Fraction Calculator
Four operations on two fractions, with the working. The common denominator step is shown separately, because that is the step that is usually skipped and usually where the answer goes wrong.
How it works
How the Fraction Calculator works
the part a result on its own leaves out
Why addition needs a common denominator
Adding means combining parts of the same size. Thirds and quarters are different sizes, so they cannot be combined until both are rewritten as twelfths. Multiplication needs no common denominator because it takes a fraction of a fraction rather than combining like parts.
Why division flips the second fraction
Dividing by a number is multiplying by its reciprocal. Dividing by 1/2 asks how many halves fit into the first fraction, which is why the answer comes out larger.
Common mistakes
Common mistakes with fractions
the errors that actually show up, not every possible slip
Adding the denominators
1/2 + 1/3 is not 2/5. Adding across the bottom is the single most common fraction error. Only the numerators are added, once the denominators match.
Not simplifying the answer
8/12 and 2/3 are the same number, but marked work almost always expects lowest terms.
Flipping the wrong fraction when dividing
In a ÷ b it is b that gets flipped, never a.
Questions
Asked often enough to answer here
answers that change how you work
Does the calculator handle negative fractions?
Yes. A minus sign can go in the numerator or in front of the fraction — both mean the same thing, and the answer keeps the denominator positive.
What about mixed numbers?
Convert to an improper fraction first: 2¾ is 11/4. The result is shown as a mixed number too whenever it is top-heavy.
Why does it show the decimal as well?
Because the fraction is exact and the decimal is often what the question wants. Repeating decimals are rounded, so the fraction is the form to trust.
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