Fraction Calculator — How to Add, Subtract, Multiply, and Divide Fractions

Adding and Subtracting Fractions

Fractions can only be added or subtracted when they share a common denominator. The process: find the Least Common Denominator (LCD), convert each fraction, then add or subtract numerators.

Example: 1/3 + 1/4

1. LCD of 3 and 4 = 12
2. Convert: 1/3 = 4/12, 1/4 = 3/12
3. Add: 4/12 + 3/12 = 7/12

Example: 5/6 − 1/4

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

The LCD is the Least Common Multiple (LCM) of the two denominators. For large numbers, the fraction calculator computes the LCM automatically.

Multiplying Fractions

Multiplication is the simplest fraction operation: multiply numerators together and denominators together, then simplify.

Example: 2/3 × 3/4

1. Multiply numerators: 2 × 3 = 6
2. Multiply denominators: 3 × 4 = 12
3. Simplify: 6/12 = 1/2

Cross-cancelling shortcut: Before multiplying, simplify across fractions. In 2/3 × 3/4, cancel the 3s: (2/1) × (1/4) = 2/4 = 1/2. Same result, smaller numbers to work with.

Dividing Fractions

Division uses the "keep, change, flip" rule: keep the first fraction, change ÷ to ×, flip the second fraction (take its reciprocal).

Example: 2/3 ÷ 4/5

1. Keep 2/3, change ÷ to ×, flip 4/5 to 5/4
2. Multiply: 2/3 × 5/4 = 10/12
3. Simplify: 10/12 = 5/6

Working with Mixed Numbers

Mixed numbers (like 2½) combine a whole number with a fraction. Before doing arithmetic, convert to improper fractions: multiply the whole number by the denominator and add the numerator.

2½ → (2 × 2 + 1) / 2 = 5/2. Now use the same rules as regular fractions. Convert back to a mixed number at the end if needed.

Simplifying Fractions

A fraction is in simplest form when the GCD (Greatest Common Divisor) of numerator and denominator is 1. To simplify, divide both by their GCD.

Example: 18/24

1. GCD(18, 24) = 6
2. 18/6 = 3, 24/6 = 4
3. Simplified: 3/4

The Simplify tab in the fraction calculator shows the GCD used and the result in fraction, mixed number, and decimal forms.

Common Mistakes to Avoid

Adding denominators

1/2 + 1/3 ≠ 2/5. You cannot add denominators. The correct answer is 3/6 + 2/6 = 5/6. Only numerators are added — after finding a common denominator.

Forgetting to simplify

Always simplify the result. 8/12 is technically correct, but 2/3 is the expected answer in most educational contexts.

Mixed number errors with subtraction

When subtracting mixed numbers where the fraction part of the first is smaller than the second, you need to borrow from the whole number. Converting both to improper fractions first avoids this pitfall entirely.