WorkedMathGlossary

Fraction Calculator

Enter two fractions and pick an operation below to instantly get the simplified result.

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Result
11/12

Fraction Operations

Addition and subtraction need a common denominator first. Multiplication and division work straight across the numerators and denominators. Every result is automatically simplified to lowest terms.

A fraction is fully simplified once the greatest common factor (GCF) of its numerator and denominator is 1. 8/12 simplifies to 2/3, for example, because the GCF of 8 and 12 is 4 — dividing both by 4 gets there in one step.

Worked example

Add 3/4 + 1/6.

Common denominator of 4 and 6 is 12: 3/4 = 9/12, and 1/6 = 2/12.

9/12 + 2/12 = 11/12

A second example, dividing: 2/3 ÷ 5/6.

Multiply by the reciprocal: 2/3 × 6/5 = 12/15.

Simplified (GCF of 12 and 15 is 3): 4/5

Common mistake

A common mistake is adding denominators along with numerators — treating 3/4 + 1/6 as 4/10. Denominators are only multiplied when finding a common denominator; they're never added directly.

Keep going

  • A fraction result that comes out improper converts directly to a mixed number; the mixed number calculator handles that conversion in either direction. Mixed Number Calculator
  • Adding or subtracting fractions with different denominators starts with a common denominator; the LCD calculator finds that shared denominator first. LCD Calculator

Frequently Asked Questions

How do you add or subtract fractions?

Convert both fractions to a common denominator, then add or subtract the numerators. a/b + c/d = (ad + bc) / bd.

How do you multiply fractions?

Multiply the numerators together and the denominators together: a/b × c/d = (a × c) / (b × d). No common denominator needed.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = a/b × d/c.

How do you simplify a fraction?

Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. 18/24 simplifies to 3/4 because the GCF of 18 and 24 is 6.

What's an equivalent fraction?

A fraction that represents the same value written with a different numerator and denominator. Multiplying (or dividing) both the top and bottom by the same nonzero number always produces an equivalent fraction, since that's really multiplying by 1.

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