Add, subtract, multiply, and divide fractions with automatic simplification.
Enter two fractions and select an operation.
1/2 + 1/4:
= (1×4 + 1×2) / (2×4) = 6/8 = 3/4
Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it. Our calculator does this automatically.
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
A fraction calculator adds, subtracts, multiplies and divides fractions, then reduces the answer to lowest terms automatically. A fraction expresses a part of a whole: the numerator on top counts how many parts you have, and the denominator below states how many equal parts make up the whole. Fractions remain essential in cooking, construction, engineering and finance, wherever exact parts matter more than decimal approximations.
Notice that multiplication is the simplest of the four, while addition and subtraction require the extra step of matching denominators. This surprises people who expect addition to be easier, and it is the source of most fraction errors.
Step 1: Find a common denominator
Step 2: Convert both fractions
Step 3: Add the numerators
Step 4: Convert the improper fraction
The total is 1 and 5/12 cups of liquid
Turning the second fraction upside down and multiplying looks like a trick, but there is a clear reason for it. Dividing by a number is the same as multiplying by its reciprocal. Dividing by 2 is multiplying by 1/2; dividing by 1/2 is multiplying by 2, which is why dividing by a fraction below one produces a larger answer.
There are 8 servings, and the answer is larger than 6 because each serving is smaller than a whole cup
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333... | 33.3% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.666... | 66.7% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
One third as a decimal is 0.3333 repeating forever. This is why fractions are still preferred in precise work: 1/3 is exact, while 0.333 is an approximation. In engineering and finance, rounding a repeating decimal early can compound into a meaningful error.
Imperial measurement is fraction-based. Timber, drill bits, spanners and pipe fittings come in halves, quarters, eighths and sixteenths. A carpenter adding 3/8 to 5/16 is doing exactly the arithmetic above, usually in their head.
Measuring cups are fractional, and halving or doubling a recipe means multiplying every fraction by the same factor. Halving 3/4 cup gives 3/8, which is not a standard cup size, which is why recipe scaling so often needs conversion to tablespoons.
US stock prices were quoted in fractions of a dollar, down to sixteenths, until decimalisation in 2001. Ownership stakes, partnership splits and interest rate movements are still commonly expressed in fractional terms.
To add two fractions without hunting for the lowest common denominator, use a/b + c/d = (ad + cb)/bd directly. The answer may not be in lowest terms, but it is always correct, and simplifying afterwards is easy. This is often faster than finding the smallest common denominator first.
This calculator is provided for educational purposes. For engineering, construction or financial applications requiring certified precision, verify results against professional standards.