Respuesta :
Solution:
Given:
[tex]\begin{gathered} \text{Jack jogged }\frac{3}{4}th\text{ of a mile} \\ \text{Jill jogged }\frac{7}{10}th\text{ of a mile} \end{gathered}[/tex]To know who jogged further, we convert the fractions to have the same common denominator and arrange the fraction in order.
We can also convert both fractions to percentages. The one with the higher percentage jogged further.
Making both fractions have the same denominator,
[tex]\begin{gathered} \frac{3}{4},\frac{7}{10} \\ \text{The common denominator is 20.} \\ \text{Hence,} \\ Jack=\frac{3}{4}=\frac{3\times5}{4\times5}=\frac{15}{20} \\ Jill=\frac{7}{10}=\frac{7\times2}{10\times2}=\frac{14}{20} \\ \\ \text{Hence, Jack jogged }\frac{15}{20}th\text{ of a mile, while Jill jogged }\frac{14}{20}th\text{ of a mile.} \\ \\ S\text{ ince }\frac{15}{20}is\text{ greater than }\frac{14}{20},\text{ then Jack jogged further than Jill.} \end{gathered}[/tex]Therefore, Jack jogged further.
Alternatively, using percentages, we multiply each fraction by 100 to take it to a percentage.
[tex]\begin{gathered} \text{Jack}=\frac{3}{4}=\frac{3}{4}\times100=75\text{ \%} \\ \text{Jill}=\frac{7}{10}\times100=70\text{ \%} \\ \\ S\text{ ince, 75\% is greater than 70\%, it means Jack jogged further than Jill.} \end{gathered}[/tex]Therefore, Jack jogged further.
