Add or subtract up to five fractions and mixed numbers. You get the answer in lowest terms as a proper or improper fraction, a mixed number and a decimal — plus every step of the math.
How to add fractions
The rule is the same in every case: the denominators must match before you can add the numerators. Here is how the calculator does it, case by case.
1. Fractions with the same denominator
Add the numerators and keep the denominator unchanged, then reduce the result if you can.
ac + bc = a + bc
For example: 1/5 + 2/5 = 3/5.
2. Fractions with different denominators
Find the least common denominator (LCD) — the smallest number both denominators divide into evenly — and rewrite each fraction over that LCD. Then add the numerators.
ab + cd = a · (L / b) + c · (L / d)L where L = LCM(b, d)
For example: 1/2 + 1/3. The LCD is 6, so 1/2 = 3/6 and 1/3 = 2/6, giving 3/6 + 2/6 = 5/6.
3. Mixed numbers
Turn each mixed number into an improper fraction first, add them, then convert the answer back to a mixed number.
Wnd = W · d + nd
For example: 2 1/4 + 1 1/2 becomes 9/4 + 3/2 = 9/4 + 6/4 = 15/4 = 3 3/4.
Never add the denominators. 1/2 + 1/3 is not 2/5 — that would be less than either fraction. Denominators name the size of the pieces; only the count of pieces is added.
Reducing the answer
Divide the numerator and the denominator by their greatest common factor (GCF). For example 8/12 has a GCF of 4, so 8/12 = 2/3. A fraction is in lowest terms when the only common factor left is 1.
Worked examples
These are the kinds of problems the calculator solves, with the answer in lowest terms.
| Problem | Least common denominator | Rewrite | Answer |
|---|
| 1/2 + 1/3 | 6 | 3/6 + 2/6 | 5/6 |
| 3/4 + 5/6 | 12 | 9/12 + 10/12 | 19/12 = 1 7/12 |
| 2 1/5 + 1 3/10 | 10 | 22/10 + 13/10 | 35/10 = 3 1/2 |
| 7/8 − 1/4 | 8 | 7/8 − 2/8 | 5/8 |
| 1/4 + 1/4 + 1/4 + 1/4 | 4 | 1/4 + 1/4 + 1/4 + 1/4 | 4/4 = 1 |
| 5/6 − 1/2 + 1/3 | 6 | 5/6 − 3/6 + 2/6 | 4/6 = 2/3 |
Frequently asked questions
How do I add fractions with different denominators?
Find the least common denominator (the LCM of the denominators), rewrite each fraction with that denominator by multiplying the top and bottom by the same number, add the numerators, and reduce the result. For 1/2 + 1/3 the LCD is 6, so you get 3/6 + 2/6 = 5/6.
What is the least common denominator?
The least common denominator is the smallest number that every denominator in the problem divides into evenly — in other words, the least common multiple of the denominators. For 4, 6 and 10 it is 60, so each fraction is rewritten over 60 before adding.
How do I add mixed numbers?
Convert each mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator, keeping the same denominator: 2 1/3 = (2 × 3 + 1)/3 = 7/3. Add the improper fractions, then divide the numerator by the denominator to turn the answer back into a mixed number.
Can this calculator subtract fractions too?
Yes. Use the +/− box between two fractions to switch it to subtraction. A subtraction can come before or after an addition, so expressions such as 5/6 − 1/2 + 1/3 are calculated left to right in one pass.
Why is the denominator not added?
A denominator tells you the size of the pieces, not how many there are. Adding denominators would change the size of the pieces as well as the count, which gives a wrong answer. Only numerators — the counts — are added once the denominators match.
Does the answer always come out reduced?
Yes. The result is automatically reduced to lowest terms by dividing the numerator and denominator by their greatest common factor, and it is also shown as an improper fraction, a mixed number and a decimal.
Can I enter negative fractions?
You can enter a negative whole number or a negative numerator, for example −2 1/3 or −7/3. The sign applies to the whole mixed number, and the calculator keeps track of it through every step.