Final answer:
After using 2/3 of his initial 16 3/4 gallons of gas, Wayne has 5 7/12 gallons of gas remaining in his car.
Step-by-step explanation:
The question asks how many gallons of gas Wayne has left in his car if he started with 16 3/4 gallons of gas and used 2/3 of it. To find the amount used, we multiply 16 3/4 gallons by 2/3. Converting 16 3/4 gallons to an improper fraction gives us 67/4 gallons. Thus, the calculation will be:
(67/4) × (2/3) = (67 × 2) / (4 × 3) = 134/12
To simplify, we divide 134 by 12, which equals 11 with a remainder of 2, or 11 1/6. This means Wayne used 11 1/6 gallons. To find out how much he has left, we subtract the amount used from the initial amount.
16 3/4 - 11 1/6 = (67/4) - (67/6)
To subtract these fractions, we need a common denominator, which is 12 in this case. The subtraction will be:
(67 × 3) / 12 - (67 × 2) / 12 = (201 - 134) / 12 = 67/12 gallons remaining.
Converting 67/12 gallons to a mixed number gives us 5 7/12 gallons remaining in Wayne's car.