Fractions Calculator
Add, subtract, multiply, and divide fractions with automatic simplification.
Add, subtract, multiply or divide any two fractions or mixed numbers. Results shown in simplest form with full working.
Choose an operation, fill in the two fractions, then press Calculate.
Enter whole number and fraction parts. Leave the whole number at 0 if not needed.
Enter any fraction to reduce it to its simplest form.
1/2 plus 1/3 is 5/6, or 0.833333 as a decimal.
Breakdown
- As a decimal
- 0.833333
- As a percentage
- 83.33%
Show your working
Assumptions
- Results are reduced to simplest form using the greatest common divisor.
- Division is performed by multiplying by the reciprocal of the second fraction.
- Decimals are shown to six significant places.
Fraction facts
- How do you add fractions with different denominators?
- Cross-multiply and add: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6.
- How do you divide by a fraction?
- Multiply by its reciprocal — flip the second fraction. 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2.
- How do you simplify a fraction?
- Divide the top and bottom by their greatest common divisor. 18/24 has a GCD of 6, giving 3/4.
- When is a fraction in simplest form?
- When the only whole number dividing both parts is 1 — its GCD is 1.
Adding fractions
To add two fractions, find a common denominator, convert each fraction, then add the numerators:
Example: 2/3 + 1/4 = (8 + 3) / 12 = 11/12
Subtracting fractions
The same process as addition, but subtract the numerators instead:
Example: 2/3 − 1/4 = (8 − 3) / 12 = 5/12
Multiplying fractions
Multiply the numerators together and the denominators together, then simplify:
Example: 2/3 × 1/4 = 2/12 = 1/6
Dividing fractions
Flip (find the reciprocal of) the second fraction, then multiply:
Example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3
Simplifying fractions
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, 12/18: GCD(12, 18) = 6, so 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3.
Mixed numbers
A mixed number (e.g. 1 1/2) combines a whole number and a proper fraction. To operate on mixed numbers, first convert them to improper fractions: 1 1/2 = (1×2 + 1)/2 = 3/2. Then apply the operation and convert back if needed.
Frequently Asked Questions
How do I add fractions with different denominators?
Find a common denominator, convert each fraction, then add the numerators: a/b + c/d = (a×d + b×c)/(b×d), then simplify. For example, 2/3 + 1/4 = (8 + 3)/12 = 11/12. Enter your fractions in the calculator above to add, subtract, multiply, or divide with full working shown. To express the answer as a percentage, try the percent calculator.
How do I multiply fractions?
Multiply the numerators together and the denominators together, then simplify: a/b × c/d = (a×c)/(b×d). For example, 2/3 × 3/4 = 6/12 = 1/2. Unlike addition, you do not need a common denominator to multiply fractions.
How do I divide fractions?
Flip the second fraction (find its reciprocal) and then multiply: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). For example, 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3. Remember: keep the first fraction, change ÷ to ×, flip the second fraction.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD). For example, 12/18: GCD = 6, so 12÷6 = 2 and 18÷6 = 3, giving 2/3. The calculator automatically simplifies all results to their lowest terms. To convert the result to a decimal, use the decimal to fraction calculator in reverse.
Worked example
Add: 2/3 + 3/4 → common denominator 12 → 8/12 + 9/12 = 17/12 = 1 5/12. Multiply: 2/3 × 3/4 = 6/12 = 1/2. Divide: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2 2/3. Mixed number: 1 1/2 + 2 1/3 → 3/2 + 7/3 → 9/6 + 14/6 = 23/6 = 3 5/6.
Related calculations
For part-to-part comparisons rather than parts of a whole, use the ratio calculator. To go from a decimal back to a fraction, the decimal to fraction converter finds the simplest exact form, and the probability calculator handles odds expressed as fractions.
Evidence & Methodology
How This Page Is Grounded
Method
Uses common-denominator arithmetic for addition and subtraction, direct products for multiplication and reciprocal multiplication for division, then simplifies.
Important limitation: A zero denominator is invalid and division by a zero fraction is rejected.
Primary Sources
- Introduction to fractions OpenStax
Quality Checks
Signs, improper fractions, simplification and zero-denominator validation are checked.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.