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The expression 12 g gives the number of kilometers a car can travel using g liters of gasoline. How many kilometers can this car travel on 5(1)/(2) liters of gasoline?

The expression 12g 12 g gives the number of kilometers a car can travel using g g liters of gasoline. How many kilometers can this car travel on 512 5 \frac{1}{2} liters of gasoline?

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Full solution

Q. The expression 12g 12 g gives the number of kilometers a car can travel using g g liters of gasoline. How many kilometers can this car travel on 512 5 \frac{1}{2} liters of gasoline?
  1. Substitute gg with 5125\frac{1}{2}: The expression 12g12g represents the distance in kilometers that the car can travel per liter of gasoline, where gg is the number of liters. To find out how far the car can travel on 5125\frac{1}{2} liters, we need to substitute gg with 5125\frac{1}{2} in the expression.
  2. Convert mixed number to improper fraction: First, we need to convert the mixed number 5125\frac{1}{2} into an improper fraction. This is done by multiplying the whole number 55 by the denominator 22 and then adding the numerator 11.\newlineCalculation: 5×2+1=10+1=115 \times 2 + 1 = 10 + 1 = 11\newlineSo, 5125\frac{1}{2} liters is the same as 112\frac{11}{2} liters.
  3. Substitute gg with 112\frac{11}{2}: Now we substitute gg with 112\frac{11}{2} in the expression 12g12g to find out the distance the car can travel.\newlineCalculation: 12×(112)=(12×11)212 \times \left(\frac{11}{2}\right) = \frac{(12 \times 11)}{2}
  4. Perform multiplication in numerator: Perform the multiplication in the numerator.\newlineCalculation: 12×11=13212 \times 11 = 132
  5. Divide to get final answer: Now, divide 132132 by 22 to get the final answer.\newlineCalculation: 1322=66\frac{132}{2} = 66
  6. Car's distance on 5125\frac{1}{2} liters: The car can travel 6666 kilometers on 5125\frac{1}{2} liters of gasoline.

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