To determine how many miles Johanna rode before lunch, we need to calculate [tex]\(\frac{3}{4}\)[/tex] of the total distance she rode to the lake, which is 7 miles.
Here are the steps:
1. Identify the total distance:
The total distance Johanna rode to the lake is 7 miles.
2. Identify the fraction of the distance ridden before lunch:
Johanna rode [tex]\(\frac{3}{4}\)[/tex] of the total distance before lunch.
3. Calculate the distance ridden before lunch:
We multiply the total distance by the fraction to find the actual distance ridden before lunch.
[tex]\[
\text{Distance before lunch} = 7 \times \frac{3}{4}
\][/tex]
4. Perform the multiplication:
[tex]\[
7 \times \frac{3}{4} = \frac{7 \times 3}{4} = \frac{21}{4}
\][/tex]
5. Convert the improper fraction to a mixed number:
[tex]\[
\frac{21}{4} = 5 \frac{1}{4}
\][/tex]
So, Johanna rode [tex]\(5 \frac{1}{4}\)[/tex] miles before lunch.
Therefore, the correct answer is:
C. [tex]\(5 \frac{1}{4}\)[/tex] miles
