Adding and Subtracting Fractions Calculator

Add and subtract fractions with step-by-step solutions and detailed explanations

Calculate Fraction Operations

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Example Calculations

Same Denominators

Addition: 1/8 + 3/8 = 4/8 = 1/2

Subtraction: 5/12 − 2/12 = 3/12 = 1/4

Just add/subtract numerators!

Different Denominators

Addition: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Subtraction: 3/4 − 1/6 = 9/12 − 2/12 = 7/12

Find LCD first!

Mixed Numbers

Addition: 2 1/3 + 1 1/4 = 7/3 + 5/4 = 43/12

Result: 43/12 = 3 7/12

Convert to improper fractions first

Simplification

Before: 6/8 + 4/8 = 10/8

After: 10/8 = 5/4 = 1 1/4

Always simplify the result

Key Rules

1.

Same Denominators

Add/subtract numerators, keep denominator

2.

Different Denominators

Find LCD, then add/subtract

3.

Mixed Numbers

Convert to improper fractions first

4.

Simplify

Reduce to lowest terms

Quick Reference

LCD (Least Common Denominator)

The smallest number divisible by all denominators

GCD (Greatest Common Divisor)

Used to simplify fractions

Mixed → Improper

Multiply whole × denominator + numerator

Improper → Mixed

Divide numerator by denominator

Understanding Fraction Addition and Subtraction

Same Denominators

When fractions have the same denominator, adding or subtracting is straightforward. You simply add or subtract the numerators and keep the denominator the same.

Example:

2/7 + 3/7 = (2+3)/7 = 5/7

Different Denominators

When denominators differ, you must:

  • • Find the Least Common Denominator (LCD)
  • • Convert both fractions to equivalent fractions with the LCD
  • • Add or subtract the new numerators
  • • Simplify the result if possible

Mixed Numbers

To work with mixed numbers, first convert them to improper fractions:

Converting 2 3/4:

2 × 4 + 3 = 11, so 2 3/4 = 11/4

Simplification

Always check if your answer can be simplified by dividing both numerator and denominator by their greatest common divisor (GCD).

Example:

8/12 = (8÷4)/(12÷4) = 2/3