Add, subtract, multiply, divide and simplify fractions instantly, with the full step-by-step working so you can learn the method, not just copy the answer.
Fraction operation
a/b + c/d
Result
76
≈ 1.1666667
Step 1. 1/2 + 2/3 = (1·3 + 2·2) / (2·3) = 7/6
Step 2. Simplify by GCD(7, 6) = 1 → 7/6
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Quick Reference
Common denominator first, then add numerators. Multiplication is straight across. Division flips the second fraction.
A fraction a/b represents a parts of a whole divided into b equal pieces. The four basic operations on fractions each follow a simple recipe: addition and subtraction require a common denominator, multiplication is straight across, and division flips the second fraction.
Simplification means dividing the numerator and denominator by their greatest common divisor (GCD). A fraction is in "lowest terms" when the GCD is 1. This calculator handles every step automatically.
Worked Examples
One example per operation, plus a bonus on simplification.
Example 1, Adding fractions
1/2 + 2/3 = ?
Common denominator
LCD(2, 3) = 6Rewrite each
1/2 = 3/6, 2/3 = 4/6Add numerators
3/6 + 4/6 = 7/6Already in lowest terms
GCD(7, 6) = 1, so 7/6 is simplifiedAlways find a common denominator before adding.
Example 2, Subtracting fractions
5/6 − 1/4 = ?
Common denominator
LCD(6, 4) = 12Rewrite each
5/6 = 10/12, 1/4 = 3/12Subtract numerators
10/12 − 3/12 = 7/12Simplify
GCD(7, 12) = 1, so 7/12 is already simplifiedSame process as addition with a minus sign.
Example 3, Multiplying fractions
3/4 × 8/9 = ?
Multiply across
(3 × 8) / (4 × 9) = 24/36Find GCD
GCD(24, 36) = 12Simplify
24/36 = 2/3Multiply numerators and denominators directly, then simplify.
Example 4, Dividing fractions
2/5 ÷ 4/7 = ?
Flip the second fraction
4/7 → 7/4Multiply
2/5 × 7/4 = 14/20Simplify
GCD(14, 20) = 2 → 7/10Dividing by a fraction = multiplying by its reciprocal.
Example 5, Simplifying improper fractions
Simplify 18/24
Find GCD
GCD(18, 24) = 6Divide both
18 ÷ 6 = 3, 24 ÷ 6 = 4Result
18/24 = 3/4Always divide both parts by their greatest common divisor.
Fractions are one of the most-used concepts in math, from measuring ingredients to algebra to engineering. This free fraction calculator does the four basic operations, addition, subtraction, multiplication, and division, plus automatic simplification, with the work shown out clearly. Use it as both a fast answer tool and a learning resource.
Adding or subtracting two fractions requires a common denominator. Find the least common denominator (LCD), rewrite each fraction with that denominator, then add or subtract the numerators. The result usually needs to be simplified, the calculator handles this automatically.
Multiplication is straightforward: multiply the two numerators and the two denominators. Division uses a clever trick, multiply the first fraction by the reciprocal of the second (flip the numerator and denominator). Always simplify the result.
A fraction is in lowest terms when the greatest common divisor (GCD) of the numerator and denominator is 1. To simplify, divide both top and bottom by their GCD. The Euclidean algorithm finds the GCD efficiently for any pair of integers.
Enter only integer numerators and denominators. Negative fractions work, put the minus sign in either the numerator or write the entire fraction as negative. For mixed numbers like 2 1/3, convert to improper form first (2 1/3 = 7/3) before entering. For more complex algebraic fractions, use the photo solver.
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