed notation

Build equivalent twelfths

Add and reduce at the end

Recipe scaling separates measured amounts from serving ratios

The flour example exposes every structural fraction step

Different fraction operations require different denominator logic

Addition and subtraction need common-sized pieces

Multiplication does not need an LCD

Division changes to reciprocal multiplication

Exact fraction output still needs a real-world measurement policy