To determine how many shoes Miley can fit on her shelf, we first need to convert the width of each shoe from a mixed number to an improper fraction.
The width of each shoe is \(2 \frac{3}{4}\) inches. Converting this to an improper fraction:
- \(2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}\) inches.
Now, we need to calculate how many shoes can fit on a 33-inch shelf. To do that, we will divide the total width of the shelf by the width of each shoe.
So we will divide:
\[ 33 \div \frac{11}{4} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ 33 \div \frac{11}{4} = 33 \times \frac{4}{11} \]
Now, let's calculate this:
- Convert 33 to a fraction: \(33 = \frac{33}{1}\).
- Multiply: \[ \frac{33}{1} \times \frac{4}{11} = \frac{33 \times 4}{1 \times 11} = \frac{132}{11} = 12. \]
Therefore, Miley can fit 12 shoes on her shelf.
Now, looking at the statements provided, we can check the correctness:
- To solve this problem, divide 33 by \(\frac{11}{4}\). (Correct - This is the correct operation to find out how many shoes fit).
- To solve this problem, multiply 33 by \(\frac{11}{4}\). (Incorrect - Multiplication is not the correct operation in this context).
- Miley’s shoe shelf can fit 12 shoes. (Correct - We calculated this).
- Miley’s shoe shelf can fit 90 shoes. (Incorrect - This is incorrect based on our calculation).
So the correct statements are:
- To solve this problem, divide 33 by \(\frac{11}{4}\).
- Miley’s shoe shelf can fit 12 shoes.