How to Add, Subtract, Multiply, and Divide Fractions
September 18, 2026
Adding and subtracting fractions requires a common denominator first; multiplying and dividing don't. Multiply straight across for multiplication, and flip the second fraction and multiply for division.
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Fractions need a common denominator before you can add or subtract their numerators. The general formula is a/b + c/d = (ad + bc) / bd, though using the least common denominator keeps the numbers smaller.
- Example: 1/4 + 1/6. Common denominator is 12: 3/12 + 2/12 = 5/12.
Multiplying Fractions
Multiplication is the simplest operation: multiply the numerators together, then multiply the denominators together — no common denominator needed.
- Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2 (simplified).
Dividing Fractions
Dividing by a fraction is the same as multiplying by its reciprocal — flip the second fraction, then multiply.
- Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 (simplified).
Simplifying a Fraction
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 12/18, the GCD is 6, so 12/18 simplifies to 2/3.
Frequently Asked Questions
Why do I need a common denominator to add fractions?
Fractions represent parts of a whole divided into a specific number of pieces — you can only add or subtract those parts directly when they're divided into the same-sized pieces, which is what a common denominator provides.
How do I multiply fractions?
Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator, then simplify if possible.
Why do you flip the second fraction when dividing?
Dividing by a number is mathematically the same as multiplying by its reciprocal (1 divided by that number) — flipping the second fraction converts the division into an equivalent multiplication problem.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD) until no common factor remains.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For example, 2¾ = (2×4 + 3)/4 = 11/4.