Add, subtract, multiply, or divide fractions and mixed numbers with a step-by-step solution. Simplify any fraction or convert it to a decimal.
How to Use This Calculator
Select a mode from the dropdown:
Arithmetic — Enter the whole number and fraction parts for both operands, choose an operation (+, −, ×, ÷), and the result appears immediately with a full step-by-step solution.
Simplify — Enter a single fraction (or mixed number) to reduce it to its lowest terms.
Convert to Decimal — Enter a fraction to see its decimal equivalent, including a note when the result is a repeating decimal.
The whole number field on the left of each fraction is optional — leave it blank for a pure fraction.
Fraction Arithmetic — How It Works
Adding and Subtracting
To add or subtract fractions, they must share a common denominator. The process:
- Convert any mixed numbers to improper fractions
- Find the least common multiple (LCM) of the denominators
- Rewrite each fraction with the common denominator
- Add or subtract the numerators
- Simplify the result and convert back to a mixed number
Example: 1/3 + 1/4
LCM(3, 4) = 12 → 4/12 + 3/12 = 7/12
Multiplying
Multiply numerators together and denominators together, then simplify.
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing
Multiply the first fraction by the reciprocal of the second.
Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Simplifying Fractions
A fraction is in simplest form when its numerator and denominator share no common factor other than 1. To simplify, divide both by their greatest common divisor (GCD).
Example: 36/48 → GCD(36, 48) = 12 → 36÷12 / 48÷12 = 3/4
Fractions and Decimals
A fraction p/q converts to a terminating decimal when the denominator (after simplifying) has only factors of 2 and 5. All other fractions produce repeating decimals.
| Fraction | Decimal | Type |
|---|
| 1/4 | 0.25 | Terminating |
| 1/3 | 0.3333… | Repeating |
| 3/8 | 0.375 | Terminating |
| 1/7 | 0.142857… | Repeating |
Frequently Asked Questions
How do you add fractions with different denominators?
Find the least common multiple (LCM) of the denominators, rewrite each fraction with that common denominator, then add the numerators. For example, 1/3 + 1/4: the LCM of 3 and 4 is 12, so 1/3 = 4/12 and 1/4 = 3/12. Adding gives 7/12.
How do you subtract mixed numbers?
Convert each mixed number to an improper fraction first, then subtract. For 2 1/2 − 1 1/3: convert to 5/2 and 4/3, find the LCM (6), rewrite as 15/6 − 8/6 = 7/6, then convert back to 1 1/6.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For 2/3 × 3/4: multiply to get 6/12, then simplify by dividing by GCD (6) to get 1/2.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second. For 2/3 ÷ 4/5: flip the second fraction to get 5/4, then multiply: 2/3 × 5/4 = 10/12 = 5/6.
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For 18/24: GCD(18, 24) = 6, so 18÷6 / 24÷6 = 3/4.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For 3/8: 3 ÷ 8 = 0.375. If the denominator has only factors of 2 and 5, the decimal terminates. Otherwise it repeats.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2 3/4 (two and three-quarters). It is equivalent to the improper fraction 11/4.
What is an improper fraction?
An improper fraction has a numerator greater than or equal to its denominator, such as 7/4. It can always be rewritten as a mixed number — in this case 1 3/4.