Fraction Calculator
Add two fractions and simplify the result.
Input sheet
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Adding fractions trips up cooks halving recipes, students doing homework, and anyone splitting measurements. This adds two fractions and reduces the answer to its simplest form.
How it works
Adds over a common denominator (d1×d2), then divides numerator and denominator by their GCD to simplify.
To add fractions you need a common denominator. This tool uses the product of the two denominators (d1 × d2), rewrites both fractions over it, adds the numerators, then divides the result by the GCD of numerator and denominator to simplify.
It also reports the decimal equivalent and the unsimplified sum, so you can see exactly how the reduction happened.
Sum = (n1 × d2 + n2 × d1) ÷ (d1 × d2), then reduced by the GCD
Worked examples
Adding 1/2 + 1/3. → 5/6
Common denominator 6: 3/6 + 2/6 = 5/6, already in lowest terms (decimal ≈ 0.8333).
Adding 1/4 + 1/4. → 1/2
Over a common denominator: 1/4 + 1/4 = 2/4, which reduces to 1/2.
Tips & gotchas
- The product of the denominators always works as a common denominator, though the least common denominator gives smaller intermediate numbers.
- A negative numerator entered as a whole number lets you subtract: adding −1/3 is the same as subtracting 1/3.
- To convert the answer to a decimal, divide the numerator by the denominator.
FAQ
Why do fractions need a common denominator to add?
You can only add like-sized pieces. Rewriting both fractions over the same denominator makes the pieces the same size, so the numerators can be summed directly.
How is the answer simplified?
By dividing both the numerator and denominator by their greatest common divisor, which reduces the fraction to lowest terms without changing its value.
Can I add more than two fractions at once?
This tool adds two at a time. For more, add the first two, then add the third to that result, and so on.
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