Fraction Calculator

To add or subtract fractions, they must have a common denominator. For example, 1/2 + 1/3 requires finding the least common multiple (LCM) of 2 and 3, which is 6. Convert: 1/2 = 3/6 and 1/3 = 2/6. Now add the numerators: 3/6 + 2/6 = 5/6. The process: (1) find the LCM of the denominators, (2) convert each fraction by multiplying numerator and denominator by the same value, (3) add or subtract the numerators, (4) keep the denominator. For subtraction, the steps are identical: 3/4 − 1/6: LCM is 12; convert to 9/12 − 2/12 = 7/12. This skill is Common Core Math for grades 4–6 in US schools and forms the foundation for algebra and advanced math.

Multiplication is simpler than addition: multiply straight across. 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12, which simplifies to 1/2. You do not need a common denominator. Division reverses the second fraction (flip numerator and denominator) then multiply: 2/3 ÷ 3/4 becomes 2/3 × 4/3 = (2 × 4)/(3 × 3) = 8/9. Always simplify by dividing both numerator and denominator by their greatest common factor (GCF). For 6/12: GCF is 6, so 6/12 ÷ 6/6 = 1/2. Worked example: 5/6 × 2/5 = 10/30 = 1/3. Division example: 5/6 ÷ 2/5 = 5/6 × 5/2 = 25/12 = 2 and 1/12.

Cooking: recipes call for 1/2 cup, 3/4 teaspoon, 2/3 tablespoon; scale a recipe up or down using fraction multiplication. Construction: lumber is sold in fractional inches (2 × 4s are actually 1.5" × 3.5"; a 7.5-foot board is 7 + 1/2 feet). Stock prices: historically quoted in fractions like 123 and 5/8 dollars, though this is becoming rare. Sports statistics: batting averages are fractions simplified to three decimals (.333 = 1/3). Music: time signatures are fractions (4/4 means 4 beats per measure, each beat is 1/4 note). These real-world applications show fractions matter beyond homework. Understanding fractions opens doors to higher math, trades, cooking, music, and finance.