Fraction Calculator

Understanding Fractions

A fraction represents a part of a whole, written as one number over another separated by a line. The top number (numerator) represents how many parts you have, while the bottom number (denominator) represents how many equal parts make up the whole.

Types of Fractions

Proper Fractions

The numerator is smaller than the denominator, representing a value less than 1. Examples: 1/2, 3/4, 5/8.

Improper Fractions

The numerator is equal to or larger than the denominator, representing a value of 1 or more. Examples: 5/4, 7/3, 9/9.

Mixed Numbers

A combination of a whole number and a proper fraction. Examples: 1 1/2, 2 3/4, 5 1/8. This calculator accepts mixed numbers and can convert between formats.

1. Addition & Subtraction (Cross-Multiplication Formula)

(a × d) ± (b × c)b × d

2. Multiplication Formula

a × cb × d

3. Division (Reciprocal Flip Formula)

a × db × c

Step-by-Step Calculation Breakdown

Example 1: Adding Different Denominators (1/3 + 1/4)

(1 × 4) + (1 × 3)3 × 4

4 + 312

712

Example 2: Multiplying Fractions (2/3 × 3/4)

2 × 33 × 4

612

Converting Between Formats

Mixed to Improper

Multiply whole number by denominator, add numerator, keep denominator.

2 3/4 = (2×4 + 3)/4 = 11/4

Improper to Mixed

Divide numerator by denominator. Quotient is whole, remainder is numerator.

11/4 = 11÷4 = 2 remainder 3 = 2 3/4

Fraction to Decimal

Divide numerator by denominator.

3/4 = 3 ÷ 4 = 0.75
1/3 = 1 ÷ 3 = 0.333...

Frequently Asked Questions

How do I add fractions with different denominators?

To add fractions with different denominators: 1) Find the Least Common Denominator (LCD) - the smallest number both denominators divide into evenly. 2) Convert each fraction to an equivalent fraction with the LCD. 3) Add the numerators and keep the LCD. 4) Simplify if possible. Example: 1/3 + 1/4 → 4/12 + 3/12 = 7/12.

How do I multiply fractions?

Multiplying fractions is straightforward: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Then simplify if possible. Example: 2/3 × 3/4 = 6/12 = 1/2. You can also cross-cancel before multiplying to make simplification easier.

How do I divide fractions?

To divide fractions, multiply by the reciprocal (flip) of the second fraction. 'Keep, Change, Flip': Keep the first fraction, change ÷ to ×, flip the second fraction. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

What is a mixed number and how do I convert it?

A mixed number has a whole number and a fraction (e.g., 2 1/3). To convert to an improper fraction: multiply the whole number by the denominator, add the numerator, keep the same denominator. 2 1/3 = (2×3 + 1)/3 = 7/3. To convert back: divide numerator by denominator—quotient is the whole number, remainder is the new numerator.

How do I simplify (reduce) a fraction?

To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides both evenly. Example: 12/18 → GCD is 6 → 12÷6 / 18÷6 = 2/3. A fraction is fully simplified when the GCD of numerator and denominator is 1.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions result in repeating decimals (1/3 = 0.333...). To convert a decimal to a fraction, count decimal places and use that as the denominator power of 10, then simplify (0.75 = 75/100 = 3/4).

Fraction Inputs

Solution Steps