Fraction Calculator: The Operations Most People Forgot After Middle School
Fraction arithmetic is one of those things most adults know they once knew. Here's the quick reference.
Addition and Subtraction: Common Denominator Required
To add or subtract fractions, they must have the same denominator.
Same denominator: just add/subtract the numerators.
3/8 + 1/8 = 4/8 = 1/2
Different denominators: find the least common denominator (LCM).
1/3 + 1/4: LCM of 3 and 4 is 12.
1/3 = 4/12; 1/4 = 3/12
4/12 + 3/12 = 7/12
Quick method when denominators share no common factors: multiply both denominators.
1/3 + 1/4: use 3×4=12 as common denominator. ✓
Multiplication: Straight Across
Multiply numerators together, multiply denominators together. No common denominator needed.
2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5
Simplify first when possible (cross-cancel) to keep numbers smaller:
2/3 × 3/5: the 3 in numerator and denominator cancel → 2/1 × 1/5 = 2/5. Same answer, less arithmetic.
Division: Multiply by the Reciprocal
Flip the second fraction, then multiply.
2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
Memory aid: "Keep, Change, Flip" — keep the first fraction, change division to multiplication, flip the second fraction.
Mixed Numbers
Convert to improper fractions first.
2¾ = (2×4 + 3)/4 = 11/4
Then apply normal fraction arithmetic. Convert back at the end if needed.
11/4 + 3/2 = 11/4 + 6/4 = 17/4 = 4¼
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Frequently Asked Questions
Why do I need a common denominator to add fractions?
A common denominator ensures you're adding pieces of the same size. When you add 1/3 + 1/4, you can't just add 1+1 and 3+4 because thirds and fourths are different units. Converting to a common denominator (12 in this case: 4/12 + 3/12) lets you add apples to apples, giving you 7/12.
Do I really have to simplify fractions, or can I leave the answer as 6/15?
You don't *have* to, but you should—6/15 and 2/5 are the same value, and 2/5 is the standard simplified form. Simplified fractions are easier to understand and compare. If you're using the calculator, it will simplify automatically, so you'll always get the cleanest answer.
What's the easiest way to remember how to divide fractions?
Use the "Keep, Change, Flip" method: keep the first fraction, change the division sign to multiplication, and flip the second fraction. So 2/3 ÷ 4/5 becomes 2/3 × 5/4, which you can solve by multiplying straight across to get 10/12 or 5/6 simplified.
How do I work with mixed numbers like 2¾ in calculations?
Convert mixed numbers to improper fractions first by multiplying the whole number by the denominator and adding the numerator: 2¾ becomes (2×4 + 3)/4 = 11/4. Then do your calculation normally—for example, 11/4 + 3/2—and convert back to a mixed number at the end if you need to (17/4 = 4¼).
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