Working with fractions without the headache
Fractions describe parts of a whole: the numerator (top number) counts how many parts you have, and the denominator (bottom number) says how many equal parts the whole is split into. Adding and subtracting fractions trips people up because you can only combine parts that are the same size — halves and quarters must first be rewritten in a shared size. Multiplying and dividing follow different, simpler rules, which is why this calculator shows the full working for whichever operation you choose, and always simplifies the answer.
The four fraction rules
For addition and subtraction the shared size is the least common denominator — the smallest number both denominators divide into. Each fraction is scaled by multiplying its top and bottom by the same amount, which changes how it is written but not its value. Division uses the reciprocal: dividing by a fraction is the same as multiplying by that fraction turned upside down. Every result is then simplified by dividing the numerator and denominator by their greatest common divisor (GCD).
Improper fractions and mixed numbers
When the numerator is larger than the denominator, such as 5/4, the fraction is called improper — it is worth more than one whole. The same value can be written as a mixed number, 1 1/4: one whole plus a proper fraction remainder. Neither form is more correct; recipes and measurements usually read better as mixed numbers, while further calculations are usually easier with improper fractions. This page shows both, plus the decimal and percentage equivalents, so you can pick the form your task needs.
Why simplification matters
2/4, 3/6 and 50/100 are all the same value as 1/2, but 1/2 is the form everyone recognises instantly. Simplifying (also called reducing to lowest terms) divides the top and bottom by their GCD — the largest number that divides both exactly. If the GCD is 1, the fraction is already as simple as it gets. Teachers require simplified answers, and simplified fractions are far easier to compare: it is obvious that 5/4 is bigger than 1, less obvious that 10/8 is.
One more habit worth building: estimate before you calculate. A fraction with a numerator close to its denominator is worth nearly one whole; a numerator half the denominator is worth about a half. If the calculator answer is nowhere near your rough estimate, a numerator and denominator have probably been swapped somewhere — and catching that swap is much easier before the answer is written down, submitted or measured out.
Worked example
Add 2/3 and 1/6. The common denominator is 6, so 2/3 becomes 4/6. Then 4/6 + 1/6 = 5/6, which is already simplified and equals about 0.8333 as a decimal.
How to use this calculator
- Enter the numerator and denominator of the first fraction.
- Enter the numerator and denominator of the second fraction.
- Choose add, subtract, multiply or divide.
- Read the simplified result, plus its mixed number, decimal and percentage forms.
- Follow the step-by-step working below to see the common denominator or reciprocal used.
Fractions, decimals and percentages are one idea
A fraction, a decimal and a percentage are three spellings of the same value: 3/4 = 0.75 = 75%. Moving between them is a core everyday skill — discounts are percentages, measurements are fractions, and money is decimal. If you work with proportions of a whole often, the Ratio Calculator covers the closely related idea of comparing two quantities, and the Scientific Calculator handles fractions inside longer expressions when you write them as divisions, such as (1/2) + (3/4).