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Answer :
To find out how many days Lena ran this week, we need to determine how many days it took her to run a total of [tex]\(17 \frac{1}{2}\)[/tex] miles, given that she runs [tex]\(2 \frac{1}{2}\)[/tex] miles each day.
1. Convert the mixed numbers to improper fractions:
- Lena ran a total of [tex]\(17 \frac{1}{2}\)[/tex] miles, which can be converted to an improper fraction:
[tex]\[
17 \frac{1}{2} = \frac{35}{2}
\][/tex]
- She runs [tex]\(2 \frac{1}{2}\)[/tex] miles each day, which can be converted to an improper fraction:
[tex]\[
2 \frac{1}{2} = \frac{5}{2}
\][/tex]
2. Calculate the number of days she ran:
- To find how many days Lena ran, divide the total number of miles by the number of miles she runs each day:
[tex]\[
\text{Number of days} = \frac{\frac{35}{2}}{\frac{5}{2}}
\][/tex]
3. Perform the division:
- When dividing fractions, multiply by the reciprocal. The reciprocal of [tex]\(\frac{5}{2}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[
\frac{35}{2} \times \frac{2}{5} = \frac{35 \times 2}{2 \times 5} = \frac{70}{10}
\][/tex]
4. Simplify the fraction:
- Simplify [tex]\(\frac{70}{10}\)[/tex] to get:
[tex]\[
\frac{70}{10} = 7
\][/tex]
Therefore, Lena ran for 7 days this week. So, the correct answer is 7 days.
1. Convert the mixed numbers to improper fractions:
- Lena ran a total of [tex]\(17 \frac{1}{2}\)[/tex] miles, which can be converted to an improper fraction:
[tex]\[
17 \frac{1}{2} = \frac{35}{2}
\][/tex]
- She runs [tex]\(2 \frac{1}{2}\)[/tex] miles each day, which can be converted to an improper fraction:
[tex]\[
2 \frac{1}{2} = \frac{5}{2}
\][/tex]
2. Calculate the number of days she ran:
- To find how many days Lena ran, divide the total number of miles by the number of miles she runs each day:
[tex]\[
\text{Number of days} = \frac{\frac{35}{2}}{\frac{5}{2}}
\][/tex]
3. Perform the division:
- When dividing fractions, multiply by the reciprocal. The reciprocal of [tex]\(\frac{5}{2}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex]:
[tex]\[
\frac{35}{2} \times \frac{2}{5} = \frac{35 \times 2}{2 \times 5} = \frac{70}{10}
\][/tex]
4. Simplify the fraction:
- Simplify [tex]\(\frac{70}{10}\)[/tex] to get:
[tex]\[
\frac{70}{10} = 7
\][/tex]
Therefore, Lena ran for 7 days this week. So, the correct answer is 7 days.
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