Fraction Calculator
Add, subtract, multiply, or divide two fractions and get an exact simplified answer, plus the mixed number, decimal, and percentage forms.
How to use this calculator
- 1Enter the numerator and denominator of the first fraction.
- 2Choose the operation you want.
- 3Enter the second fraction the same way.
- 4Read the simplified result, and use the step panel to see how the answer was reached.
How it works
Fraction arithmetic
a/b + c/d = (ad + cb) / bd a/b − c/d = (ad − cb) / bd a/b × c/d = ac / bd a/b ÷ c/d = a/b × d/c = ad / bc Simplify by dividing both parts by their GCF
Multiplication is the simple case: multiply across the top and across the bottom. Division is multiplication by the reciprocal — flip the second fraction and multiply. Addition and subtraction need a common denominator first, and multiplying the denominators together always produces one, though not always the smallest. Simplifying at the end fixes that.
Worked example
3/4 ÷ 2/4 becomes 3/4 × 4/2 = 12/8. The greatest common factor of 12 and 8 is 4, so the simplified answer is 3/2 — which is 1½ as a mixed number, or 1.5 as a decimal.
Fraction Calculator: the complete guide
Dividing fractions: why you flip the second one
Dividing by a number means asking how many of it fit into the first quantity. Dividing by 1/2 asks how many halves fit — which is why dividing by a fraction less than one makes the answer larger, a result that feels backwards until you say it out loud.
Mechanically, dividing by c/d is the same as multiplying by d/c, because c/d × d/c = 1. Multiplying by the reciprocal cancels the divisor and leaves the answer. "Keep, change, flip" is the classroom mnemonic: keep the first fraction, change ÷ to ×, flip the second.
Common denominators for adding and subtracting
You cannot add quarters to thirds any more than you can add metres to feet — the pieces are different sizes. Rewriting both fractions over a common denominator makes the pieces the same size, and then the numerators simply add.
Multiplying the two denominators always gives a valid common denominator, and it is what the formula above uses. The least common denominator is the LCM of the two, which keeps the numbers smaller and often means less simplifying at the end. For 1/4 and 1/6, multiplying gives 24 while the LCM is 12 — both work, but 12 is tidier.
Simplifying, mixed numbers, and improper fractions
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. Dividing both by their greatest common factor gets there in a single step — no repeated halving required.
An improper fraction has a numerator at least as large as its denominator, like 12/8. The mixed-number form 1½ is easier to picture, while the improper form is easier to compute with, which is why you convert mixed numbers to improper fractions before multiplying or dividing and convert back only at the end.
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator, rewrite both fractions over it, add the numerators, then simplify. Multiplying the denominators always works; using their least common multiple keeps the numbers smaller. The step panel above shows both stages.
Why is dividing by a fraction the same as multiplying by its reciprocal?
Because a fraction and its reciprocal multiply to 1. Multiplying the numerator and denominator of a division by the reciprocal of the divisor turns the denominator into 1, leaving just the multiplication. It is the same trick as rationalising a denominator.
Can I enter mixed numbers directly?
Convert them to improper fractions first. For 2¾, multiply the whole number by the denominator and add the numerator: 2 × 4 + 3 = 11, so enter 11 as the numerator and 4 as the denominator. The result is shown in both forms.
What about negative fractions?
Enter the minus sign on either the numerator or the denominator — the calculator normalises the sign onto the numerator and simplifies from there. Two negatives cancel, so −3/−4 is the same as 3/4.