Final answer:
To find the lowest common denominator of 1/2, 5/6, and 2/9, determine the unique factors of the denominators, taking the highest power of all prime factors. The LCD is 18, allowing the fractions to be converted to 9/18, 15/18, and 4/18 respectively, for straightforward addition or subtraction.
Step-by-step explanation:
To find the lowest common denominator (LCD) for the fractions 1/2, 5/6, and 2/9, you first need to identify all the unique factors that make up the denominators. Here, we have the numbers 2, 6, and 9. The number 6 is divisible by 2, so we only need to consider the factors of 6 and 9. The prime factorization of 6 is 2 × 3, and for 9, it is 3 × 3 (or 32). To get the lowest common denominator, we take the highest powers of all the prime factors involved: 2 and 32. Thus, the LCD is 2 × 32 or 18. Now, convert each fraction to an equivalent fraction with the LCD as the new denominator. The fraction 1/2 becomes 9/18, 5/6 becomes 15/18, and 2/9 becomes 4/18. Now, these fractions can be easily added or subtracted.