Fraction Calculator
Add, subtract, multiply, or divide two fractions and get the simplified result plus the full step-by-step working.
Fraction Calculator — input your values
What does this math calculator do?
The fraction calculator handles all four basic operations on two fractions: addition, subtraction, multiplication, and division. You enter the numerator and denominator of each fraction, and the calculator returns the result simplified to lowest terms together with its decimal value.
Every calculation is broken into the same steps a teacher would write on the board: finding a common denominator for addition and subtraction, multiplying across for multiplication, and flipping the second fraction for division. The final step always cancels the greatest common divisor so the answer is fully reduced.
Formula and variables
Addition and subtraction use the least common denominator; multiplication multiplies straight across; division flips the second fraction and multiplies.
| Symbol | Meaning |
|---|---|
| a, b | Numerator and denominator of the first fraction |
| c, d | Numerator and denominator of the second fraction |
| lcm | Least common multiple of the denominators |
Worked example
You need 1/2 cup of sugar and the recipe calls for another 1/4 cup. How much sugar do you need in total?
- The common denominator of 2 and 4 is 4, so 1/2 = 2/4.
- 2/4 + 1/4 = 3/4 cup of sugar.
Answer: You need 3/4 cup of sugar.
Tips and common mistakes
Tips
- For addition and subtraction, use the least common denominator, not just any common denominator — it keeps the numbers small.
- Check that the final fraction is fully simplified by confirming the numerator and denominator share no common factor other than 1.
- When dividing fractions, 'keep, change, flip': keep the first fraction, change ÷ to ×, and flip the second fraction.
- An improper fraction (numerator larger than denominator) is perfectly valid — you do not have to convert it to a mixed number.
Common mistakes to avoid
- Adding numerators and denominators separately instead of converting to a common denominator first.
- Forgetting to flip the second fraction before multiplying when dividing.
- Using a denominator of zero, which makes the fraction undefined.
Fraction Calculator — frequently asked questions
How do I add fractions with different denominators?
Convert both fractions to the least common denominator, then add the numerators. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common divisor. For 8/12 the gcd is 4, so the fraction reduces to 2/3.
How do I divide fractions?
Flip the second fraction and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.
What is a least common denominator?
It is the smallest number that both denominators divide into evenly, also called the least common multiple of the denominators.
Can the calculator handle negative fractions?
Yes. Negative numerators and denominators are supported, and the result is always normalized so the denominator is positive.
What does a simplified fraction with denominator 1 mean?
It means the fraction is a whole number. For example, 6/3 simplifies to 2/1, which is just 2.