How fractions are combined
Multiplication and division are the easy cases. To multiply, multiply the numerators together and the denominators together. To divide, flip the second fraction and multiply, so a/b ÷ c/d becomes a/b × d/c.
Addition and subtraction need a common denominator first. The calculator scales each fraction so both share the same bottom number, combines the numerators, and then reduces. It uses the product of the two denominators as the common base, which always works even when it is not the smallest option.
Reading the reduced result
Every answer is shown in lowest terms, meaning the numerator and denominator share no common factor other than 1. The calculator finds that shared factor with the greatest common divisor and divides both parts by it.
The sign is kept in the numerator, so a negative result appears as -3/4 rather than 3/-4. A decimal equivalent is shown alongside the fraction so you can compare or paste it elsewhere.
Tips for cleaner fractions
These habits help you sanity-check the output and work faster by hand.
- A result equal to a whole number shows a denominator of 1, such as 4/1.
- If the numerator is larger than the denominator the value is an improper fraction (greater than 1), which is normal and correct.
- Reducing before multiplying keeps the numbers small and easier to verify.
- Two fractions are equal when their cross products match: a/b = c/d when a × d = b × c.
Common mistakes
The most frequent error is adding numerators and denominators straight across, which is wrong. 1/2 + 1/3 is not 2/5; you must convert to a common denominator first to get 5/6.
A denominator can never be zero, since dividing by zero is undefined. Dividing by a fraction whose numerator is zero is also blocked, because that is the same as dividing by zero.
Formula
a/b (op) c/d, then reduce by gcd