To determine if Susan's claim is correct, we need to add the distances she walks and compare it to the distance she claims. Here's a step-by-step solution:
1. Susan to Janice:
The distance from Susan's house to Janice's house is [tex]\(\frac{1}{8}\)[/tex] mile.
2. Janice to Denise:
The distance from Janice's house to Denise's house is [tex]\(\frac{3}{5}\)[/tex] mile.
3. Total Distance Walked:
To find the total distance Susan walks, we add the two distances:
[tex]\[
\text{Total Distance} = \frac{1}{8} + \frac{3}{5}
\][/tex]
4. Common Denominator:
To add these fractions, we need a common denominator. The least common denominator (LCD) of 8 and 5 is 40. We convert the fractions:
[tex]\[
\frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}
\][/tex]
[tex]\[
\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}
\][/tex]
5. Add the Fractions:
Now, add the two fractions:
[tex]\[
\frac{5}{40} + \frac{24}{40} = \frac{5 + 24}{40} = \frac{29}{40}
\][/tex]
6. Convert to Decimal:
Convert [tex]\(\frac{29}{40}\)[/tex] to a decimal to facilitate comparison:
[tex]\[
\frac{29}{40} = 0.725
\][/tex]
7. Claimed Distance:
Susan claims that the total distance she walks is [tex]\(\frac{13}{20}\)[/tex] mile. Convert [tex]\(\frac{13}{20}\)[/tex] to a decimal:
[tex]\[
\frac{13}{20} = 0.65
\][/tex]
8. Compare Distances:
Compare the actual total distance walked with the claimed distance:
[tex]\[
\text{Actual Total Distance} = 0.725 \, \text{mile}
\][/tex]
[tex]\[
\text{Claimed Total Distance} = 0.65 \, \text{mile}
\][/tex]
Since [tex]\(0.725 \neq 0.65\)[/tex], Susan's claim is incorrect.
Conclusion:
The actual total distance Susan walks is 0.725 mile, whereas she claims to walk 0.65 mile. Therefore, Susan's claim is not correct.
