CalcLibrary

Fraction Calculator

Add, subtract, multiply, or divide two fractions. See the result as a simplified fraction, a decimal, and a mixed number.

Examples

Add a half and a quarter

Decimal value
0.75
Numerator (simplified)
3
Denominator (simplified)
4
Mixed number
3/4

Simplified result: 3/4 (≈ 0.7500).

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Examples

How It Works

Formula

ab+cd=a⋅d+c⋅bb⋅d\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + c \cdot b}{b \cdot d}

ab−cd=a⋅d−c⋅bb⋅d\frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - c \cdot b}{b \cdot d}

ab×cd=a⋅cb⋅d\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

ab÷cd=a⋅db⋅c\frac{a}{b} \div \frac{c}{d} = \frac{a \cdot d}{b \cdot c}

Variables

aa

Numerator of the first fraction

bb

Denominator of the first fraction

cc

Numerator of the second fraction

dd

Denominator of the second fraction

Enter two fractions and pick an operation. The calculator combines them with the standard rule for that operation, then divides numerator and denominator by their greatest common divisor (GCD) to give the simplest form. Sign stays on the numerator; the denominator is always positive.

Frequently Asked Questions

01What is a proper vs improper fraction?
A proper fraction has |numerator| smaller than the denominator (e.g. 3/4). An improper fraction has |numerator| ≥ denominator (e.g. 5/4). Improper fractions can be rewritten as a mixed number, like 1 1/4.
02Why simplify the result?
Simplifying divides numerator and denominator by their greatest common divisor (GCD), giving the smallest equivalent form. 6/8 simplifies to 3/4 — same value, easier to read.
03How do I convert a decimal to a fraction?
Write the decimal as a fraction over a power of 10 (0.75 = 75/100), then simplify by dividing top and bottom by their GCD (75/100 = 3/4).
04How do I add fractions with different denominators?
Find a common denominator (the product of the two works, then simplify). Multiply each numerator by the other denominator and add: a/b + c/d = (a·d + c·b) / (b·d).
05What are common mistakes when multiplying fractions?
A typical mistake is finding a common denominator first — you do not need one to multiply. Just multiply numerators together and denominators together, then simplify.

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