Chapter 4, Problem 29CR

To determine

To find which team won the greater fraction of the game

Answer to Problem 29CR

My friends team won the greater fraction of the game.

Explanation of Solution

Given information:

Two Teams- My & my friends team

My Teams winning fraction is 14 out of 20 games, so $\frac{14}{20}$

My friends Teams winning fraction is 18 out of 24 games, so $\frac{18}{24}$

Let my teams winning fraction be A & my friends teams winning fraction be B.

A= $\frac{14}{20}$

B= $\frac{18}{24}$

Formula Used: Least Common Denominator

Calculation:

The first step here is to identify the Least Common Denominator for both fractions. So, break the denominators into its multiples-

  $\frac{14}{20}=\frac{7\times 2}{5\times 2\times 2}$

For the other fraction, it is-

  $\frac{18}{24}=\frac{3\times 3\times 2}{2\times 3\times 2\times 2}$

In the above fractions, it is clear that the LCD is4.

In the second step, extract the LCD, and rewrite the fractions as-

  $\frac{14}{20}=\frac{1}{4}\left(\frac{14}{5}\right)$

And the other one as-

  $\frac{18}{24}=\frac{1}{4}\left(\frac{18}{6}\right)$

Now our fractions are reduced to

  $\left(\frac{14}{5}\right)$ and $\left(\frac{18}{6}\right)$

now make the denominators of both fractions same by multiplying each fractions denominator, with the numerator & denominator of the other fraction.

So for first fraction-

  $\frac{14}{5}\times \frac{6}{6}=\frac{84}{30}$

And for the second fraction

  $\frac{18}{6}\times \frac{5}{5}=\frac{90}{30}$

Now, both the fractions have same denominator 30.

  $\frac{84}{30},\frac{90}{30}$

Since 84 is less than 90, so the first fraction A is less than the second one B.

  $\frac{14}{20}<\frac{18}{24}$

Conclusion-

  $\frac{14}{20}<\frac{18}{24}$

Hence, my friends team won the greater fraction of the game.