Question

Miley has a shoe shelf 33 inches wide. If each of her shoes is 2
3
4
inches wide, how many shoes can she fit on the shelf?

Which statements are correct? Check all that apply.
To solve this problem, divide 33 by StartFraction 11 Over 4 EndFraction.
To solve this problem, multiply 33 by StartFraction 11 Over 4 EndFraction.
Miley’s shoe shelf can fit 12 shoes.
Miley’s shoe shelf can fit 90 shoes.

Answer 1

To determine how many shoes can fit on Miley's shelf, we can follow these steps:

1. **Convert the width of each shoe to an improper fraction**: Each shoe is \( \frac{11}{4} \) inches wide.

2. **Divide the total shelf width by the width of each shoe**:

We need to find how many \( \frac{11}{4} \) inch shoes can fit into a 33 inch shelf.

This can be solved by performing the division:

\[
33 \div \frac{11}{4}
\]

Dividing by a fraction involves multiplying by its reciprocal:

\[
33 \times \frac{4}{11}
\]

We can treat 33 as \(\frac{33}{1}\):

\[
\frac{33}{1} \times \frac{4}{11} = \frac{33 \times 4}{1 \times 11} = \frac{132}{11} = 12
\]

So, the number of shoes that can fit on the shelf is **12**.

Now we can evaluate the given statements:

1. **To solve this problem, divide 33 by StartFraction 11 Over 4 EndFraction.**
- This statement is correct.

2. **To solve this problem, multiply 33 by StartFraction 11 Over 4 EndFraction.**
- This statement is incorrect; you should divide, not multiply.

3. **Miley’s shoe shelf can fit 12 shoes.**
- This statement is correct.

4. **Miley’s shoe shelf can fit 90 shoes.**
- This statement is incorrect; we determined that she can fit 12 shoes.

So, the correct answers are:

- To solve this problem, divide 33 by StartFraction 11 Over 4 EndFraction.
- Miley’s shoe shelf can fit 12 shoes.