A runner runs `1 1/4` laps of a 5 lap race. What fractional part of the race remains to be run?

Options

A. `15//4`
B. `4//5`
C. `5//6`
D. `2//3`

Answer

To find the fractional part of the race that remains to be run after a runner has completed \(1 \frac{1}{4}\) laps of a 5-lap race, we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The runner has completed \(1 \frac{1}{4}\) laps. To convert this mixed number to an improper fraction:
\[ 1 \frac{1}{4} = 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \]

### Step 2: Determine the total laps of the race
The total number of laps in the race is given as 5 laps.

### Step 3: Calculate the remaining laps
To find the remaining laps, we subtract the laps completed from the total laps:
\[ \text{Remaining laps} = \text{Total laps} - \text{Laps completed} = 5 - \frac{5}{4} \]

### Step 4: Convert the total laps to a fraction with the same denominator
To perform the subtraction, we need to express 5 as a fraction with a denominator of 4:
\[ 5 = \frac{20}{4} \]

### Step 5: Perform the subtraction
Now we can subtract the laps completed from the total laps:
\[ \text{Remaining laps} = \frac{20}{4} - \frac{5}{4} = \frac{20 - 5}{4} = \frac{15}{4} \]

### Step 6: Express the remaining laps as a fractional part of the race
The fractional part of the race that remains to be run is:
\[ \text{Fractional part remaining} = \frac{15}{4} \]

### Conclusion
Thus, the fractional part of the race that remains to be run is \(\frac{15}{4}\).

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