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Fraction Calculator

With the defaults, 3/4 + 2/5 = 23/20, or 1.15. This calculator adds, subtracts, multiplies, and divides two fractions and reduces the answer to lowest terms, with the decimal equivalent alongside; addition and subtraction use cross-multiplication over a common denominator, multiplication multiplies straight across, and division multiplies by the reciprocal.

Result
23/20
= 1.1500
Visualized
3/4
+
2/5
Inputs
Operation
/ + /
Already in lowest terms
23/20 shares no common factor above 1, so it can't be reduced any further.
As a mixed number
23/20 is more than one whole: 23 ÷ 20 = 1 remainder 3, which reads as 1 3/20.
Ask a follow-up
Uses your inputs above
23/20 result. Want to try a variation?

The math

Reviewed 2026
Formula
+ / − : (n₁d₂ ± n₂d₁) / (d₁d₂) × : (n₁n₂) / (d₁d₂) ÷ : (n₁d₂) / (d₁n₂)

Related calculators

Percentage
GCD / LCM

Example: how fraction is calculated

Step-by-step with default inputs

Suppose you put the default values into Fraction Calculator:

Operation
+
A num
3
A denom
4
B num
2
B denom
5

Plug those into the formula + / − : (n₁d₂ ± n₂d₁) / (d₁d₂) and the result is:

Result
23/20

How to calculate fraction by hand

  1. To add 3/4 and 2/5 by hand, cross-multiply: 3 × 5 = 15 and 2 × 4 = 8.
  2. Add the cross products to get the new numerator: 15 + 8 = 23 (subtract instead for the − operation).
  3. Multiply the denominators to get the new denominator: 4 × 5 = 20.
  4. Reduce by the greatest common divisor of numerator and denominator — GCD(23, 20) = 1, so 23/20 is already in lowest terms.
  5. Convert to a decimal if you need one: 23 ÷ 20 = 1.15.

How does the fraction calculator work?

Addition and subtraction use the common-denominator identity n₁/d₁ ± n₂/d₂ = (n₁·d₂ ± n₂·d₁) / (d₁·d₂): cross-multiply each numerator against the opposite denominator, combine, and put the result over the product of the denominators. Multiplication multiplies numerators together and denominators together, and division inverts the second fraction and multiplies, giving (n₁·d₂) / (d₁·n₂). After the operation, the calculator reduces the result to lowest terms by dividing numerator and denominator by their greatest common divisor, found with the Euclidean algorithm. Using d₁·d₂ rather than the least common denominator changes nothing about the final answer — the GCD reduction lands in the same place — it just makes the intermediate fraction larger. The decimal shown underneath is the reduced numerator divided by the denominator, rounded to four places.

Last reviewed July 2, 2026 · Editorial policy

Frequently asked questions

How do you add fractions with different denominators?

Rewrite both over a common denominator, then add the numerators. The fastest route is cross-multiplication: 3/4 + 2/5 = (3×5 + 2×4) / (4×5) = 23/20. Any common denominator works — reducing at the end gives the same answer.

How do you divide one fraction by another?

Multiply by the reciprocal: flip the second fraction and multiply straight across, so 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. Dividing by a fraction smaller than 1 always gives a result larger than the number you started with.

Why is the answer shown as 23/20 instead of a mixed number?

The calculator reports improper fractions in lowest terms, with the decimal (1.15) underneath. To convert to a mixed number, divide: 23 ÷ 20 is 1 remainder 3, so 23/20 equals 1 and 3/20.

How do you reduce a fraction to lowest terms?

Divide the numerator and denominator by their greatest common divisor. For 8/20 the GCD is 4, so it reduces to 2/5. When the GCD is 1, as with 23/20, the fraction is already fully reduced.

How accurate is this fraction calculator?

The math is deterministic — the same inputs always produce the same output, and the formula is shown above. Accuracy of the answer for your situation depends on how well your inputs match reality and how well the formula models the question.

How do I share my result?

Hit Share at the top of the page. Every input you change is encoded in the URL, so a permalink reproduces exactly what you see. No account needed.