Final answer:
To express 6 1/2 cm for 1 1/3 gallons as a fraction in lowest terms, convert to improper fractions, form the ratio, multiply by the reciprocal of the denominator, and simplify, resulting in the fraction 39/8 cm/gallon.
Step-by-step explanation:
To express the rate of 6 1/2 cm for 1 1/3 gallons as a fraction in lowest terms, follow the steps below:
To express the rate as a fraction in lowest terms, we need to convert both the numerator and the denominator to the same unit of measure. We have 6 1/2 cm for 1 1/3 gallons.
First, convert the gallons to centimeters using the conversion factor of 4 quarts in a gallon. Multiply 1 1/3 by 4 to get 5 1/3 quarts. Then, convert the quarts to centimeters using the conversion factor of 0.94635 liters in a quart and 1000 milliliters in a liter.
Multiply 5 1/3 by 0.94635 and 1000 to get approximately 5032.87 cm. Finally, the rate 6 1/2 cm for 5032.87 cm can be expressed as a fraction in lowest terms by dividing both sides by 6.5. The fraction in lowest terms is approximately 1/770.
First convert the mixed numbers to improper fractions: 6 1/2 becomes 13/2 cm, and 1 1/3 becomes 4/3 gallons.
Next, create a fraction with these two values: (13/2) cm / (4/3) gallons.
Now, to simplify this rate, multiply by the reciprocal of the denominator, (3/4).
After multiplying the fractions, you get (13/2) * (3/4) = 39/8, which is the rate in centimeters per gallon.
Last, reduce the fraction to lowest terms if possible. In this case, 39/8 is in its lowest form.
Therefore, the rate of 6 1/2 cm for 1 1/3 gallons expressed as a fraction in lowest terms is 39/8 cm/gallon.