Fraction Calculator

Perform operations on simple/stacked mixed numbers, simplify fractions, and convert between decimals.

Step-by-Step Derivation

1. Convert mixed numbers: Fraction 1 = 3/4, Fraction 2 = 2/5

2. LCD of 4 and 5 is 20

3. Convert: 15/20 + 8/20 = 23/20

5. Express as mixed number: 1 3/20

Result

23 / 20

Decimal:1.15

Mixed Number:1 3/20

Visual Preview (Subdivisions)

Understanding fraction arithmetic and simplification

Arithmetic operations on fractions calculate numerators based on denominators. For additions or subtractions, the calculator converts values using the Least Common Denominator (LCD).

Simplifying fractions dividing both values by the Greatest Common Divisor (GCD). Mixed numbers combine whole units and proper fractional remainders.

Built and maintained by Meet Shah · Last updated 12 August 2026

What this tool is used for

Adding or subtracting fractions with different denominators without finding the common one by hand.
Checking homework working step by step rather than only the answer.
Simplifying a fraction to its lowest terms.
Multiplying mixed numbers for a recipe or a measurement.
Confirming a result you reached a different way.

Frequently Asked Questions

How does it simplify a fraction?: With Euclid's algorithm: replace (a, b) with (b, a mod b) until b is zero, and the last non-zero value is the greatest common divisor. 24/36 has a GCD of 12, giving 2/3. A negative denominator is normalised away, so 3/−4 becomes −3/4.
How do I enter a negative fraction?: Put the minus on the whole number for a mixed number — −1 1/2 is read as −(1 × 2 + 1)/2 = −3/2 — or on the numerator for a proper fraction such as −3/4. Everything is converted to an improper fraction first, so the sign belongs to the whole value.
Why doesn't 0.333333 convert to 1/3?: The decimal converter is exact rather than a repeating-decimal detector: it takes the digits after the point over the matching power of ten and simplifies, so 0.333333 becomes 333333/1000000. 0.375 gives 375/1000 → 3/8. For a third, type 1/3 directly.
How is division carried out?: By multiplying by the reciprocal: a/b ÷ c/d = a/b × d/c. That is why dividing by a fraction smaller than 1 makes the result bigger. If the divisor's numerator is zero the reciprocal would have a zero denominator, so the tool refuses rather than showing Infinity.
Why convert mixed numbers before adding?: Because 2 1/2 + 1 3/4 cannot be added part by part without carrying. As improper fractions they are 5/2 and 7/4; over the common denominator 4 that is 10/4 + 7/4 = 17/4, which converts back to 4 1/4. The step list shows each stage.

Common errors and gotchas

Adding numerators and denominators separately, which is the single most common fraction mistake there is.
Forgetting to convert a mixed number before multiplying or dividing.
Dividing by a fraction rather than multiplying by its reciprocal.
Leaving the result unsimplified when the question asked for lowest terms.
Cancelling across an addition, which is only valid across multiplication.