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3/4 + 2/3 = 17/12, which is 1 5/12 — and 1 2/3 × 2 1/4 is exactly 3 3/4. Every form, every time, reduced automatically.
Fraction arithmetic is where homework goes wrong: finding common denominators, flipping divisors, converting mixed numbers back and forth, and remembering to reduce at the end. This calculator takes two fractions or mixed numbers, applies any of the four operations, and shows the result as an improper fraction, a mixed number, a reduced fraction, and a decimal — the exact answer and the practical answer side by side.
Students use it mid-homework: 3/4 + 2/3 = 17/12 (1 5/12), 1 2/3 × 2 1/4 = 3 3/4 — improper, mixed, reduced, and decimal, every form at once.
Find a common denominator — the least common multiple of the two denominators — convert both fractions to that denominator, then add the numerators and reduce. Example: 3/4 + 2/3. The LCM of 4 and 3 is 12, so 3/4 becomes 9/12 and 2/3 becomes 8/12; the sum is 17/12, which is the mixed number 1 5/12. Multiplication and division are actually easier: multiply straight across (numerator × numerator, denominator × denominator), and for division, invert the second fraction and multiply. The step everyone forgets is reducing — always divide numerator and denominator by their greatest common divisor at the end: 15/20 is not done until it is 3/4.
A mixed number combines a whole number and a proper fraction — 3 3/4 means 3 + 3/4. Improper fractions (numerator ≥ denominator, like 15/4) are better for calculating; mixed numbers are better for communicating, because "3 3/4 cups of flour" is instantly readable while "15/4 cups" makes most people pause. The professional convention: calculate in improper form, present in mixed form. Converting is mechanical: multiply the whole number by the denominator and add the numerator to go improper (1 2/3 → 5/3), and divide to go back (15/4 → 3 remainder 3 → 3 3/4). This calculator shows both forms so you never have to convert by hand.
Divide the numerator by the denominator: 3/4 = 0.75, 5/8 = 0.625. Some fractions never terminate — 1/3 is 0.333... forever — so decimals are sometimes approximations while fractions are always exact. That is why recipes and carpentry stay fractional: 1/3 cup is exact, 0.33 cups is not. The worth-memorizing conversions: 1/2 = 0.5, 1/4 = 0.25, 1/8 = 0.125, 1/16 = 0.0625 — the binary fractions that dominate US measurement (tape measures, drill bits, stock quotes before 2001). Going the other way, 0.375 as a fraction: put it over 1000 (375/1000) and reduce by 125 to get 3/8.