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Victoria's car used 4/5 of a gallon to travel 21 miles. At what rate does the car use gas, in miles per gallon?

Sagot :

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]

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