The four operations, rule by rule
Adding and subtracting are the operations that demand a common denominator, because you can only count pieces that are the same size. Halves and thirds become sixths: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. The calculator handles the conversion and then simplifies — dividing the top and bottom by their greatest common divisor — so 6/8 comes back as 3/4. Multiplying needs no common denominator: straight across the top and straight across the bottom, so 3/4 × 2/5 = 6/20 = 3/10. Dividing is multiplying by the flipped second fraction: 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 2. That result surprises people the first time — how can dividing make something bigger? Because the question is really "how many quarters fit into a half?", and the answer is two.
Improper fractions and mixed numbers
When the numerator is larger than the denominator — 7/3, say — the fraction is called improper, and it is usually friendlier as a mixed number: 7/3 = 2 1/3, two whole units and a third of another. Kitchens and workshops speak in mixed numbers (2 1/2 cups of flour, a board 5 3/4 inches long), while algebra prefers improper fractions because they are easier to multiply and divide. This calculator shows both, plus the decimal, so you can move between a recipe, a tape measure and a phone calculator without translating by hand.
Fractions you will meet in the wild
| Fraction | Decimal | Percent | Where it shows up |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half an hour, half a cup |
| 1/3 | 0.333… | 33.3% | A third of a yard is 12 inches |
| 1/4 | 0.25 | 25% | Quarter inch, quarter past the hour |
| 3/8 | 0.375 | 37.5% | Wrench and drill-bit sizes |
| 5/8 | 0.625 | 62.5% | Plywood and bolt sizes |
| 7/8 | 0.875 | 87.5% | Almost-an-inch measurements |
The repeating decimal for thirds is worth a word: 1/3 is exactly 0.333…, never quite 0.33, which is why three thirds can seem to add to 0.99 on a decimal calculator while the fraction answer is exactly 1. Fractions keep perfect precision for these values; decimals are the approximation.
Helping with homework, honestly
The fastest way to check a child's fraction homework — or your own recipe scaling — is to run the problem here and then work backwards from the answer: does 5/6 sit sensibly between 1/2 and 1? Is the product of two proper fractions smaller than both, as it must be? Calculators verify; those sanity checks are what actually teach the feel of fractions. For scaling a recipe, multiply each ingredient fraction by the scaling fraction (3/2 to make half as much again) with the multiply setting.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions over a common denominator, then add the numerators. For 1/2 + 1/3, the common denominator is 6: 3/6 + 2/6 = 5/6. This calculator finds the common ground and simplifies the answer automatically.
How do I multiply fractions?
Multiply straight across: numerators together, denominators together, then simplify. 3/4 × 2/5 = 6/20 = 3/10. No common denominator is needed for multiplication or division.
How do I divide fractions?
Flip the second fraction (its reciprocal) and multiply. 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Dividing by a fraction smaller than 1 gives an answer larger than what you started with, which is why the result can look surprising.
What is a mixed number?
A mixed number combines a whole number with a proper fraction: 7/3 is 2 1/3, because 7 thirds make two wholes (6/3) with one third left over. Tape measures, recipes and woodworking plans are usually written in mixed numbers.
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