How fraction arithmetic works
A fraction is a division waiting to happen: 3/4 means 3 ÷ 4. Multiplying and dividing fractions is straightforward because you can work on tops and bottoms directly. Adding and subtracting need one extra step — the pieces have to be the same size first, which is what a common denominator does. The calculator keeps everything as whole numbers, so the answer is exact rather than a rounded decimal.
The rules
a/b + c/d = (a·d + c·b) / (b·d) a/b − c/d = (a·d − c·b) / (b·d) a/b × c/d = (a·c) / (b·d) a/b ÷ c/d = (a·d) / (b·c) Mixed: w n/d = (w·d + n) / d
Every result is reduced by dividing the top and bottom by their greatest common divisor (found with Euclid's algorithm).
Worked examples
Divide: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. The GCD of 15 and 8 is 1, so it's already simplified: 15/8 = 1 7/8 = 1.875.
Subtract: 3/4 − 5/6 = (18 − 20) / 24 = −2/24 = −1/12.
Mixed numbers: 2 1/4 + 1 2/3 = 9/4 + 5/3 = (27 + 20) / 12 = 47/12 = 3 11/12.
Limitations
- Inputs must be whole numbers; denominators can't be zero, and you can't divide by a fraction equal to zero.
- The decimal is rounded to 10 significant places; repeating decimals such as 1/3 are cut off.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, add the numerators, then simplify. For 1/4 + 2/3, the common denominator is 12: 3/12 + 8/12 = 11/12. Multiplying the two denominators always gives a common denominator; the least common multiple gives the smallest one.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second — flip the second fraction upside down. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
How do I enter a mixed number?
Use the whole-number box for the whole part and the top and bottom boxes for the fraction. For 2 1/4, enter 2, 1 and 4. For a negative mixed number such as −1 1/2, put the minus sign on the whole number only.
What does it mean to simplify a fraction?
Dividing the numerator and denominator by their greatest common divisor until they share no common factor. 18/24 has a greatest common divisor of 6, so it simplifies to 3/4. The value doesn't change, only how it is written.
Can I enter decimals?
Not in the fraction boxes — they take whole numbers so the answer stays exact. To turn a decimal like 0.375 into a fraction, write it over a power of ten (375/1000) and simplify, which gives 3/8.