To determine which ratio is less than \(\frac{15}{24}\), we can compare each of the options to \(\frac{15}{24}\).
First, let's simplify \(\frac{15}{24}\): \[ \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \]
Now let's convert each option to a decimal or a common fraction for easier comparison:
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One-half: \[ \frac{1}{2} = \frac{4}{8} \]
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\(\frac{7}{8}\): This is already in the correct form and is equal to \(0.875\).
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\(\frac{19}{24}\): To compare, we'll convert it to a decimal: \[ 19 \div 24 \approx 0.7917 \]
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\(\frac{6}{8}\) (which simplifies to \(\frac{3}{4}\)): \[ \frac{3}{4} = 0.75 \]
Now, we can compare each option with \(\frac{5}{8} = 0.625\):
- \(\frac{1}{2} = 0.5\) (less than \(\frac{5}{8}\)): This is a candidate.
- \(\frac{7}{8} = 0.875\) (greater than \(\frac{5}{8}\)): not a candidate.
- \(\frac{19}{24} \approx 0.7917\) (greater than \(\frac{5}{8}\)): not a candidate.
- \(\frac{6}{8} = \frac{3}{4} = 0.75\) (greater than \(\frac{5}{8}\)): not a candidate.
The only ratio that is less than \(\frac{15}{24}\) is \(\frac{1}{2}\).
Thus, the answer is: \[ \text{One-half} \]
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