Fraction Calculator

About Fraction Calculator

This fraction calculator performs addition, subtraction, multiplication, and division of fractions with step-by-step solutions. It handles mixed numbers, improper fractions, and automatically simplifies results.

How to Use

Enter whole numbers (optional) and fractions in the input fields
Leave whole number blank or enter 0 if you only have a fraction
Select the operation (+, -, ×, ÷)
Click Calculate to see the result and steps
Results are automatically simplified to lowest terms

Fraction Operations

Adding Fractions

To add fractions, find a common denominator (usually the LCM), adjust numerators, then add.

Example: 1/4 + 1/6
Common denominator: 12
3/12 + 2/12 = 5/12

Subtracting Fractions

Similar to addition - find common denominator, adjust numerators, then subtract.

Example: 3/4 - 1/3
Common denominator: 12
9/12 - 4/12 = 5/12

Multiplying Fractions

Multiply numerators together and denominators together. Simplify the result.

Example: 2/3 × 3/4
(2 × 3) / (3 × 4) = 6/12 = 1/2

Dividing Fractions

Multiply by the reciprocal (flip the second fraction).

Example: 2/3 ÷ 1/4
2/3 × 4/1 = 8/3 = 2 2/3

Fraction Terms

Term	Definition	Example
Numerator	Top number of a fraction	In 3/4, the numerator is 3
Denominator	Bottom number of a fraction	In 3/4, the denominator is 4
Mixed Number	Whole number plus fraction	2 1/3
Improper Fraction	Numerator ≥ denominator	7/3
Proper Fraction	Numerator < denominator	2/3
Equivalent Fractions	Same value, different form	1/2 = 2/4 = 3/6

Simplifying Fractions

To simplify a fraction, divide both numerator and denominator by their Greatest Common Divisor (GCD).

Example: Simplify 12/16
GCD(12, 16) = 4
12 ÷ 4 = 3
16 ÷ 4 = 4
Result: 3/4

Converting Between Forms

Mixed Number to Improper Fraction

Multiply whole number by denominator, add numerator, place over denominator.

Example: 2 3/4
(2 × 4) + 3 = 11
Result: 11/4

Improper Fraction to Mixed Number

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

Example: 11/4
11 ÷ 4 = 2 remainder 3
Result: 2 3/4

Common Fraction Conversions

Fraction	Decimal	Percentage
1/2	0.5	50%
1/3	0.333...	33.33%
1/4	0.25	25%
1/5	0.2	20%
1/8	0.125	12.5%
3/4	0.75	75%
2/3	0.666...	66.67%

Tips for Working with Fractions

Always simplify your final answer to lowest terms
Check if denominators are the same before adding/subtracting
When multiplying, you can cancel common factors before multiplying
Remember: dividing by a fraction = multiplying by its reciprocal
Zero cannot be a denominator (division by zero is undefined)