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Read the problem below and choose the correct answer.

In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most.

For the season so far:
- Jana has hit the ball 12 times out of 15 attempts.
- Tasha hit the ball 9 times out of 10 attempts.

Which player has a better batting average?

A. Tasha, because she has the highest ratio since [tex]$0.9 > 0.8$[/tex].
B. Tasha, because she has the highest ratio since [tex]$\frac{27}{30} > \frac{24}{30}$[/tex].
C. Jana, because she has the highest ratio since [tex]$0.9 > 0.8$[/tex].
D. Jana, because she has the highest ratio since [tex]$\frac{27}{30} > \frac{24}{30}$[/tex].

Answer :

To determine which player has a better batting average, we need to compare their ratios of hits to attempts.

First, let's find Jana's batting average:

Jana's hits to attempts ratio is [tex]\( \frac{12}{15} \)[/tex].

Next, we simplify this ratio to get Jana's batting average. Dividing the numerator and the denominator by their greatest common divisor, which is 3, we get:

[tex]\[ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \][/tex]

[tex]\[ \frac{4}{5} = 0.8 \][/tex]

So, Jana's batting average is 0.8.

Now, let's find Tasha's batting average:

Tasha's hits to attempts ratio is [tex]\( \frac{9}{10} \)[/tex].

We simplify this ratio to get Tasha's batting average (note that this is already in simplified form):

[tex]\[ \frac{9}{10} = 0.9 \][/tex]

So, Tasha's batting average is 0.9.

Next, to compare their ratios accurately, we can convert both batting averages to the same common denominator. We'll convert both ratios to be out of 30 attempts:

For Jana:
[tex]\[ 0.8 \times 30 = 24 \][/tex]

For Tasha:
[tex]\[ 0.9 \times 30 = 27 \][/tex]

So, Jana's batting average ratio out of 30 is [tex]\( \frac{24}{30} \)[/tex] and Tasha's batting average ratio out of 30 is [tex]\( \frac{27}{30} \)[/tex].

Comparing these two ratios, [tex]\( \frac{27}{30} \)[/tex] is greater than [tex]\( \frac{24}{30} \)[/tex].

Thus, Tasha has a better batting average with a ratio higher than Jana's.

So the correct answer is:
- Tasha, because she has the highest ratio since [tex]\( \frac{27}{30} > \frac{24}{30} \)[/tex].

Thanks for taking the time to read Read the problem below and choose the correct answer In baseball each time a player attempts to hit the ball it is recorded The ratio. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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