What a fraction actually represents
A fraction is a division waiting to happen: the numerator on top is how many parts you have, and the denominator on the bottom is how many equal parts the whole was split into. Three quarters means three of the four pieces a whole was cut into. This is why every operation on fractions comes back to one idea — you can only combine pieces that are the same size, which is what a common denominator guarantees. Keep that picture in mind and the rules below stop being arbitrary.
Adding and subtracting
Fractions can only be added when they describe the same sized pieces, which means finding a common denominator first. Multiplying the two denominators always works: 3/4 + 5/6 becomes 18/24 + 20/24 = 38/24, which simplifies to 19/12. Using the lowest common denominator (12 here) keeps the numbers smaller, but the answer is identical once simplified.
Multiplying and dividing
Multiplication needs no common denominator — multiply across the top and across the bottom. Division means multiplying by the reciprocal: 3/4 ÷ 5/6 is the same as 3/4 × 6/5 = 18/20 = 9/10. Flip the second fraction, then multiply.
Working with whole numbers
To combine a fraction with a whole number, write the whole number as a fraction over one. Adding 2 to 3/4 means 2/1 + 3/4; convert to quarters (8/4 + 3/4) to get 11/4, or the mixed number 2 3/4. Multiplying is simpler: 3 times 2/5 is just 6/5, because you multiply only the numerator. The calculator accepts whole numbers directly, but knowing the trick makes mental math faster.
Turning a fraction into a decimal or percentage
A fraction is a division, so 3/4 is simply 3 divided by 4, which is 0.75. To get a percentage, multiply the decimal by 100 — 0.75 becomes 75%. Some fractions divide cleanly; others, like 1/3, produce a repeating decimal (0.333...) that never ends, which is why fractions are often the more precise way to write a value. When you need the percentage form specifically, the percentage calculator does it in one step.
Common mistakes to avoid
- Adding across the top and bottom. 1/2 + 1/3 is not 2/5. You need a common denominator first; the answer is 5/6.
- Forgetting to simplify. 18/24 is correct but not finished — reduced, it is 3/4. Always simplify to lowest terms.
- Flipping the wrong fraction when dividing. To divide by a fraction you multiply by its reciprocal, and it is the second fraction (the divisor) that flips, not the first.
- Mixing up mixed numbers. 2 3/4 means two and three quarters (11/4), not two times three quarters.
Simplifying
To reduce a fraction to lowest terms, divide the numerator and the denominator by their greatest common divisor. The calculator uses the Euclidean algorithm: repeatedly replace the larger number with the remainder of dividing it by the smaller, until nothing is left over.
Mixed numbers and decimals
An improper fraction such as 19/12 can be written as the mixed number 1 7/12. Recipes and measurements prefer mixed numbers; further calculation is easier with improper fractions. The decimal form is exact when the denominator's only prime factors are 2 and 5; otherwise it repeats, and the figure shown here is rounded. To turn a fraction straight into a percentage, the percentage calculator is quicker.