Guide
How to Add and Simplify Fractions: Same and Different Denominators
To add fractions, first make their pieces the same size. Then add the numerators and simplify. For example, 1/2 + 1/3 = 5/6, not 2/5. Here is how to get that answer and check it.
When the denominators already match
The numerator is the top number; the denominator is the bottom number. In 2/7, you have two pieces, each one a seventh. Adding 2/7 and 3/7 gives five sevenths: (2 + 3)/7 = 5/7. The piece size has not changed, so the denominator stays 7.
Adding the denominators would change the size of the pieces. That is why 1/4 + 1/4 is 2/4, or 1/2, rather than 2/8. Two quarters make a half, not a quarter.
When the denominators are different
Rewrite both fractions with a common denominator. For 1/2 + 1/3, use 6: multiply the top and bottom of 1/2 by 3 to get 3/6, and the top and bottom of 1/3 by 2 to get 2/6. Now add: 3/6 + 2/6 = 5/6.
The general formula is a/b + c/d = (a × d + c × b)/(b × d). Multiplying both denominators always gives a common denominator, though it may not be the smallest. Using their least common multiple often makes the hand calculation easier.
Simplify by dividing both numbers by their GCD
A fraction is simplified when its numerator and denominator share no positive divisor greater than 1. Divide both by their greatest common divisor (GCD). For 2/3 + 1/6, cross-multiplication gives 15/18. Both numbers divide by 3, so the simplified result is 5/6.
An answer larger than 1 is still valid. For example, 3/4 + 3/4 = 6/4 = 3/2, which is also 1 1/2. The calculator displays the simplified fraction as 3/2 rather than as a mixed number.
Negative fractions, zero, and decimals
Subtraction can be written as addition of a negative fraction. To calculate 1/2 − 1/3, enter 1/2 and −1/3: the result is 1/6. A negative sign belongs in the numerator for this tool; denominators must be positive whole numbers.
To convert a fraction to a decimal, divide its numerator by its denominator. For 5/6, that is 0.8333…; the repeated digits mean a displayed decimal is rounded. Opposite fractions such as 1/2 and −1/2 add to zero, displayed as 0/1. A denominator of zero is never valid.
Check your fraction addition
Enter the first numerator and denominator, then the second pair. The Fraction Calculator adds the two fractions and shows their simplified sum alongside a decimal value. It is an addition tool, not a selector for multiplication or division.
Use whole-number numerators between −1,000,000 and 1,000,000 and denominators from 1 to 1,000,000. For a mixed number, convert it first: 1 1/2 becomes 3/2. Keep the fraction result when you need an exact answer rather than a rounded decimal.
Try it yourself
Put this guide into practice with our free Fraction Calculator — no sign-up, no download.
Open the Fraction Calculator