Fraction Calculator – Add, Subtract, Multiply, Divide & Simplify Fractions

What is a Fraction?

A fraction represents a part of a whole quantity or a ratio between two integers. Think of a pie sliced into equal portions: the denominator (bottom number) represents the total number of equal slices in the pie, while the numerator (top number) represents how many slices you currently have.

In a proper fraction, the numerator is smaller than the denominator (e.g. 3/4). In an improper fraction, the numerator is greater than or equal to the denominator (e.g. 7/4), which can also be written as a mixed number (1 3/4).

How to Perform Fraction Operations

The four basic arithmetic operations each follow distinct algebraic rules:

1. Addition & Subtraction

Fractions must share a common denominator before numerators can be added or subtracted.

a/b + c/d = (a·d + b·c) / (b·d)
Example: 1/2 + 1/3 = (3 + 2) / 6 = 5/6

2. Multiplication

Multiply numerators together and denominators together directly.

(a/b) × (c/d) = (a·c) / (b·d)
Example: 3/4 × 2/3 = 6/12 = 1/2

3. Division (Reciprocal Method)

Multiply the first fraction by the reciprocal (flipped version) of the second.

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a·d) / (b·c)
Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3

4. Simplification (GCD Reduction)

Divide both numerator and denominator by their Greatest Common Divisor.

Simplify: GCD(24, 36) = 12
24 ÷ 12 / 36 ÷ 12 = 2/3

Converting Between Decimals & Fractions

Converting decimals to fractions involves converting the decimal portion into a power-of-10 ratio:

Decimal to Fraction: Count the digits after the decimal point to form the power-of-10 denominator (e.g. 0.375 has 3 digits, giving 375/1000). Reduce by the GCD (125) to get 3/8.
Fraction to Decimal: Perform simple division of the numerator by the denominator (e.g. 3 ÷ 8 = 0.375).

Frequently Asked Questions

How do I add or subtract fractions with different denominators?+

To add or subtract fractions with different denominators, first find a common denominator by calculating the Least Common Multiple (LCM) or multiplying the denominators. Convert both fractions into equivalent fractions with the common denominator, add or subtract the numerators, and simplify the result using the Greatest Common Divisor (GCD).

How do I convert a decimal into a fraction?+

To convert a decimal into a fraction, place the decimal numbers over a power of 10 corresponding to the number of decimal places (for example, 0.75 becomes 75/100). Then, simplify the fraction by dividing both numerator and denominator by their Greatest Common Divisor (75/100 reduces to 3/4).

How do I simplify a fraction to lowest terms?+

To simplify a fraction to lowest terms, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both numbers by that GCD. For example, for 24/36, the GCD is 12. Dividing 24 and 36 by 12 gives 2/3.

How do I divide one fraction by another?+

To divide by a fraction, multiply by its reciprocal (flip the second fraction). For example, (1/2) ÷ (3/4) becomes (1/2) × (4/3) = 4/6, which simplifies to 2/3.

What is the difference between an improper fraction and a mixed number?+

An improper fraction has a numerator that is greater than or equal to its denominator (e.g. 7/4). A mixed number combines a whole integer and a proper fraction (e.g. 1 3/4). Both represent the exact same numeric value.

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