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To determine which driver used fewer gallons of gas per mile, we can calculate the gas consumption rate (in gallons per mile) for both Beth and Martha.

### Step 1: Calculate Beth’s Gas Consumption Rate
Beth drove **45 miles** and used **\(3 \frac{3}{4}\) gallons** of gas.

1. Convert \(3 \frac{3}{4}\) to an improper fraction:
   \[
   3 \frac{3}{4} = \frac{15}{4} \text{ gallons}
   \]

2. Divide the gallons by the miles to find the gallons per mile:
   \[
   \frac{15}{4} \div 45 = \frac{15}{4} \times \frac{1}{45} = \frac{15}{180} = \frac{1}{12} \text{ gallons per mile}
   \]

### Step 2: Calculate Martha’s Gas Consumption Rate
Martha drove **85 miles** and used **\(5 \frac{2}{3}\) gallons** of gas.

1. Convert \(5 \frac{2}{3}\) to an improper fraction:
   \[
   5 \frac{2}{3} = \frac{17}{3} \text{ gallons}
   \]

2. Divide the gallons by the miles to find the gallons per mile:
   \[
   \frac{17}{3} \div 85 = \frac{17}{3} \times \frac{1}{85} = \frac{17}{255} \approx 0.0667 \text{ gallons per mile}
   \]

### Step 3: Compare the Consumption Rates
- Beth’s gas consumption rate: \(\frac{1}{12} \approx 0.0833\) gallons per mile
- Martha’s gas consumption rate: \(\approx 0.0667\) gallons per mile

Since **0.0667** (Martha’s rate) is less than **0.0833** (Beth’s rate), **Martha used fewer gallons of gas per mile**.

Would you like a detailed breakdown of each step or have any questions?

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Here are some related questions for further practice:
1. How would you calculate the gas consumption rate if only partial miles were driven?
2. What if Beth and Martha had used the same amount of gas? How would their consumption rates compare then?
3. How can you convert a decimal to a fraction when calculating consumption rates?
4. If Martha had driven 100 miles, how would that affect her gas consumption rate?
5. How would the solution change if both drivers drove the same number of miles?

**Tip:** Always convert mixed numbers to improper fractions to simplify calculations involving ratios.

Beth drove 45 miles and used 3 3/4 gallons of gas. Martha drove 85 miles and used 5 2/3 gallons of gas. Which driver used fewer gallons of gas per mile?

Learn how to compare gas consumption rates to determine which driver, Beth or Martha, used fewer gallons per mile. This solution involves converting mixed numbers to improper fractions and calculating ratios for accurate comparison. Suitable for Grade 6-7 students.

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