Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step working. Includes mixed numbers, simplification, decimal conversions, and arbitrary-precision support for very large integers.

Fraction Calculator

Combine two fractions with any of the four operations.

First fraction

Operation

Second fraction

Mixed Numbers Calculator

Enter each value as a whole number plus a fractional part.

First mixed number

Operation

Second mixed number

Simplify Fractions Calculator

Reduce a fraction to its lowest terms.

Fraction

Decimal to Fraction Calculator

Convert a finite decimal number to a simplified fraction.

Decimal number

Fraction to Decimal Calculator

Convert a fraction to its decimal representation.

Fraction

Big Number Fraction Calculator

Same as the main calculator, but supports arbitrarily large integers.

First numeratorFirst denominatorOperation

Second numeratorSecond denominator

What is a fraction?

A fraction represents a part of a whole. It is written as two numbers separated by a bar — the numerator on top and the denominator below. The denominator says how many equal pieces the whole is cut into; the numerator counts how many of those pieces you have.

A fraction whose numerator is smaller than its denominator (like 3/4) is a proper fraction. When the numerator is greater than or equal to the denominator (like 7/4), it is improper and can also be written as a mixed number such as 1 3/4.

Fractions explained, operation by operation

Each card pairs a plain-English rule with the formula, a small diagram and a worked example — so the concept and the arithmetic sit side by side.

Anatomy of a fraction

The numerator counts the pieces you have; the denominator counts the equal pieces in the whole. Three of four equal slices is written 3/4.

a / b

anumerator (pieces you have)·bdenominator (equal pieces in the whole)

Example

Given

pizza cut into 4

take 3 slices

Substitute

3 / 4

Answer

3/4 (proper)

Adding & subtracting — common denominator first

Only pieces of the same size can be combined. Rewrite each fraction over a common denominator (LCM keeps numbers small), add or subtract the numerators, then simplify.

a/b ± c/d = (a·d ± c·b) / (b·d)

b·dshared denominator·a·d, c·brewritten numerators

Example

Given

1/2 + 2/3

Substitute

3/6 + 4/6

Answer

7/6 = 1 1/6

Multiplying — straight across

Multiplication needs no common denominator. Multiply the numerators for the new top, multiply the denominators for the new bottom, then reduce.

a/b × c/d = (a·c) / (b·d)

a·cproduct of numerators·b·dproduct of denominators

Example

Given

2/5 × 3/4

Substitute

(2·3) / (5·4) = 6/20

Answer

3/10

Dividing — multiply by the reciprocal

Dividing by c/d is the same as multiplying by d/c. Flip the second fraction upside down, then multiply straight across as usual.

a/b ÷ c/d = a/b × d/c

d/creciprocal of the divisor

Example

Given

3/4 ÷ 2/5

Substitute

3/4 × 5/2 = 15/8

Answer

15/8 = 1 7/8

Simplifying — divide by the GCF

A fraction is in lowest terms when the numerator and denominator share no factor above 1. Find their greatest common factor (GCF) and divide both sides by it.

a/b = (a÷g) / (b÷g)

g = GCF(a

ggreatest common factor of a and b

Example

Given

18/24

Substitute

GCF = 6 → 18÷6 / 24÷6

Answer

3/4

Converting between fractions and decimals

To convert a fraction to a decimal, divide numerator by denominator. To convert a finite decimal, use a power of 10 as the denominator based on the digits after the point, then simplify by the GCF.

0.d₁d₂…dₙ = (digits) / 10ⁿ

nnumber of decimal places

Example

Given

0.375

Substitute

375/1000

GCF = 125

Answer

3/8

Features of this calculator

Six tools in one page — main calculator, mixed numbers, simplify, decimal↔fraction, and a big-integer mode.
Full step-by-step working for every operation (common denominator, product, reciprocal, GCF reduction).
Auto-simplifies every result to lowest terms and shows both improper and mixed-number forms.
Handles arbitrarily large numerators and denominators via the big-number mode — no precision loss.
Copy any answer or download the result panel as a PNG for notes and homework.
Keyboard-friendly inputs with clear validation for zero denominators and malformed entries.

Frequently asked questions

+How do I add fractions with different denominators?

Rewrite each fraction with a common denominator (the product of the two denominators always works, or use the least common multiple to keep numbers smaller), add the numerators, keep the denominator, then simplify. For example 1/2 + 2/3 becomes 3/6 + 4/6 = 7/6.

+What is a mixed number?

A mixed number combines a whole number and a proper fraction, like 1 3/4. It represents the same value as the improper fraction 7/4 — you can convert between the two by multiplying the whole number by the denominator and adding the numerator.

+How do I simplify a fraction to lowest terms?

Find the greatest common factor (GCF) of the numerator and denominator, then divide both by that GCF. For example 18/24 has GCF 6, so it simplifies to 3/4. This calculator does this automatically for every result.

+How do I divide fractions?

Multiply the first fraction by the reciprocal of the second (flip the second fraction upside down, then multiply straight across). For example 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8.

+How do I convert a decimal to a fraction?

Count the digits after the decimal point, write the number without the point as the numerator, and use 10 raised to that count as the denominator, then simplify. 0.375 has three decimal places, so it becomes 375/1000 = 3/8.

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