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Answer :
To solve the problem of finding out what fraction of the route the cyclist covered in total, follow these steps:
1. Understand the Fractions:
- In the morning, the cyclist covers [tex]\(\frac{2}{5}\)[/tex] of the route.
- In the afternoon, the cyclist covers [tex]\(\frac{1}{3}\)[/tex] of the route.
2. Find a Common Denominator:
- To add fractions, we first need a common denominator. The denominators here are 5 and 3. The smallest common multiple of 5 and 3 is 15.
3. Convert Each Fraction:
- Convert [tex]\(\frac{2}{5}\)[/tex] to a fraction with a denominator of 15. Multiply both the numerator and denominator by 3 to get [tex]\(\frac{6}{15}\)[/tex].
- Convert [tex]\(\frac{1}{3}\)[/tex] to a fraction with a denominator of 15. Multiply both the numerator and denominator by 5 to get [tex]\(\frac{5}{15}\)[/tex].
4. Add the Fractions:
- Now that both fractions have the same denominator, we can add them:
[tex]\(\frac{6}{15} + \frac{5}{15} = \frac{11}{15}\)[/tex].
5. Conclusion:
- The cyclist covered [tex]\(\frac{11}{15}\)[/tex] of the route in total.
So, the fraction of the route the cyclist covered in total is [tex]\(\frac{11}{15}\)[/tex], which matches answer option ;) [tex]$11 / 15$[/tex].
1. Understand the Fractions:
- In the morning, the cyclist covers [tex]\(\frac{2}{5}\)[/tex] of the route.
- In the afternoon, the cyclist covers [tex]\(\frac{1}{3}\)[/tex] of the route.
2. Find a Common Denominator:
- To add fractions, we first need a common denominator. The denominators here are 5 and 3. The smallest common multiple of 5 and 3 is 15.
3. Convert Each Fraction:
- Convert [tex]\(\frac{2}{5}\)[/tex] to a fraction with a denominator of 15. Multiply both the numerator and denominator by 3 to get [tex]\(\frac{6}{15}\)[/tex].
- Convert [tex]\(\frac{1}{3}\)[/tex] to a fraction with a denominator of 15. Multiply both the numerator and denominator by 5 to get [tex]\(\frac{5}{15}\)[/tex].
4. Add the Fractions:
- Now that both fractions have the same denominator, we can add them:
[tex]\(\frac{6}{15} + \frac{5}{15} = \frac{11}{15}\)[/tex].
5. Conclusion:
- The cyclist covered [tex]\(\frac{11}{15}\)[/tex] of the route in total.
So, the fraction of the route the cyclist covered in total is [tex]\(\frac{11}{15}\)[/tex], which matches answer option ;) [tex]$11 / 15$[/tex].
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