Fraction Calculator
Operation
Result5/6
Decimal0.833333
Steps1/2 + 1/3 = 5/6 = 5/6
This fraction calculator adds, subtracts, multiplies, and divides two fractions and returns the answer in fully simplified form along with its decimal equivalent. Each result is reduced using the greatest common divisor, so 4/8 collapses to 1/2 automatically. It is useful for homework, cooking conversions, woodworking measurements, and any task where exact fractional values matter more than rounded decimals.
Formula
a/b + c/d = (a*d + c*b) / (b*d), then divide by gcd; a/b / c/d = (a*d) / (b*c)
- a/b
- The first fraction (numerator a over denominator b)
- c/d
- The second fraction (numerator c over denominator d)
- gcd
- Greatest common divisor used to reduce the result to lowest terms
How it works
- Enter the numerator and denominator of the first fraction, choose an operation (+, -, x, or /), then enter the second fraction.
- For addition and subtraction the calculator puts both fractions over a common denominator; for multiplication it multiplies numerators and denominators directly; for division it multiplies by the reciprocal of the second fraction.
- The raw result is then reduced by dividing the numerator and denominator by their greatest common divisor, and the simplified fraction plus its decimal value are displayed.
Worked examples
Add 1/2 and 1/3.
- Find a common denominator: 2 x 3 = 6.
- Convert and add: (1 x 3) + (1 x 2) = 3 + 2 = 5 over 6.
- The result 5/6 is already in lowest terms (gcd of 5 and 6 is 1).
1/2 + 1/3 = 5/6, which is approximately 0.8333 as a decimal.
Divide 3/4 by 2/5.
- Multiply by the reciprocal: 3/4 x 5/2.
- Multiply across: (3 x 5) over (4 x 2) = 15 over 8.
- 15/8 is already reduced (gcd of 15 and 8 is 1).
3/4 / 2/5 = 15/8, which equals 1.875 as a decimal.
Frequently asked questions
- Does the calculator simplify the answer automatically?
- Yes. Every result is reduced to lowest terms by dividing the numerator and denominator by their greatest common divisor, so you always see the simplest equivalent fraction.
- What happens if I enter a zero denominator?
- A fraction cannot have a denominator of zero, so the calculator returns no result in that case. Dividing by a fraction whose numerator is zero is likewise undefined and produces no answer.
- How are negative fractions handled?
- A negative sign on either the numerator or denominator is carried through the arithmetic and normalized so the simplified result keeps the sign on the numerator, which is the standard convention.
- Can it convert the fraction to a decimal?
- Yes. Alongside the simplified fraction, the calculator divides the numerator by the denominator to show the decimal equivalent, which is handy when you need a quick approximate value.