Fraction Calculator
A fraction shows a part of a whole: the numerator (top) counts the parts and the denominator (bottom) says how many equal parts make the whole. This calculator combines two fractions with any of the four operations, then reduces the answer to lowest terms and also shows it as a mixed number and a decimal.
How to use the fraction calculator
- Type the numerator and denominator of each fraction. Whole numbers can be entered with a denominator of 1.
- Choose add, subtract, multiply or divide.
- Read the simplified fraction, the mixed number and the decimal, and follow the steps to see the method.
Formula
- Add / subtract: a/b ± c/d = (ad ± cb) / bd
- Multiply: a/b × c/d = ac / bd
- Divide: a/b ÷ c/d = a/b × d/c = ad / bc
- Simplify: divide the numerator and denominator by their greatest common factor (GCF).
Worked examples
Adding unlike fractions
1/2 + 1/3: the common denominator is 6, so 3/6 + 2/6 = 5/6. The calculator uses the cross-multiplied form (1×3 + 1×2) / (2×3) = 5/6, which is already in lowest terms.
Dividing fractions
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8. As a mixed number that is 1 7/8, and as a decimal 1.875.
Understanding fractions in depth
A fraction is a division that has not been carried out yet. Writing 3/4 means “3 divided by 4”, which is 0.75. This is why the denominator can never be 0 and why every fraction can be written as a decimal that either ends or repeats.
Types of fractions
| Type | Example | How to recognise it |
|---|---|---|
| Proper | 3/8 | Numerator smaller than the denominator; value below 1 |
| Improper | 11/4 | Numerator at least the denominator; value 1 or more |
| Mixed number | 2 3/4 | A whole number plus a proper fraction |
| Equivalent | 1/2 = 2/4 = 50/100 | Same value written with different numbers |
Why the common denominator works
You can only add pieces of the same size. Thirds and halves are different sizes, so we cut both into sixths: 1/2 becomes 3/6 and 1/3 becomes 2/6. Now the pieces match and adding is just counting them. Multiplication is different: taking 1/2 of 1/3 means splitting a third into two, which makes sixths, so 1/2 × 1/3 = 1/6 with no common denominator needed.
Where fractions show up
Cooking (3/4 cup), carpentry (5/16 inch), music (3/4 time), probability (the chance of two events) and finance (a 1/8 point change in a rate). Getting comfortable with them makes ratios, percentages and algebra much easier later.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- Add 2/3 + 3/4.
Show answer
Simplified fraction: 17/12
- Multiply 5/6 × 9/10.
Show answer
Simplified fraction: 3/4
- Subtract 7/8 − 1/6.
Show answer
Simplified fraction: 17/24
Common mistakes to avoid
- Adding denominators. 1/2 + 1/3 is not 2/5. You must first rewrite both fractions over a common denominator.
- Forgetting to flip the second fraction when dividing.
- Leaving the answer unsimplified. 6/8 and 3/4 are the same value, but 3/4 is the standard form.
Frequently asked questions
How do you add fractions with different denominators?
Rewrite them over a common denominator, add the numerators, and keep the denominator. For 1/2 + 1/3 use 6: 3/6 + 2/6 = 5/6.
How do you simplify a fraction?
Find the greatest common factor of the numerator and denominator and divide both by it. For 12/18 the GCF is 6, giving 2/3. Our GCF and LCM calculator can find it.
What is a mixed number?
A whole number plus a proper fraction, such as 1 7/8. It is another way to write an improper fraction like 15/8.
What happens if a denominator is zero?
Division by zero is undefined, so the calculator asks you to enter a valid denominator.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.