Math
Fraction Calculator
Enter two fractions to see the result of all four operations, each reduced to its simplest form.
The link carries your figures, so it reopens on exactly these numbers.
The formula
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)
Worked example
Adding two thirds and three quarters
- 2/3 + 3/4 = (2 × 4 + 3 × 3) / (3 × 4) = 17/12
- 17/12 = 1 5/12 as a mixed number
- 2/3 − 3/4 = (2 × 4 − 3 × 3) / (3 × 4) = −1/12
Where this goes wrong
Adding the tops and the bottoms separately
1/2 + 1/3 is not 2/5. Adding numerators and denominators separately gives a number between the two fractions — the mediant — not their sum. The correct route finds a common denominator first: 3/6 + 2/6 = 5/6.
Questions
- How do I add fractions with different denominators?
- Find a common denominator by multiplying each fraction's top and bottom so the bottoms match. Then add the numerators and keep that bottom. 1/3 + 1/4 becomes 4/12 + 3/12 = 7/12.
- Why do you flip the second fraction to divide?
- Dividing by a fraction is the same as multiplying by its reciprocal. 2/3 ÷ 4/5 becomes 2/3 × 5/4 because dividing by four fifths asks how many four-fifths fit in two thirds, which is the same question as multiplying by five quarters.
- What if one of the numbers is a whole number?
- Write it as a fraction over 1. Five is 5/1, so 5 + 1/3 is 5/1 + 1/3 = 15/3 + 1/3 = 16/3.