How to Add, Subtract, Multiply and Divide Fractions

Fractions are everywhere - from cooking recipes to construction measurements. Whether you're doubling a recipe or calculating material costs, knowing how to work with fractions is essential.

Our Fraction Calculator handles complex calculations instantly, but understanding the methods helps you verify results and solve problems by hand.

Understanding Fractions

• Numerator: Top number (parts you have)
• Denominator: Bottom number (parts in the whole)
• Proper fraction: Numerator < denominator (e.g., 2/5)
• Improper fraction: Numerator ≥ denominator (e.g., 5/4)
• Mixed number: Whole + fraction (e.g., 2 1/3)

How to Add Fractions

Need a common denominator:

Example: 1/4 + 2/3

1. Find LCD: 12
2. Convert: 1/4 = 3/12, 2/3 = 8/12
3. Add numerators: 3/12 + 8/12 = 11/12

How to Subtract Fractions

Same process as addition:

Example: 5/6 - 1/4

1. LCD: 12
2. Convert: 5/6 = 10/12, 1/4 = 3/12
3. Subtract: 10/12 - 3/12 = 7/12

How to Multiply Fractions

Multiply straight across (no common denominator needed):

Example: 3/4 × 2/5

3 × 2 = 6, 4 × 5 = 20 → 6/20 = 3/10

How to Divide Fractions

Flip and multiply (keep, change, flip):

Example: 3/4 ÷ 1/2

3/4 × 2/1 = 6/4 = 3/2 = 1 1/2

Converting Mixed Numbers

Mixed to Improper: Multiply whole × denominator, add numerator

2 3/4 = (2 × 4 + 3)/4 = 11/4

Improper to Mixed: Divide numerator by denominator

11/4 = 11 ÷ 4 = 2 remainder 3 = 2 3/4

Simplifying Fractions

Divide both numbers by their greatest common divisor (GCD):

18/24: GCD is 6 → 18÷6 / 24÷6 = 3/4

Frequently Asked Questions

Why flip when dividing fractions?

Dividing by a fraction equals multiplying by its reciprocal. 6 ÷ 2 = 6 × 1/2 = 3. The same principle applies to fractions.

How do I know if a fraction is fully simplified?

When numerator and denominator share no common factors except 1. If GCD = 1, it's simplified.