Question

A racecar driver has completed 12 1/2 laps of a 50 lap race. What fractional part of the race remains?

• A. 1/4
• B. 1/5
• C. 3/4
• D. 4/5
• E. 75/2

Hint:

When dealing with fractions involving decimals, it's often easiest to convert them to whole numbers first. Also, remember that 0.5 is 1/2, 0.25 is 1/4, and 0.75 is 3/4. Recognizing that 37.5 is 3/4 of 50 could lead to a very quick answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The problem asks for the remaining part of the race to be expressed as a fraction of the total race distance. We need to find the number of laps remaining and divide it by the total number of laps.
Step 2: Detailed Explanation:
First, identify the total number of laps and the number of laps completed.
Total laps = 50.
Laps completed = 12 1/2 = 12.5.
Next, calculate the number of laps remaining.
\[ \text{Laps remaining} = \text{Total laps} - \text{Laps completed} \] \[ \text{Laps remaining} = 50 - 12.5 = 37.5 \] Now, express the remaining laps as a fraction of the total laps.
\[ \text{Fraction remaining} = \frac{\text{Laps remaining}}{\text{Total laps}} = \frac{37.5}{50} \] To simplify this fraction, we can multiply the numerator and denominator by 10 to remove the decimal.
\[ \frac{37.5 \times 10}{50 \times 10} = \frac{375}{500} \] Now, find the greatest common divisor (GCD) of 375 and 500 to simplify the fraction. Both numbers are divisible by 25.
\[ 375 = 25 \times 15 \] \[ 500 = 25 \times 20 \] So, \( \frac{375}{500} = \frac{15}{20} \).
This fraction can be simplified further by dividing both the numerator and denominator by 5.
\[ \frac{15 \div 5}{20 \div 5} = \frac{3}{4} \] Step 3: Final Answer:
The fractional part of the race that remains is 3/4.