Chapter 3.1, Problem 52PPS

To determine

To find:The order of the players based on their batting averages from greatest to least.

Answer to Problem 52PPS

  $\frac{46}{60}>\frac{49}{65}>\frac{35}{47}>\frac{36}{50}>\frac{51}{73}$

Explanation of Solution

Given information:

The table shows the number of times at bat and hits that players on Rawson Middle School team had last season.

Player	Hits	At Bats
Kristen	35	47
Cho	51	73
Brooke	36	50
Alma	49	65
Jessica	46	60

Calculation:

Divide the number of hits by number of bats.

The batting average of Kristen is $\frac{35}{47}$

  $\begin{array}{r}\hfill 0.744\\ \hfill 47\overline{)35.000}\\ \hfill \frac{-329}{210}\\ \hfill \frac{-188}{220}\\ \hfill \frac{-188}{32}\end{array}$

Therefore, $\frac{35}{47}=0.744$ .

The batting average of Cho is $\frac{51}{73}$

  $\begin{array}{r}\hfill 0.698\\ \hfill 73\overline{)51.000}\\ \hfill \frac{-438}{720}\\ \hfill \frac{-657}{630}\\ \hfill \frac{-584}{46}\end{array}$

Therefore, $\frac{51}{73}=0.698$ .

The batting average of Brooke is $\frac{36}{50}$

  $\begin{array}{r}\hfill 0.72\\ \hfill 50\overline{)36.00}\\ \hfill \frac{-350}{100}\\ \hfill \frac{-100}{0}\end{array}$

Therefore, $\frac{36}{50}=0.72$ .

The batting average of Alma is $\frac{49}{65}$ .

  $\begin{array}{r}\hfill 6.753\\ \hfill 65\overline{)49.000}\\ \hfill \frac{-455}{350}\\ \hfill \frac{-325}{250}\\ \hfill \frac{-195}{55}\end{array}$

Therefore, $\frac{49}{65}=0.753$

The batting average of Jessica is $\frac{46}{60}$ .

  $\begin{array}{r}\hfill 60\begin{array}{c}\hfill 0.766\\ \hfill \overline{)46.000}\end{array}\\ \hfill \frac{-420}{400}\\ \hfill \frac{-360}{400}\\ \hfill \frac{-360}{40}\end{array}$

Therefore, $\frac{46}{60}=0.766$ .

Now arrange all the numbers from greatest to least.

  $0.766>0.753>0.744>0.72>0.698$

Therefore, $\frac{46}{60}>\frac{49}{65}>\frac{35}{47}>\frac{36}{50}>\frac{51}{73}$