To determine how many bottles of water a cooler contains, given that the cooler has 5 gallons of water and each bottle contains [tex]\(\frac{1}{8}\)[/tex] of a gallon, we need to follow these steps:
1. Understand the volume of one bottle: We know that one bottle holds [tex]\(\frac{1}{8}\)[/tex] of a gallon of water.
2. Identify the total volume of the cooler: The cooler holds a total of 5 gallons of water.
3. Calculate the number of bottles the cooler can contain: We need to determine how many [tex]\(\frac{1}{8}\)[/tex] gallon bottles can fit into 5 gallons. This can be found by dividing the total volume of the cooler by the volume of one bottle.
Mathematically, this is represented as:
[tex]\[
\text{Number of bottles} = \frac{\text{Total volume of the cooler}}{\text{Volume of one bottle}}
\][/tex]
Plugging in the values:
[tex]\[
\text{Number of bottles} = \frac{5 \text{ gallons}}{\frac{1}{8} \text{ gallon per bottle}}
\][/tex]
4. Simplify the division: Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of [tex]\(\frac{1}{8}\)[/tex] is 8. So,
[tex]\[
\text{Number of bottles} = 5 \times 8
\][/tex]
Therefore:
[tex]\[
\text{Number of bottles} = 40
\][/tex]
So, the cooler containing 5 gallons of water can hold 40 bottles of water, each bottle being [tex]\(\frac{1}{8}\)[/tex] of a gallon.
