About this calculator
The Fraction Calculator adds, subtracts, multiplies, and divides two fractions while showing each stage of the working. It is useful for students checking homework, parents helping with revision, and anyone who wants to see why a fraction answer is correct rather than only seeing the final result.
fraction calculator method
For addition and subtraction, fractions first need a common denominator. For multiplication, multiply across the numerators and denominators. For division, multiply by the reciprocal of the second fraction.
- a/b + c/d = (ad + bc) / bd
- a/b - c/d = (ad - bc) / bd
- a/b x c/d = ac / bd
- a/b ÷ c/d = a/b x d/c
How to use the fraction calculator
- Enter the numerator and denominator for the first fraction.
- Choose add, subtract, multiply, or divide.
- Enter the second fraction.
- For addition or subtraction, review the LCD step.
- For multiplication or division, review the cross multiplication or reciprocal step.
- Check the simplified answer, mixed number, and decimal result.
Worked examples
Add unlike denominators
Input: 1/3 + 1/4
Calculation: LCD = 12, so 1/3 = 4/12 and 1/4 = 3/12
Result: 7/12
Divide fractions
Input: 2/3 ÷ 3/4
Calculation: Multiply by the reciprocal: 2/3 x 4/3
Result: 8/9
Why the common denominator matters
Fractions can only be added or subtracted directly when they describe the same size pieces. The LCD converts each fraction into equivalent pieces of the same size.
When to use mixed numbers
Improper fractions are often easier for calculation. Mixed numbers are often easier to read as final answers, especially in school work or measurements.
Learning and homework note
This calculator is for learning, checking, and general educational use. It shows the method so students can compare each step with their own working, but it should not replace learning the underlying fraction rules.
- Check that every denominator is not zero.
- Negative fractions can be written in more than one equivalent form.
- Rounding may affect decimal or percentage displays.
Frequently asked questions
Does this show the working?
Yes. The fraction calculators are designed to show the main steps, not just the final answer.
Does it simplify answers?
Yes. Fraction answers are reduced to lowest terms where simplification is part of the method.
Can denominators be zero?
No. A denominator of zero is undefined in fraction arithmetic.
Can I use negative fractions?
Yes, but pay attention to signs. The calculator normalises signs so the denominator stays positive.
Why might my teacher write the answer differently?
Equivalent fractions and mixed numbers can represent the same value. Check whether the question asks for improper fraction, mixed number, decimal, or simplest form.
Related calculators
- Simplify Fractions Calculator
- Mixed Number Calculator
- LCD Calculator