How it works
Fraction arithmetic follows fixed rules once fractions share a common denominator (for addition and subtraction) or multiply across numerators and denominators (for multiplication). Addition/subtraction: find the least common denominator (LCD), convert each fraction, combine numerators, simplify. Multiplication: multiply numerators and denominators directly, then simplify. Division: multiply the first fraction by the reciprocal of the second (flip numerator and denominator of the divisor). The engine computes the raw result, divides numerator and denominator by their greatest common divisor (GCD) to lowest terms, and reports the decimal equivalent. Worked example: 1/2 + 1/3. LCD of 2 and 3 is 6. 1/2 = 3/6, 1/3 = 2/6. Sum = 5/6. Decimal = 5 ÷ 6 = 0.8333… Multiplication example: 2/3 × 3/4 = 6/12 = 1/2 = 0.5. Division: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Always reject denominator zero — undefined. Mixed numbers (1½) convert to improper fractions first (3/2) before operating.
Formula
Add/sub: a/b ± c/d = (ad ± bc)/bd (then simplify) | Mul: a/b × c/d = ac/bd | Div: a/b ÷ c/d = a/b × d/c
Tips
- Simplify only after the operation — cross-cancel before multiplying if you do it by hand.
- Convert mixed numbers to improper fractions before entering (1½ → 3/2).
- A denominator of 1 means the result is a whole number.
- Check the decimal output when comparing fractions to percents or currency.
Frequently asked questions
- What is 1/2 plus 1/3?
- 5/6, which equals approximately 0.8333 in decimal form.
- How do you divide fractions?
- Multiply by the reciprocal: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
- What is 3/4 as a decimal?
- 0.75. The calculator returns the decimal for any result automatically.
- Why simplify fractions?
- Lowest terms (5/6 not 10/12) are the standard mathematical form and easier to read in further calculations.