Fraction Calculator

Fractions represent parts of a whole: the denominator says how many equal parts the whole is split into, and the numerator says how many of those parts you have. Adding and subtracting fractions requires a common denominator — you cannot add thirds and eighths directly, any more than you can add apples and oranges. The standard move is to convert each fraction to an equivalent one with the least common denominator, add or subtract the numerators, and keep the denominator. Multiplication is simpler: multiply straight across, numerators times numerators and denominators times denominators. Division is multiplication by the reciprocal: flip the second fraction and multiply, which is why dividing by 1/2 doubles a number.

The classic mistakes are adding denominators (1/2 + 1/3 is not 2/5, it is 5/6) and forgetting to simplify the result. Always reduce the final answer by dividing numerator and denominator by their greatest common divisor: 10/12 becomes 5/6, and 4/8 becomes 1/2. Mixed numbers add one more step — convert 1 and 3/8 to the improper fraction 11/8 before operating, then convert back at the end. This calculator shows each step so you can follow the common-denominator and reciprocal logic rather than just copying an answer, which is what actually builds the skill for exams. One more tool for the kit: converting between fractions, decimals, and percents fluently. 3/8 is 0.375 is 37.5 percent — divide the numerator by the denominator for the decimal, multiply by 100 for the percent. Kitchen measuring cups (1/4, 1/3, 1/2) reward this fluency daily: doubling a recipe that calls for 2/3 cup gives 4/3 = 1 and 1/3 cups, and knowing that 1/3 cup is about 5 tablespoons plus a teaspoon saves a conversion chart lookup.