Add, subtract, multiply, or divide any two fractions and see the full worked solution. Just type your fractions below to get a simplified answer with every step explained.
Instant Fraction Calculator
Instant calculator · no sign-up · need the full method? Use the step-by-step solver below.
Prefer a full step-by-step explanation?
Free · Step-by-step worked solutions · Works on any device
What this fraction calculator does
This fraction calculator handles the four core operations on fractions: addition, subtraction, multiplication, and division. Enter two fractions, choose what you want to do with them, and our AI engine walks you through each step to a fully simplified answer.
It works with proper fractions (like \( \tfrac{2}{3} \)), improper fractions (like \( \tfrac{7}{4} \)), and mixed numbers (like \( 1\tfrac{1}{2} \)). Whenever an answer can be reduced, the calculator shows you how it cancels common factors so you understand the result, not just the final number.
Key idea
To add or subtract fractions you need a common denominator. To multiply, multiply straight across. To divide, flip the second fraction and multiply.
Worked examples
Example 1: Adding unlike denominators
Add \( \dfrac{1}{3} + \dfrac{2}{5} \). The denominators differ, so first find a common one. The least common denominator of 3 and 5 is 15.
$$\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}, \qquad \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$$Now the denominators match, so add the numerators:
$$\frac{5}{15} + \frac{6}{15} = \frac{11}{15}$$Since 11 and 15 share no common factor, this is already in lowest terms.
Example 2: Multiplying and simplifying
Multiply \( \dfrac{3}{4} \times \dfrac{2}{9} \). With multiplication you do not need a common denominator — just multiply across the top and across the bottom.
$$\frac{3}{4} \times \frac{2}{9} = \frac{3 \times 2}{4 \times 9} = \frac{6}{36}$$Now simplify. Both 6 and 36 are divisible by 6:
$$\frac{6}{36} = \frac{6 \div 6}{36 \div 6} = \frac{1}{6}$$Example 3: Dividing fractions
Divide \( \dfrac{5}{6} \div \dfrac{2}{3} \). To divide, keep the first fraction, flip the second to its reciprocal, and multiply.
$$\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{5 \times 3}{6 \times 2} = \frac{15}{12}$$Reduce by dividing the top and bottom by 3, then write it as a mixed number:
$$\frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$$Common mistake
Don’t add the denominators when you add fractions. \( \dfrac{1}{3} + \dfrac{2}{5} \) is not \( \dfrac{3}{8} \). You only combine numerators after the denominators are the same.
How to use the fraction calculator
- Type the first and second fraction into the input fields, using the equation editor for mixed numbers or improper fractions when you need them.
- Select the operation you want — add, subtract, multiply, or divide.
- Press solve to see the simplified answer along with each step, so you can follow the method and check your own work.
Tip
Always reduce your final answer. If the numerator and denominator share a common factor, divide both by it until no common factor remains.
Related step-by-step guides
- How to Add, Subtract, Multiply and Divide Fractions — a full walkthrough of all four operations with practice problems.
- How to Calculate Percentages — convert fractions to percentages and back with confidence.
Keep solving
Once your fractions are sorted, tackle bigger problems with our Equation Solver or work through expressions step by step in the Algebra Solver.
