To compare the two fractions \( \frac{15}{4} \) and \( \frac{17}{5} \), we can find a common denominator or convert them to decimal form.
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Finding a common denominator: The least common multiple (LCM) of the denominators 4 and 5 is 20.
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Convert \( \frac{15}{4} \) to have a denominator of 20: \[ \frac{15}{4} = \frac{15 \times 5}{4 \times 5} = \frac{75}{20} \]
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Convert \( \frac{17}{5} \) to have a denominator of 20: \[ \frac{17}{5} = \frac{17 \times 4}{5 \times 4} = \frac{68}{20} \]
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Now, we can compare \( \frac{75}{20} \) and \( \frac{68}{20} \):
- Since 75 is greater than 68, we have: \[ \frac{75}{20} > \frac{68}{20} \]
Thus: \[ \frac{15}{4} > \frac{17}{5} \]
- Converting to decimal form:
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Convert \( \frac{15}{4} \): \[ 15 \div 4 = 3.75 \]
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Convert \( \frac{17}{5} \): \[ 17 \div 5 = 3.4 \]
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Since \( 3.75 > 3.4 \), it also confirms that: \[ \frac{15}{4} > \frac{17}{5} \]
Therefore, \( \frac{15}{4} \) is greater than \( \frac{17}{5} \).