Respuesta :
We know the total number of gallons of gas used: 5 1/6
We know the number of gallons used per hour: 5/9
The total number of gallons used is equal to the number of gallons used per hour times the number of hours
gallons = gallons per hour * hours
Substitute the information we are given
5 1/6 = 5/9 * h
We use the variable h since we do not know the hours.
Divide each side by 5/9 to isolate the number of hours.
[tex]\frac{5\text{ 1/6}}{\frac{5}{9}}=\text{ h}[/tex]Now we need to change the mixed number to a improper fraction.
Take the denominator and multiply by the whole number then add the numerator
6*5 +1 = 30 +1 = 31
Then divide by the denominator
[tex]\frac{\frac{31}{6}}{\frac{5}{9}}=h[/tex]Now use copy dot flip to change this to multiplication.
[tex]\frac{31}{6}\cdot\text{ }\frac{9}{5}\text{ = h}[/tex][tex]\frac{31}{2}\cdot\frac{3}{5}=h[/tex]We found this by dividing ther 9 and the 6 by 3
This gives us 93/10 for h
But this is an improper fraction. Changing this to a mixed number
93/10 = 9 3/10 hours
