Loading...
A fraction represents a part of a whole, written as numerator/denominator (a/b). The numerator shows how many parts you have, while the denominator shows the total number of equal parts. Fraction arithmetic follows specific rules: addition and subtraction require common denominators, multiplication combines numerators and denominators directly, and division involves multiplying by the reciprocal.
Addition/Subtraction
Find common denominator, then add/subtract numerators
Multiplication
Multiply numerators, multiply denominators
Division
Keep first, flip second, then multiply
Enter fractions and click Calculate to see the result
To add or subtract fractions, find a common denominator, convert each fraction, then add/subtract numerators. To multiply fractions, multiply numerators and denominators directly. To divide fractions, multiply by the reciprocal (flip the second fraction). Always simplify the result by dividing by the GCD.
Step 1: Find the Least Common Denominator (LCD) of the two denominators. Step 2: Convert each fraction to an equivalent fraction with the LCD. Step 3: Add the numerators together. Step 4: Keep the common denominator. Step 5: Simplify if possible. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
Subtraction follows the same process as addition: find a common denominator, convert both fractions, then subtract the numerators. Example: 3/4 - 1/6: LCD is 12. Convert: 9/12 - 2/12 = 7/12. Watch for negative results if the second fraction is larger.
Multiplication is simpler than addition: multiply the numerators together, then multiply the denominators together. (a/b) × (c/d) = (a×c)/(b×d). Example: 2/3 × 4/5 = 8/15. You can also cross-cancel before multiplying to keep numbers smaller.
To divide fractions, multiply by the reciprocal (flip the second fraction). (a/b) ÷ (c/d) = (a/b) × (d/c). Remember: Keep the first fraction, Change to multiplication, Flip the second fraction. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
The LCD is the Least Common Multiple (LCM) of the denominators. Methods: (1) List multiples of each denominator until you find the smallest common one. (2) Use prime factorization and take the highest power of each prime. (3) For two numbers, LCD = (a × b) / GCD(a, b). Example: LCD of 4 and 6 is 12.
Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD. A fraction is fully simplified when the GCD is 1 (numerator and denominator share no common factors except 1). Example: 12/18: GCD is 6, so 12/18 = 2/3.
A proper fraction has a numerator smaller than its denominator (like 3/4), representing less than one whole. An improper fraction has a numerator equal to or greater than its denominator (like 7/4), representing one or more wholes. Improper fractions can be converted to mixed numbers: 7/4 = 1¾.
Mixed to improper: multiply whole number by denominator, add numerator, keep denominator. 3½ = (3×2 + 1)/2 = 7/2. Improper to mixed: divide numerator by denominator. Quotient is whole number, remainder is new numerator. 7/2 = 3 remainder 1, so 3½.