Final answer:
The common denominator for 1/8 and 2/3 is 24. To convert the fractions to equivalent fractions with this common denominator, we get 3/24 and 16/24 respectively. Hence, the answer is D. 24.
Step-by-step explanation:
To find a common denominator for the fractions 1/8 and 2/3, we need to find a number that both 8 and 3 can evenly divide into. This number will be the Least Common Multiple (LCM) of 8 and 3.
The multiples of 8 are 8, 16, 24, 32, and so on, while the multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, and so on. The smallest multiple that both lists share is 24, so the least common denominator is 24.
Now, to write equivalent fractions with the common denominator of 24, we multiply the numerator and denominator of each fraction by the number that turns their denominator into 24:
- For 1/8, we multiply by 3/3 (since 8 × 3 = 24), resulting in (1 × 3)/(8 × 3) = 3/24.
- For 2/3, we multiply by 8/8 (since 3 × 8 = 24), resulting in (2 × 8)/(3 × 8) = 16/24.
Therefore, the equivalent fractions with a common denominator of 24 are 3/24 and 16/24, and the correct answer to the question is D. 24.