What 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.

Why 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.

How 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).

How 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).

What 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.

MATMathematics

Fraction Calculator

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

Numerator 1

Denominator 1

Operation

Numerator 2

Denominator 2

Try an example

Enter values above to see results

How It Works

Formula

\frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + c \cdot b}{b \cdot d}

\frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - c \cdot b}{b \cdot d}

\frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

\frac{a}{b} \div \frac{c}{d} = \frac{a \cdot d}{b \cdot c}

Where

$a$: Numerator of the first fraction
$b$: Denominator of the first fraction
$c$: Numerator of the second fraction
$d$: 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.

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