Fractions are arithmetic's most human form — you count parts of a whole rather than abstract decimals. The rules for combining them are consistent, and once you see why common denominators exist, they stop being memorization.
Why common denominators
You can't add halves and quarters directly because they're different-size pieces. Scaling both to the same denominator — quarters, say — makes the pieces equal, so the numerators just add. Multiplication and division skip this step: numerators multiply with numerators, and division flips the second fraction.
Simplification
The answer after combining often isn't in its simplest form — 6/8 means the same as 3/4. Dividing the numerator and denominator by their greatest common divisor expresses the result in lowest terms, which is how people read and use fractions.
Fractions and decimals
Every fraction is a division: 3/4 is 3 ÷ 4 = 0.75. The two views are interchangeable, which is why the calculator shows both — decimals for precision and calculation, fractions for meaning and comparison.
Frequently asked questions
Find a common denominator (multiply the denominators), scale each numerator, add, then simplify. For 1/2 + 1/4: scale 1/2 to 2/4, add to 1/4 → 3/4.
Flip the second fraction and multiply. For 1/2 ÷ 1/4: flip 1/4 to 4/1 and multiply → 1/2 × 4/1 = 4/2 = 2.
One where the numerator and denominator share no common factor — for example 3/4 rather than 6/8. Simplification divides both by their greatest common divisor.