Question

Lindsay went for a drive. she used 8/3 gallon of gas every 4/5 of an hour. solve for her gallons per hour

Answer 1

To find gallons per hour, divide gallons by hours.

... (8/3 gallons)/(4/5 hour) = (8/3)×(5/4) gallons/hour = 10/3 gallons/hour

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Comment on dividing fractions

There are a couple of ways you can do this without a calculator. One is to multiply the numerator fraction by the inverse of the denominator fraction. That is what we have done here.

Another is to make the denominators of both fractions the same. (Here, 15 works.) Then you have ...

`\displaystyle(\left((8)/(3)\right))/(\left((4)/(5)\right))=(\left((8)/(3)\cdot(5)/(5)\right))/(\left((4)/(5)\cdot(3)/(3)\right))\\\\=(\left((40)/(15)\right))/(\left((12)/(15)\right))=(40)/(12)\\\\=(4\cdot 10)/(4\cdot 3)=(10)/(3)`

You can also remove a factor of 4 from numerator and denominator early on, so you have (2/3)/(1/5) = (10/15)/(3/15) = 10/3, or = (2/3)×(5/1) = 10/3.