Math
Fraction Calculator
Enter two fractions and an operation to get the answer as a simplified fraction, a mixed number, and a decimal.
Calculation inputs
Use whole numbers for the numerators and denominators.
Results
No result yet
Complete the fields and select Calculate to show results here.
About this calculator
This calculator adds, subtracts, multiplies, or divides two fractions and returns the answer as a simplified fraction, a mixed number, and a decimal. It is built for students checking homework and anyone who needs to combine fractional quantities without doing the arithmetic by hand.
How the calculation works
- Addition and subtraction use a common denominator: (a×d ± c×b) ÷ (b×d)
- Multiplication multiplies across: (a×c) ÷ (b×d)
- Division multiplies by the reciprocal: (a×d) ÷ (b×c)
- The result is reduced by dividing both parts by their greatest common divisor
Notes and assumptions
A negative result carries the sign on the numerator, and whole-number results are shown without a denominator.
How it works in plain English
Enter the numerator and denominator for each fraction and choose an operation. For addition and subtraction, the calculator finds a common denominator by multiplying the two denominators together, adjusts each numerator to match, and then adds or subtracts the numerators. For multiplication, it multiplies the numerators together and the denominators together. For division, it multiplies the first fraction by the reciprocal of the second, which means flipping the second fraction's numerator and denominator before multiplying.
Once it has a raw result, the calculator simplifies it by dividing both the numerator and denominator by their greatest common divisor, so the fraction is shown in its lowest terms. It also converts that simplified fraction into a mixed number when the numerator is larger than the denominator, and into a decimal by dividing the numerator by the denominator.
A denominator of zero is never allowed, since dividing by zero is undefined, and dividing by a fraction whose numerator is zero is blocked for the same reason.
The formula
- Addition/subtraction: a/b ± c/d = (a x d ± c x b) / (b x d)
- Multiplication: a/b x c/d = (a x c) / (b x d)
- Division: a/b ÷ c/d = a/b x d/c = (a x d) / (b x c)
Worked example
Adding 3/4 and 5/6: find the common denominator by multiplying 4 and 6 to get 24. Scale 3/4 to 18/24 and 5/6 to 20/24, then add the numerators to get 38/24. Dividing both parts by their greatest common divisor, 2, simplifies this to 19/12.
As a mixed number that is 1 and 7/12, and as a decimal it is approximately 1.5833. The calculator displays all three forms at once so you can use whichever fits your work.
If you then wanted to multiply that result, 19/12, by 2/3, you would multiply the numerators to get 38 and the denominators to get 36, giving 38/36. Dividing both parts by their greatest common divisor, 2, simplifies that to 19/18, which as a mixed number is 1 and 1/18, and as a decimal is approximately 1.0556. Each step follows the same simplify-and-convert process regardless of which operation you choose.
Frequently asked questions
How does the calculator simplify a fraction?
It finds the greatest common divisor (the largest number that divides evenly into both the numerator and denominator) and divides both parts by it. This produces the smallest possible whole-number numerator and denominator that still represent the same value, which is what 'simplified' or 'lowest terms' means.
What happens if I enter a negative numerator?
Negative numerators are supported and carried through the whole calculation normally. The sign follows standard arithmetic rules, so a negative fraction added to a positive one behaves like subtraction, and multiplying two negative fractions returns a positive result.
Why can't the denominator be zero?
A fraction with a zero denominator has no defined value, because dividing by zero is not a valid mathematical operation. The calculator blocks this case and shows a message instead of attempting a calculation that has no real answer.
Can I use this for improper fractions?
Yes, you can enter any whole numbers for the numerator and denominator, including cases where the numerator is larger than the denominator. The result is simplified and also shown as a mixed number, which separates out the whole-number part for easier reading.
Why does dividing fractions flip the second one?
Dividing by a number is the same as multiplying by its reciprocal, which is why dividing by a fraction means flipping its numerator and denominator and then multiplying. This is a standard rule of fraction arithmetic rather than something specific to this calculator.