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Math  /  Numbers & Operations

QuestionUnit Rates for Ratios with Fractions, Part 2 - Instruction - Clever I Partal
Kara's family is thinking about renting an SUV that can travel 6236 \frac{2}{3} miles on 16\frac{1}{6} gallon of gas. Kara wants to know the gas mileage of the SUV.
What is the SUV's gas mileage in miles per gallon? 20316=\frac{\frac{20}{3}}{\frac{1}{6}}= □\square

Studdy Solution

STEP 1

1. We are given a distance of 623 6 \frac{2}{3} miles that the SUV can travel.
2. This distance is covered using 16 \frac{1}{6} gallon of gas.
3. We need to find the gas mileage in miles per gallon.

STEP 2

1. Convert mixed numbers to improper fractions.
2. Set up the division for the unit rate.
3. Simplify the division to find the unit rate.

STEP 3

Convert the mixed number 623 6 \frac{2}{3} to an improper fraction.
623=3×6+23=18+23=203 6 \frac{2}{3} = \frac{3 \times 6 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}

STEP 4

Set up the division for the unit rate, which is the gas mileage in miles per gallon.
20316 \frac{\frac{20}{3}}{\frac{1}{6}}

STEP 5

To divide by a fraction, multiply by its reciprocal.
203×61=20×63×1=1203 \frac{20}{3} \times \frac{6}{1} = \frac{20 \times 6}{3 \times 1} = \frac{120}{3}

STEP 6

Simplify the fraction to find the gas mileage.
1203=40 \frac{120}{3} = 40
The SUV's gas mileage is:
40 miles per gallon\boxed{40 \text{ miles per gallon}}

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