Final answer:
The least common denominator (LCD) for the fractions 2/3 and 3/4 is 12. To rename these fractions with the LCD, multiply the numerators and denominators to get equivalent fractions: 2/3 becomes 8/12 and 3/4 becomes 9/12.
Step-by-step explanation:
To rename the fractions 2/3 and 3/4 using the least common denominator (LCD), we first need to determine the LCD for both fractions. The LCD is the least common multiple (LCM) of the two denominators. In this case, the denominators are 3 and 4. Since 3 and 4 have no common factors other than 1, the LCM of 3 and 4 is simply their product, which is 12. Hence, the LCD for these fractions is 12.
Now, we adjust each fraction so that they both have the denominator of 12. To do this, we find what number we need to multiply the denominator of each fraction by to get 12 and then multiply both the numerator and denominator of each fraction by this number:
- For 2/3, multiply both the numerator and denominator by 4 to get (2×4)/(3×4) = 8/12.
- For 3/4, multiply both the numerator and denominator by 3 to get (3×3)/(4×3) = 9/12.
Therefore, when renamed with the least common denominator, 2/3 becomes 8/12 and 3/4 becomes 9/12.