Question

Simplify the following expression.


49/60 − 1/4
A.
11/20




B.
29/60




C.
6/7




D.
17/30

Answer 1

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. \( \frac{17}{30} \)**