Fraction Calculator — Add, Subtract, Multiply & Divide Fractions

Fraction Calculator — Overview

Fractions represent parts of a whole: 1/2 (one-half), 3/4 (three-fourths), 5/8 (five-eighths). Many people find fractions confusing compared to decimals, but they're essential for cooking (½ cup flour), construction (3/4 inch bolt), engineering (5/32 tolerance), and mathematics.

The challenge with fractions: adding 1/3 + 1/4 isn't as simple as 1/7. You need a common denominator. Multiplying is easier (2/3 × 3/4 = 6/12 = 1/2). Dividing requires flipping the second fraction. Most calculators show decimals; this one works with fractions directly, showing results in simplified form.

This calculator handles: (1) add, subtract, multiply, divide fractions, (2) simplify fractions to lowest terms, (3) convert fractions to decimals, (4) convert decimals to fractions, (5) work with mixed numbers (2 3/4), (6) find common denominators, and (7) compare fractions.

Fraction Calculator

What Are Fractions? — Parts of a Whole

Fraction Definition: A number representing a part of a whole. Consists of numerator (top, how many parts) and denominator (bottom, how many parts in total).

Example: A pizza cut into 8 slices. You eat 3 slices. That's 3/8 of the pizza (3 slices out of 8 total).

Parts of a Fraction:

• Numerator: Top number (how many parts you have)
• Denominator: Bottom number (how many equal parts in total)
• Fraction Bar: Line between numerator and denominator (means "divide")

Types of Fractions:

• Proper Fraction: Numerator < Denominator. 3/4, 1/2 (less than 1)
• Improper Fraction: Numerator ≥ Denominator. 5/4, 7/3 (equal to or more than 1)
• Mixed Number: Whole number + fraction. 1 3/4 (one and three-fourths)
• Equivalent Fractions: Different fractions with same value. 1/2 = 2/4 = 3/6
• Simplified Fraction: Fraction in lowest terms. 6/8 simplified = 3/4

Fraction Operations Explained

Step-by-Step Fraction Operations

Example 1: Add 1/3 + 1/4

Step 1: Find Common Denominator

Denominators are 3 and 4. LCD = 12 (3 × 4)

Step 2: Convert Fractions

1/3 = 4/12 (multiply numerator and denominator by 4)

1/4 = 3/12 (multiply numerator and denominator by 3)

Step 3: Add Numerators

4/12 + 3/12 = 7/12

Step 4: Check if Simplifiable

GCD(7, 12) = 1, so 7/12 is already simplified.

Example 2: Multiply 2/3 × 3/4

Step 1: Multiply Numerators

2 × 3 = 6

Step 2: Multiply Denominators

3 × 4 = 12

Step 3: Write Result

6/12

Step 4: Simplify

GCD(6, 12) = 6, so 6/12 ÷ 6/6 = 1/2

Example 3: Divide 2/3 ÷ 3/4

Step 1: Flip Second Fraction (Reciprocal)

3/4 → 4/3

Step 2: Multiply

2/3 × 4/3 = 8/9

Step 3: Check if Simplifiable

GCD(8, 9) = 1, so 8/9 is already simplified.

Finding Common Denominators (LCD)

To add or subtract fractions with different denominators, you need a common denominator. The LCD (Least Common Denominator) is the smallest number that all denominators divide into evenly.

Method 1: List Multiples

Find LCD of 3 and 4:

• Multiples of 3: 3, 6, 9, 12, 15, 18...
• Multiples of 4: 4, 8, 12, 16, 20...
• First common: 12 = LCD

Method 2: Prime Factorization

Find LCD of 12 and 18:

• 12 = 2² × 3
• 18 = 2 × 3²
• LCD = 2² × 3² = 4 × 9 = 36

Method 3: For Two Numbers

LCD = (num1 × num2) ÷ GCD(num1, num2)

Real-World Fraction Examples

Example A: Cooking (Adding Fractions)

Recipe calls for 1/3 cup flour + 1/4 cup sugar. How much total?

• 1/3 + 1/4 = 4/12 + 3/12 = 7/12 cup total
• Real-world: you'd measure about 3/4 cup (7/12 ≈ 0.583, close to 2/3)

Example B: Construction (Multiplying Fractions)

A beam is 3/4 inch thick. You need to cut it in half. What's the new thickness?

• 3/4 × 1/2 = 3/8 inch
• Your saw blade has thickness, so real measurement ≈ 3/8 inch

Example C: Dividing Pizza (Dividing Fractions)

You have 3/4 of a pizza and want to divide it equally among 3 friends. How much does each get?

• 3/4 ÷ 3 = 3/4 × 1/3 = 3/12 = 1/4 pizza per friend

Example D: Comparing Fractions (Which is More?)

Is 5/8 or 3/5 larger?

• Convert to decimal: 5/8 = 0.625, 3/5 = 0.600
• Or use common denominator: 5/8 = 25/40, 3/5 = 24/40
• 5/8 is slightly larger

Glossary

• Fraction: Number representing part of a whole (numerator/denominator)
• Numerator: Top number of a fraction (how many parts)
• Denominator: Bottom number of a fraction (parts in total)
• Proper Fraction: Numerator < denominator (less than 1)
• Improper Fraction: Numerator ≥ denominator (1 or more)
• Mixed Number: Whole number + fraction (e.g., 2 3/4)
• Equivalent Fractions: Different fractions with same value (1/2 = 2/4)
• Simplified Fraction: Fraction reduced to lowest terms
• GCD (Greatest Common Divisor): Largest number dividing both numerator and denominator
• LCD (Least Common Denominator): Smallest denominator all fractions share
• Reciprocal: Fraction flipped upside down (3/4 → 4/3)

Frequently Asked Questions

Related Calculators

• Decimal to Fraction Calculator — Convert decimals to fractions
• Percentage Calculator — Calculate percentages (related to fractions)
• Average Calculator — Find average of numbers
• Ratio Calculator — Compare quantities using ratios