To determine how many metal sheets, each having a thickness of [tex]\(\frac{5}{8}\)[/tex] cm, can fit into a height of 30 cm, follow these steps:
1. Identify the thickness of one sheet.
- Each metal sheet has a thickness of [tex]\(\frac{5}{8}\)[/tex] cm.
2. Identify the total height available for the sheets.
- The total height available is 30 cm.
3. Set up the division to find the number of sheets that fit into the total height.
- To find the number of sheets, divide the total height by the thickness of one sheet:
[tex]\[
\text{Number of sheets} = \frac{\text{Total height}}{\text{Thickness of one sheet}}
\][/tex]
4. Perform the division.
- Plugging in the values, we get:
[tex]\[
\text{Number of sheets} = \frac{30 \text{ cm}}{\frac{5}{8} \text{ cm}}
\][/tex]
5. Simplify the division.
- Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore:
[tex]\[
\frac{30 \text{ cm}}{\frac{5}{8} \text{ cm}} = 30 \text{ cm} \times \frac{8}{5} = 30 \times \frac{8}{5}
\][/tex]
6. Calculate the multiplication.
- First, multiply 30 by 8:
[tex]\[
30 \times 8 = 240
\][/tex]
- Then, divide the result by 5:
[tex]\[
\frac{240}{5} = 48
\][/tex]
Thus, [tex]\(\mathbf{48}\)[/tex] sheets of metal, each with a thickness of [tex]\(\frac{5}{8}\)[/tex] cm, fit into a total height of 30 cm.
