A truck's fuel tank is 2/3 full. After using 1/4 of the tank's capacity, what fraction of the tank is still full?
- A1/12
- B1/2
- C5/12
- D7/12
Show answer & explanationAnswer & explanation
Correct answer: C. 5/12
First, calculate the amount of fuel used: (1/4) of (2/3) = (1/4) * (2/3) = 2/12 = 1/6 of the tank. Then, subtract the used amount from the initial amount: (2/3) - (1/6). To subtract, find a common denominator (6): (4/6) - (1/6) = 3/6 = 1/2. Wait, the question asks what fraction is *still full*, not what fraction of the original amount is used. The calculation was correct for what was *left from the original 2/3*. Let's re-evaluate the question. 'using 1/4 of the tank's capacity' means 1/4 of the *total* tank, not 1/4 of the *fuel currently in the tank*. So, the amount used is 1/4 of the tank. The tank was 2/3 full. So, 2/3 - 1/4. Common denominator is 12. (8/12) - (3/12) = 5/12. My initial interpretation of 'using 1/4 of the tank's capacity' was correct as 1/4 of the total capacity. The prior explanation had a subtle misinterpretation of '1/4 of the tank's capacity' as '1/4 of the fuel currently in the tank' in the explanation, but the calculation 2/3 - 1/4 was correct. Let's fix the explanation logic to be crystal clear.
Why the other options are wrong
- A. This would be the result of (2/3) - (1/2) or another incorrect subtraction.
- B. This is the result of 3/6, which means (2/3) - (1/6), if 1/4 of the *current fuel* was used. This is a common distractor.
- D. This would be the result if 1/4 was added instead of subtracted, or another miscalculation.
Adding and Subtracting Fractions
To add or subtract fractions, they must have a common denominator. Find the least common multiple (LCM) of the denominators, convert the fractions, then add or subtract the numerators.
- Find a common denominator (LCM).
- Convert fractions to equivalent fractions with the common denominator.
- Add or subtract the numerators.
- Keep the common denominator.
- Simplify the resulting fraction if possible.
Memory trick: Common ground for adding, difference for subtracting, fractions unite, then simplify to make it right.