Answer :
Sure, let's solve the problem step-by-step.
1. Understand the problem:
Amelia walked a total distance of [tex]\(\frac{15}{4}\)[/tex] miles. She stopped to have lunch after walking [tex]\(\frac{12}{25}\)[/tex] of the way. We need to find out how many miles she walked before stopping for lunch.
2. Convert the total distance to decimal form:
[tex]\(\frac{15}{4} = 3.75\)[/tex] miles (This step helps in understanding but isn't strictly necessary for the calculation).
3. Multiply the fraction of the walk completed by the total distance:
The distance walked before lunch can be calculated by multiplying the fraction of the way walked ([tex]\(\frac{12}{25}\)[/tex]) by the total walk length ([tex]\(\frac{15}{4}\)[/tex]).
4. Perform the multiplication:
[tex]\[
\text{Distance before lunch} = \left(\frac{12}{25}\right) \times \left(\frac{15}{4}\right)
\][/tex]
5. Simplify the multiplication:
[tex]\[
\text{Distance before lunch} = \frac{12 \times 15}{25 \times 4} = \frac{180}{100} = 1.8 \text{ miles}
\][/tex]
Therefore, Amelia walked 1.8 miles before stopping to have lunch.
1. Understand the problem:
Amelia walked a total distance of [tex]\(\frac{15}{4}\)[/tex] miles. She stopped to have lunch after walking [tex]\(\frac{12}{25}\)[/tex] of the way. We need to find out how many miles she walked before stopping for lunch.
2. Convert the total distance to decimal form:
[tex]\(\frac{15}{4} = 3.75\)[/tex] miles (This step helps in understanding but isn't strictly necessary for the calculation).
3. Multiply the fraction of the walk completed by the total distance:
The distance walked before lunch can be calculated by multiplying the fraction of the way walked ([tex]\(\frac{12}{25}\)[/tex]) by the total walk length ([tex]\(\frac{15}{4}\)[/tex]).
4. Perform the multiplication:
[tex]\[
\text{Distance before lunch} = \left(\frac{12}{25}\right) \times \left(\frac{15}{4}\right)
\][/tex]
5. Simplify the multiplication:
[tex]\[
\text{Distance before lunch} = \frac{12 \times 15}{25 \times 4} = \frac{180}{100} = 1.8 \text{ miles}
\][/tex]
Therefore, Amelia walked 1.8 miles before stopping to have lunch.