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Answer:
26.25 miles per gallon of gas.
Step-by-step explanation:.
1. We know the car traveled 21 miles using [tex]\frac{4}{5}[/tex] of a gallon of gas.
2. To find out how many miles the car can travel using 1 whole gallon of gas, we need to see how many [tex]\frac{4}{5}[/tex]gallons fit into 21 miles.
Let's set up the problem:
[tex]\text{Rate} = \frac{\text{Miles}}{\text{Gallons}} = \frac{21 \text{ miles}}{\frac{4}{5} \text{ gallon}}[/tex]
To make this easier, we can change the division of a fraction into multiplication:
[tex]\text{Rate} = 21 \text{ miles} \div \frac{4}{5} \text{ gallon}[/tex]
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\sf \frac{4}{5}\: is\: \frac{5}{4}:[/tex]
[tex]\text{Rate} = 21 \text{ miles} \times \frac{5}{4}[/tex]
Now multiply:
[tex]\text{Rate} = 21 \times \frac{5}{4} = \frac{21 \times 5}{4} = \frac{105}{4} = 26.25[/tex]