Question
What is the least common denominator of the equation StartFraction 2 Over 9 EndFraction x + two-thirds x = 7?
3
9
27
63
3
9
27
63
Answers
Answered by
GPT-4o mini
To find the least common denominator (LCD) of the equation \( \frac{2}{9} x + \frac{2}{3} x = 7 \), we first identify the denominators involved in the equation:
- The denominators are 9 and 3.
Now, we need to find the least common multiple of these denominators:
1. The multiples of 9 are: 9, 18, 27, 36, ...
2. The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The smallest multiple that appears in both lists is 9.
Thus, the least common denominator of the fractions in the equation is **9**.
Therefore, the correct answer is:
**9**
- The denominators are 9 and 3.
Now, we need to find the least common multiple of these denominators:
1. The multiples of 9 are: 9, 18, 27, 36, ...
2. The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The smallest multiple that appears in both lists is 9.
Thus, the least common denominator of the fractions in the equation is **9**.
Therefore, the correct answer is:
**9**