Find the least common denominator (LCD) of 9/4 and 1/8.
Understand the Problem
The question is asking to find the least common denominator (LCD) of the fractions 9/4 and 1/8. This involves determining the smallest multiple that both denominators (4 and 8) can divide into without leaving a remainder.
Answer
The least common denominator (LCD) of $ \frac{9}{4} $ and $ \frac{1}{8} $ is 8.
Answer for screen readers
The least common denominator (LCD) of $ \frac{9}{4} $ and $ \frac{1}{8} $ is 8.
Steps to Solve
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Identify the denominators The denominators of the fractions are 4 and 8.
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Find multiples of each denominator List a few multiples of each denominator:
- Multiples of 4: 4, 8, 12, 16, ...
- Multiples of 8: 8, 16, 24, ...
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Determine the least common multiple (LCM) Look for the smallest multiple that appears in both lists of multiples. The smallest common multiple is 8.
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Conclusion Thus, the least common denominator (LCD) of the fractions $ \frac{9}{4} $ and $ \frac{1}{8} $ is 8.
The least common denominator (LCD) of $ \frac{9}{4} $ and $ \frac{1}{8} $ is 8.
More Information
The least common denominator is essential for adding or subtracting fractions. It allows us to work with fractions that have different denominators by finding a common base.
Tips
- Overlooking multiples: Sometimes, students may skip listing enough multiples and miss the least common one. To avoid this, ensure to list a sufficient number of multiples for each denominator.
- Confusing the numerator with the denominator: It’s important to focus on the denominators when finding the LCD, rather than mixing them with numerators.
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