Fraction Calculator
Work with two fractions at once: add, subtract, multiply or divide them and get the answer as a simplified fraction, a decimal and a mixed number, with every step of the reduction shown.
The answer is always reduced with the greatest common divisor, so 6/8 is shown as 3/4.
Formula and calculation
Worked example
To add 1/2 and 3/4, put both over the common denominator 4: 2/4 + 3/4 = 5/4. The calculator reports 5/4, which is 1.25 as a decimal and 1 1/4 as a mixed number.
Why fractions get reduced
Reducing does not change the value — it changes how the same amount is written. 6/8 and 3/4 cover exactly the same distance on a ruler; reducing just divides the numerator and denominator by their greatest common divisor (2, in this case). Lowest terms make comparison and further arithmetic easier: 3/4 is visibly bigger than 2/3, while 9/12 versus 8/12 takes a moment. The step-by-step table here always shows the GCF that was applied, so you can reproduce the reduction by hand.
Mixed numbers and improper fractions
A mixed number such as 2 1/2 is shorthand for 2 + 1/2, which is 5/2 as an improper fraction (2 × 2 + 1 = 5 over the same denominator 2). To convert back, divide the numerator by the denominator: 5 ÷ 2 is 2 with a remainder of 1, so 1/2. Cooks and carpenters work in mixed numbers; algebra almost always uses improper fractions, because multiplying and dividing mixed numbers directly is where most mistakes happen. This calculator accepts either form and reports both.
What the results mean
- Result
- The answer as a fraction in lowest terms — the numerator and denominator have no common factor left, so 6/8 is always reported as 3/4.
- Decimal
- The same answer written as a decimal. It is exact when the fraction ends (1/4 = 0.25) and repeating when it does not (1/3 = 0.3333…).
- Mixed number
- The answer as a mixed number — a whole number next to a proper fraction, like 1 1/2. This is the form used in recipes and measurements; improper forms like 3/2 are preferred in algebra.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions with a common denominator, then add only the numerators. For 1/2 + 1/3 the smallest common denominator is 6: 3/6 + 2/6 = 5/6. The steps table shows the least common denominator used for your numbers.
Why isn't 1/2 + 1/3 equal to 2/5?
Because denominators cannot be added — they count how many pieces each whole is cut into, not how much you have. You must first cut both into equal pieces: 3/6 + 2/6, which is 5/6, a little less than 1. Adding 1/2 and 1/3 should land near 0.83, and 2/5 is only 0.4.
How do I turn a mixed number into a fraction?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. 2 1/2 becomes (2 × 2 + 1)/2 = 5/2. Type mixed numbers straight in, like 2 1/2, and the calculator converts them for you.
What does simplifying a fraction mean?
Dividing the numerator and denominator by their greatest common divisor until nothing is left to cancel. 12/18 becomes 2/3 (both divided by 6). The value never changes — only the way it is written. The calculator always reports the reduced form.