Jerry's motorcycle tank holds $6 \frac{1}{2}$ gallons of gas. There are $3 \frac{3}{4}$ gallons of gas currently in the tank. How much more gasoline will it take to fill the tank? (Simplify your answer and write it as a mixed number.)
Answer (1)
Convert the mixed numbers to improper fractions: 6 2 1 = 2 13 and 3 4 3 = 4 15 .
Find a common denominator and subtract: 2 13 − 4 15 = 4 26 − 4 15 = 4 11 .
Convert the improper fraction back to a mixed number: 4 11 = 2 4 3 .
The amount of gasoline needed to fill the tank is 2 4 3 gallons.
Explanation
Problem Setup First, we need to determine how much gasoline is needed to fill Jerry's motorcycle tank. We know the tank's full capacity is 6 2 1 gallons, and it currently contains 3 4 3 gallons. To find the difference, we will subtract the current amount from the full capacity.
Convert to Improper Fractions Convert the mixed numbers to improper fractions. This makes subtraction easier. 6 2 1 = 2 6 × 2 + 1 = 2 12 + 1 = 2 13 3 4 3 = 4 3 × 4 + 3 = 4 12 + 3 = 4 15
Subtract the Fractions Now, subtract the current amount of gasoline from the full capacity: 2 13 − 4 15 To subtract these fractions, we need a common denominator. The least common denominator of 2 and 4 is 4. So, we convert 2 13 to a fraction with a denominator of 4: 2 13 = 2 × 2 13 × 2 = 4 26 Now we can subtract: 4 26 − 4 15 = 4 26 − 15 = 4 11
Convert Back to Mixed Number Convert the improper fraction 4 11 back to a mixed number. To do this, we divide 11 by 4: 11 ÷ 4 = 2 with a remainder of 3 So, 4 11 is equal to 2 4 3 .
Final Answer Therefore, it will take 2 4 3 gallons of gasoline to fill the tank.
Examples
Imagine you're baking a cake and the recipe calls for 6 2 1 cups of flour. You check your flour container and see you only have 3 4 3 cups. To figure out how much more flour you need to add, you perform the same calculation we did in the problem. This helps ensure your cake turns out perfectly!
