To simplify the expression \( \frac{49}{60} - \frac{1}{4} \), we need a common denominator.
The least common multiple (LCM) of 60 and 4 is 60.
Now, we can rewrite \( \frac{1}{4} \) with a denominator of 60:
\[ \frac{1}{4} = \frac{1 \times 15}{4 \times 15} = \frac{15}{60} \]
Now, we can subtract:
\[ \frac{49}{60} - \frac{15}{60} = \frac{49 - 15}{60} = \frac{34}{60} \]
Next, we simplify \( \frac{34}{60} \). The greatest common divisor (GCD) of 34 and 60 is 2.
Dividing both the numerator and denominator by 2, we get:
\[ \frac{34 \div 2}{60 \div 2} = \frac{17}{30} \]
Thus, the simplified expression is \( \frac{17}{30} \).
So the answer is:
D. \( \frac{17}{30} \)
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