Find trusted answers to your questions with the help of IDNLearn.com's knowledgeable community. Discover trustworthy solutions to your questions quickly and accurately with help from our dedicated community of experts.

2. A sheet of metal is [tex]\frac{5}{8} \text{ cm}[/tex] thick. How many sheets of such metal are in a stack [tex]30 \text{ cm}[/tex] high?

Sagot :

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.