How to Calculate with Fractions
A fraction represents a part of a whole: the numerator (top) counts the parts, and the denominator (bottom) says how many parts make one whole. To add or subtract fractions, they must share a common denominator; to multiply, multiply straight across; to divide, multiply by the reciprocal of the second fraction.
a/b × c/d = ac / bd
a/b ÷ c/d = a/b × d/c = ad / bc
After any operation, the result should be reduced to lowest terms by dividing the numerator and denominator by their greatest common factor. This calculator does that automatically and also shows the answer as a mixed number and a decimal.
To add 3/4 + 5/6: the least common denominator of 4 and 6 is 12. Rewrite as 9/12 + 10/12 = 19/12, which is the mixed number 1 7/12 ≈ 1.5833.
Fraction Rules at a Glance
| Operation | Rule | Example |
|---|---|---|
| Add | Common denominator, add tops | 1/2 + 1/3 = 5/6 |
| Subtract | Common denominator, subtract tops | 3/4 − 1/2 = 1/4 |
| Multiply | Straight across | 2/3 × 3/5 = 6/15 = 2/5 |
| Divide | Keep, change, flip | 1/2 ÷ 1/4 = 2 |
Common Mistakes to Avoid
- Adding denominators: 1/2 + 1/3 is not 2/5 — denominators are units, not quantities to add.
- Forgetting to simplify: 6/8 is correct but 3/4 is the expected final form.
- Flipping the wrong fraction when dividing: only the second fraction (the divisor) is inverted.
Frequently Asked Questions
How do you add fractions with different denominators?
Rewrite both fractions with a common denominator (the least common multiple of the two denominators), add the numerators, and simplify. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do you simplify a fraction?
Divide the numerator and denominator by their greatest common factor (GCF). For 18/24, the GCF is 6, so 18/24 simplifies to 3/4.
How do you divide fractions?
Multiply by the reciprocal of the second fraction — “keep, change, flip.” So 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What is an improper fraction and a mixed number?
An improper fraction has a numerator larger than its denominator, like 7/4. The same value written as a whole number plus a fraction, 1 3/4, is a mixed number. Both are correct; mixed numbers are just easier to picture.
Cite This Calculator
Using this calculator in an assignment, article or lesson? Copy a ready-made citation — or the link snippet if you're referencing it from a web page.
The CalculatorsGuide Editorial Team. (2026). Fraction Calculator. CalculatorsGuide. Retrieved from https://www.calculatorsguide.com/math/fraction-calculator/