Let's solve this problem step by step:
1. Determine the amount of modeling clay Raul has:
Raul has [tex]\(\frac{4}{5}\)[/tex] pound of modeling clay.
2. Determine the capacity of each bag:
Each bag can hold [tex]\(\frac{1}{10}\)[/tex] pound of clay.
3. Calculate the number of bags Raul can fill:
To find out how many bags Raul can fill, we need to divide the total amount of modeling clay by the amount each bag can hold. Mathematically, this division can be expressed as:
[tex]\[
\text{Number of bags} = \frac{\frac{4}{5}}{\frac{1}{10}}
\][/tex]
4. Simplify the division of fractions:
To simplify [tex]\(\frac{\frac{4}{5}}{\frac{1}{10}}\)[/tex], we multiply the numerator by the reciprocal of the denominator:
[tex]\[
\frac{4}{5} \div \frac{1}{10} = \frac{4}{5} \times \frac{10}{1}
\][/tex]
5. Perform the multiplication:
Now, multiply the fractions:
[tex]\[
\frac{4}{5} \times \frac{10}{1} = \frac{4 \times 10}{5 \times 1} = \frac{40}{5} = 8
\][/tex]
6. Result:
Raul can fill 8 bags with the modeling clay he has.
Therefore, Raul will be able to fill 8 bags, given that each bag holds [tex]\(\frac{1}{10}\)[/tex] pound of clay and he has [tex]\(\frac{4}{5}\)[/tex] pound of modeling clay in total.
