How many quarters are there in 18$\frac{3}{4}$ ?

Question

Accepted Answer

To determine how many quarters are in 18$\frac{3}{4}$, we need to convert the mixed number into quarters. A quarter is equivalent to $\frac{1}{4}$ of a whole.

1. **Convert the Mixed Number to an Improper Fraction:**
   - 18$\frac{3}{4}$ can be expressed as an improper fraction. 
   - Multiply the whole number 18 by 4 (since there are 4 quarters in a whole), which gives 72.
   - Add the numerator of the fractional part, which is 3, to 72. This results in 75.
   - Therefore, 18$\frac{3}{4}$ is equivalent to $\frac{75}{4}$.

2. **Determine the Number of Quarters:**
   - Since each quarter is $\frac{1}{4}$, the number of quarters in $\frac{75}{4}$ is simply the numerator, which is 75.

Therefore, the correct answer is Option 2: 75.

**Explanation for Incorrect Options:**

- **Option 1 (68):** This option is incorrect because when converting 18$\frac{3}{4}$ to quarters, the calculation results in 75, not 68. The process of converting the mixed number to an improper fraction and counting the quarters confirms this.

- **Option 3 (72):** This option is incorrect because it represents the number of quarters in 18 whole units (18 x 4 = 72), but it does not account for the additional $\frac{3}{4}$, which adds 3 more quarters, making the total 75.

- **Option 4 (35):** This option is incorrect because it significantly underestimates the number of quarters in 18$\frac{3}{4}$. The correct calculation shows that there are 75 quarters, not 35.

In conclusion, the correct answer is Option 2: 75, as it accurately reflects the number of quarters in 18$\frac{3}{4}$.