Fraction Calculator - Add, Subtract, Multiply & Divide Fractions

Free fraction calculator to add, subtract, multiply, and divide fractions. Simplify fractions to lowest terms, convert to decimals, and display mixed numbers.

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Fraction Calculator

Free fraction calculator to add, subtract, multiply, and divide fractions. Simplify fractions to lowest terms, convert to decimals, and display mixed numbers.

iAbout This Calculator

Working with fractions can be challenging, but our free fraction calculator makes it easy. Whether you need to add, subtract, multiply, or divide fractions, this tool handles all the math for you. It automatically finds the common denominator, performs the calculation, simplifies the result to its lowest terms, and converts improper fractions to mixed numbers. Perfect for students learning fraction arithmetic, teachers preparing lessons, or anyone who needs quick and accurate fraction calculations. Simply enter your fractions and get instant results with step-by-step explanations.

?How to Use

1
Select the operation you want to perform: add, subtract, multiply, or divide.
2
Enter the numerator (top number) and denominator (bottom number) of the first fraction.
3
Enter the numerator and denominator of the second fraction.
4
Click Calculate to see the result.
5
Review the simplified fraction, decimal equivalent, and mixed number (if applicable) in the results.

fFormula

\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

For addition and subtraction, fractions must have a common denominator. For multiplication, multiply numerators together and denominators together. For division, multiply by the reciprocal of the second fraction.

a/b: First fraction (numerator a, denominator b)
c/d: Second fraction (numerator c, denominator d)
LCD: Least Common Denominator (smallest number divisible by both denominators)
GCD: Greatest Common Divisor (used to simplify the result)

Examples

Adding Fractions

Inputs: fraction1: 1/4, fraction2: 1/2, operation: add

3/4

Convert 1/2 to 2/4, then add: 1/4 + 2/4 = 3/4

Subtracting Fractions

Inputs: fraction1: 5/6, fraction2: 1/3, operation: subtract

1/2

Convert to common denominator 6: 5/6 - 2/6 = 3/6 = 1/2

Multiplying Fractions

Inputs: fraction1: 2/3, fraction2: 3/4, operation: multiply

1/2

Multiply numerators and denominators: (2x3)/(3x4) = 6/12 = 1/2

Dividing Fractions

Inputs: fraction1: 3/4, fraction2: 1/2, operation: divide

1 1/2

Multiply by reciprocal: 3/4 x 2/1 = 6/4 = 3/2 = 1 1/2

Use Cases

Math Homework

Help students check their fraction arithmetic homework and understand the step-by-step process.

Cooking & Recipes

Scale recipes up or down by multiplying or dividing ingredient fractions.

Construction & Woodworking

Calculate measurements in fractions of inches for precise cutting and fitting.

Music Theory

Add and compare note durations expressed as fractions of whole notes.

Financial Calculations

Work with fractional shares, percentages, and proportions in business contexts.

Frequently Asked Questions

How do I add fractions with different denominators?

First, find the least common denominator (LCD) of both fractions. Convert each fraction to an equivalent fraction with the LCD. Then add the numerators while keeping the denominator the same. Finally, simplify if possible.

What is a mixed number?

A mixed number has a whole number part and a fraction part, like 2 3/4. It's used when the fraction's numerator is larger than its denominator. Our calculator automatically converts improper fractions to mixed numbers.

How do I multiply fractions?

Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Then simplify the result. For example: 2/3 x 4/5 = 8/15.

Why do we flip the second fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped). This is because division asks 'how many of the second fraction fit in the first?' Multiplying by the reciprocal gives us that answer.

How do I simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 12/18: GCD is 6, so 12/6 = 2 and 18/6 = 3, giving 2/3.

Conclusion

The fraction calculator is an essential tool for anyone working with fractions, from students learning basic arithmetic to professionals needing quick calculations. By providing step-by-step breakdowns, automatic simplification, and multiple result formats, this calculator helps you understand the process while getting accurate answers. Bookmark this page for easy access whenever you need to work with fractions.