Fraction Calculator

Enter two fractions and an operation.

Fractions trip up adults more than any other arithmetic topic

The rules for fraction arithmetic are counterintuitive by design. Adding 1/2 and 1/3 does not equal 2/5 — it equals 5/6, because you need a common denominator first. Multiplying fractions is actually easier than adding them: multiply numerators, multiply denominators, simplify. Most calculation errors in cooking, construction, and finance come from misapplied fraction rules, particularly forgetting to find the least common denominator before adding or subtracting.

Simplification matters because unsimplified fractions obscure the real relationship. 48/64 and 3/4 are identical values, but 3/4 is immediately readable as 'three quarters' while 48/64 requires mental effort to interpret. This calculator always reduces results to lowest terms automatically, and shows the decimal equivalent alongside the fraction so you can verify your answer makes intuitive sense before using it.

Frequently asked questions

How do I add fractions with different denominators?
Find the <strong>least common denominator (LCD)</strong> — the smallest number both denominators divide into evenly. For 1/4 + 1/6, the LCD is 12. Convert both fractions: 3/12 + 2/12 = 5/12. The mistake most people make is multiplying denominators together (giving 24) instead of finding the actual LCD, which produces a correct but unsimplified result that is harder to work with downstream.
What is the difference between a proper fraction, improper fraction, and mixed number?
A <strong>proper fraction</strong> has a numerator smaller than the denominator (3/4). An <strong>improper fraction</strong> has a numerator equal to or greater than the denominator (7/4). A <strong>mixed number</strong> combines a whole number and proper fraction (1 3/4). They all represent the same value. Most calculators and formulas expect improper fractions for arithmetic, but mixed numbers are easier to read in context. This calculator accepts and outputs both forms.
Why does dividing by a fraction seem backwards?
Dividing by a fraction is the same as multiplying by its reciprocal — you flip the second fraction and multiply. So 3/4 divided by 2/5 becomes 3/4 times 5/2, which equals 15/8. The intuition: dividing by 1/2 should give you twice as many pieces, and multiplying by 2/1 does exactly that. This rule is not a trick; it is a direct consequence of what division means mathematically.
When should I use fractions instead of decimals?
Use fractions when <strong>exact values matter and repeating decimals would introduce error</strong>. 1/3 as a decimal is 0.333... — truncating that in a multi-step calculation introduces cumulative error. In cooking and woodworking, standard measurements (1/8 inch, 1/4 cup) are defined as fractions and do not translate cleanly to decimals. In financial calculations, use decimals. In legal descriptions of land, use fractions. The context tells you which form is authoritative.

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