How it works
A fraction is one whole number divided by another: the top number (the numerator) says how many parts you have, and the bottom number (the denominator) says how many equal parts make a whole. So 3/4 means three parts out of four.
Enter two numbers, pick an operation, and the calculator gives the answer in simplest form, as a mixed number, and as a decimal. You can type fractions (3/4), mixed numbers (1 1/2), whole numbers (5), decimals (0.75), and negative numbers (-2/3). Every step is shown, using the same method taught in school.
The math is exact. Fractions are worked out with whole numbers only, so the answer is never off by a tiny rounding error. Only the decimal is rounded, to 6 places.
The formula
Each operation has its own rule. In these, a/b and c/d are the two fractions.
Add or subtract: first rewrite both fractions over the same bottom number, then add or subtract the tops.
a/b + c/d = (a × (L ÷ b) + c × (L ÷ d)) / L
- L is the least common denominator (LCD): the smallest number both b and d divide into. For 4 and 3 it’s 12.
Multiply: multiply the tops and multiply the bottoms.
a/b × c/d = (a × c) / (b × d)
Divide: flip the second fraction and multiply. Flipping a fraction gives its reciprocal.
a/b ÷ c/d = a/b × d/c, as long as c isn’t 0
Simplify: divide the top and bottom by their greatest common factor (GCF), the largest number that divides both. For 20/12, the GCF is 4, so 20/12 = 5/3.
Mixed numbers are turned into fractions first: multiply the whole number by the bottom and add the top, so 1 3/4 = (1 × 4 + 3)/4 = 7/4. Decimals become their digits over 10, 100, or 1,000, so 0.75 = 75/100 = 3/4.
Worked example
Want this with your own numbers? See Show the work above.
Add 3/4 and 2/3.
- Both numbers are already fractions.
- The least common denominator of 4 and 3 is 12.
- Rewrite both over 12: 3/4 = 9/12, because 3 × 3 = 9 and 4 × 3 = 12. And 2/3 = 8/12, because 2 × 4 = 8 and 3 × 4 = 12.
- Add the tops and keep the bottom: 9/12 + 8/12 = (9 + 8)/12 = 17/12.
- 17 and 12 share no factor except 1, so 17/12 is already in simplest form.
As a mixed number that’s 1 5/12 (12 goes into 17 once, with 5 left over). As a decimal it’s about 1.416667; the 6s repeat forever.
FAQ
How do you add fractions with different denominators?
Find the least common denominator, the smallest number both bottom numbers divide into. Rewrite each fraction over it by multiplying its top and bottom by the same number, then add the tops. For 1/2 + 1/3, the LCD is 6, so it’s 3/6 + 2/6 = 5/6.
How do you divide fractions?
Flip the second fraction upside down and multiply. So 2/5 ÷ 3/7 is 2/5 × 7/3 = 14/15. You can’t divide by a fraction with 0 on top, because that’s dividing by 0.
How do you turn a mixed number into an improper fraction?
Multiply the whole number by the bottom number, add the top, and keep the same bottom. For 3 1/3, that’s 3 × 3 + 1 = 10, so 3 1/3 = 10/3. To go back, divide the top by the bottom: 10 ÷ 3 is 3 with 1 left over, so 10/3 = 3 1/3.
How do you simplify a fraction?
Divide the top and bottom by the largest number that goes into both (the greatest common factor). For 210/385, that number is 35, so 210/385 = 6/11. A fraction is in simplest form when the only number that divides both is 1.
Where does the minus sign go in a negative mixed number?
In front, and it applies to the whole thing: -1 7/8 means -(1 7/8), which is -15/8. Type the minus sign before the whole number. A negative fraction like -3/4 is the same as 3/-4 or -(3/4).
Why is the decimal sometimes rounded?
Some fractions have decimals that never end. 1/3 is 0.333… with 3s forever, and 17/12 is 1.41666… with 6s forever. The calculator rounds the decimal to 6 places and says so, but the fraction answer is always exact.
Sources
- Multiplying and dividing fractions, and simplifying: OpenStax Prealgebra 2e, section 4.2, Multiply and Divide Fractions
- Mixed numbers: OpenStax Prealgebra 2e, section 4.3, Multiply and Divide Mixed Numbers and Complex Fractions
- Adding and subtracting with the least common denominator: OpenStax Prealgebra 2e, section 4.5, Add and Subtract Fractions with Different Denominators
Cite this page
APA (7th edition)
Mathlark. (2026, September 30). Fraction calculator. https://mathlark.com/math/fraction-calculator/
MLA (9th edition)
"Fraction Calculator." Mathlark, 30 Sept. 2026, mathlark.com/math/fraction-calculator/.