Fraction Calculator — Free Add and Subtract Online Tool

About the Fraction Calculator

Working with fractions is a foundational math skill used in cooking, construction, sewing, woodworking, and countless academic subjects. But finding common denominators, simplifying results, and converting between mixed numbers and improper fractions can be tedious and error-prone.

Our fraction calculator handles it all:

• All four operations: Addition, subtraction, multiplication, and division
• Automatic simplification: Reduces results to lowest terms
• Mixed number support: Converts between improper fractions and mixed numbers
• Decimal conversion: Shows the decimal equivalent for every result
• Step-by-step work: See how the calculation is performed

How Fraction Operations Work

Adding Fractions

To add fractions, you need a common denominator:

1. Find the least common denominator (LCD) of the two fractions
2. Convert each fraction to an equivalent fraction with the LCD
3. Add the numerators
4. Keep the denominator the same
5. Simplify if possible

Example: 2/3 + 1/4

• LCD of 3 and 4 is 12
• 2/3 = 8/12, 1/4 = 3/12
• 8/12 + 3/12 = 11/12
• Result: 11/12 (already simplified)

Subtracting Fractions

Same process as addition, but subtract the numerators:

Example: 5/6 - 1/3

• LCD of 6 and 3 is 6
• 1/3 = 2/6
• 5/6 - 2/6 = 3/6
• Simplify: 3/6 = 1/2

Multiplying Fractions

Multiply straight across—no common denominator needed:

1. Multiply the numerators
2. Multiply the denominators
3. Simplify if possible

Example: 2/3 × 3/5

• (2 × 3) / (3 × 5) = 6/15
• Simplify: 6/15 = 2/5

Shortcut: Cancel common factors before multiplying: 2/3 × 3/5 = 2/1 × 1/5 = 2/5

Dividing Fractions

Multiply by the reciprocal of the second fraction:

1. Flip the second fraction (numerator becomes denominator, and vice versa)
2. Change the division sign to multiplication
3. Multiply as usual

Example: 3/4 ÷ 2/5

• 3/4 × 5/2 = (3 × 5) / (4 × 2) = 15/8
• As mixed number: 1 7/8

Simplifying Fractions

To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD):

Example: Simplify 18/24

• GCD of 18 and 24 is 6
• 18 ÷ 6 = 3
• 24 ÷ 6 = 4
• Simplified: 3/4

Converting Between Forms

Improper Fraction to Mixed Number

Divide the numerator by the denominator:

• Quotient = whole number
• Remainder = new numerator
• Denominator stays the same

Example: 17/5

• 17 ÷ 5 = 3 remainder 2
• Mixed number: 3 2/5

Mixed Number to Improper Fraction

1. Multiply the whole number by the denominator
2. Add the numerator
3. Keep the denominator the same

Example: 4 2/7

• (4 × 7) + 2 = 30
• Improper fraction: 30/7

Fraction to Decimal

Divide numerator by denominator:

Example: 3/8

• 3 ÷ 8 = 0.375

Decimal to Fraction

1. Write the decimal as a fraction with denominator 10, 100, 1000, etc.
2. Simplify

Example: 0.625

• 625/1000
• Simplify: 5/8

Real-World Fraction Uses

Scenario	Fraction Application
Cooking	Doubling a recipe that calls for 3/4 cup flour
Woodworking	Cutting a 8 1/2 inch board into 3 equal pieces
Sewing	Adding 5/8 inch seam allowance
Construction	Measuring stud spacing at 16 3/4 inches
Pharmacy	Mixing medication in a 2:3 ratio
Time management	Spending 1/4 of the day on a project

Frequently Asked Questions

What is the difference between a proper and improper fraction?

A proper fraction has a numerator smaller than the denominator (e.g., 3/4). An improper fraction has a numerator equal to or larger than the denominator (e.g., 7/4).

How do I find the least common denominator?

Find the least common multiple (LCM) of the two denominators. For 6 and 8, the multiples are 6, 12, 18, 24... and 8, 16, 24... so the LCD is 24.

Can I cancel when adding fractions?

No. You can only cancel common factors when multiplying fractions. When adding or subtracting, you must find a common denominator first.

What is a reciprocal?

The reciprocal of a fraction is the fraction flipped upside down. The reciprocal of 3/4 is 4/3. A number multiplied by its reciprocal equals 1.

Why do we need common denominators for addition but not multiplication?

Addition combines parts of the same size. You can't directly add 1/3 and 1/4 because the pieces are different sizes. Multiplication is repeated addition or scaling, so the denominators interact through multiplication.

Related Calculators

• Decimal to Fraction Calculator - Convert decimals to fractions
• Percentage Calculator - Convert fractions to percentages
• Average Calculator - Calculate means with fractions
• Scientific Calculator - Advanced calculations with fractions
• Ratio Calculator - Work with proportional relationships