How many quarters are there in `18 (3)/(4)` ?

Options

A. 35
B. 68
C. 75
D. 72

Explanation

To find out how many quarters are there in \( 18 \frac{3}{4} \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
A mixed number consists of a whole number and a fraction. To convert \( 18 \frac{3}{4} \) into an improper fraction, we can use the formula:

\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator}\right) + \text{Numerator} \]

In this case, the whole number is 18 and the fraction is \( \frac{3}{4} \).

\[ 18 \frac{3}{4} = \left(18 \times 4\right) + 3 = 72 + 3 = 75 \]

So, \( 18 \frac{3}{4} \) can be expressed as \( \frac{75}{4} \).

### Step 2: Determine how many quarters are in the improper fraction
A quarter is represented as \( \frac{1}{4} \). To find out how many quarters are in \( \frac{75}{4} \), we can divide \( \frac{75}{4} \) by \( \frac{1}{4} \):

\[ \text{Number of quarters} = \frac{75}{4} \div \frac{1}{4} \]

Dividing by a fraction is the same as multiplying by its reciprocal:

\[ \frac{75}{4} \times 4 = 75 \]

### Conclusion
Thus, there are **75 quarters** in \( 18 \frac{3}{4} \).

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