Chapter 7.2, Problem 42PPS

(a)

To determine

To find the fraction of total students, which prefer each, ride & fraction of each in simplest form, then as a decimal and percent form.

Answer to Problem 42PPS

Ride	Fraction	Decimal	Percent
Tilting Ride	$\frac{140}{560}=\frac{1}{4}$	$\frac{1}{4}=0.25$	$0.25\times 100=25\%$
Ferris Wheel	$\frac{56}{560}=\frac{1}{10}$	$\frac{1}{10}=0.1$	$0.1\times 100=10\%$
Carousel	$\frac{28}{560}=\frac{1}{20}$	$\frac{1}{20}=0.05$	$0.05\times 100=5\%$
Roller coaster	$\frac{252}{560}=\frac{9}{20}$	$\frac{9}{20}=0.45$	$0.45\times 100=45\%$
Bumper Cars	$\frac{84}{560}=\frac{3}{20}$	$\frac{3}{20}=0.15$	$0.15\times 100=5\%$

Explanation of Solution

Given:

  

Concept Used:

In order to convert a fraction into a decimal we have to divide the numerator by the denominator.

Then to turn the decimal into a percent multiply the result by $100$

Calculation:

The total number of students are $140+56+28+252+84=560$

Ride	Fraction	Decimal	Percent
Tilting Ride	$\frac{140}{560}=\frac{1}{4}$	$\frac{1}{4}=0.25$	$0.25\times 100=25\%$
Ferris Wheel	$\frac{56}{560}=\frac{1}{10}$	$\frac{1}{10}=0.1$	$0.1\times 100=10\%$
Carousel	$\frac{28}{560}=\frac{1}{20}$	$\frac{1}{20}=0.05$	$0.05\times 100=5\%$
Roller coaster	$\frac{252}{560}=\frac{9}{20}$	$\frac{9}{20}=0.45$	$0.45\times 100=45\%$
Bumper Cars	$\frac{84}{560}=\frac{3}{20}$	$\frac{3}{20}=0.15$	$0.15\times 100=5\%$

Conclusion:

Ride	Fraction	Decimal	Percent
Tilting Ride	$\frac{140}{560}=\frac{1}{4}$	$\frac{1}{4}=0.25$	$0.25\times 100=25\%$
Ferris Wheel	$\frac{56}{560}=\frac{1}{10}$	$\frac{1}{10}=0.1$	$0.1\times 100=10\%$
Carousel	$\frac{28}{560}=\frac{1}{20}$	$\frac{1}{20}=0.05$	$0.05\times 100=5\%$
Roller coaster	$\frac{252}{560}=\frac{9}{20}$	$\frac{9}{20}=0.45$	$0.45\times 100=45\%$
Bumper Cars	$\frac{84}{560}=\frac{3}{20}$	$\frac{3}{20}=0.15$	$0.15\times 100=5\%$

(b)

To determine

To write fraction of each as an equivalent fraction with a denominator of $100$

Answer to Problem 42PPS

Hence, a fraction into an equivalent fraction with a denominator of $100$ are

  $\frac{25}{100},\frac{1}{100},\frac{5}{100},\frac{45}{100},\frac{15}{100}$

Explanation of Solution

Given:

  

Concept Used:

To change a fraction into an equivalent fraction with a denominator of $100$ :

Establish how many times the given denominator divides into  $100$ ,

Multiply both the numerator and the denominator by that number

Calculation:

As per given information,

  $\begin{array}{l}\frac{1}{4}=\frac{1\times 25}{4\times 25}=\frac{25}{100},\frac{1}{10}=\frac{1\times 10}{10\times 10}=\frac{1}{100},\frac{1}{20}=\frac{1\times 5}{20\times 5}=\frac{5}{100},\\ \frac{9}{20}=\frac{9\times 5}{20\times 5}=\frac{45}{100},\frac{3}{20}=\frac{3\times 5}{20\times 5}=\frac{15}{100}\end{array}$

Conclusion:

  $\therefore$ A fraction into an equivalent fraction with a denominator of $100$ are

  $\frac{25}{100},\frac{1}{100},\frac{5}{100},\frac{45}{100},\frac{15}{100}$

(c)

To determine

To compare the result of part (a) and (b)

Answer to Problem 42PPS

  $\therefore$ Numerator of the fraction with a denominator of $100$ is the same as the percent.

Explanation of Solution

Given:

  

Concept Used:

As per above mentioned table in part (a) & (b),

Calculation:

The numerator of the fraction with a denominator of $100$ is the same as the percent.

Conclusion:

Thus, the numerator of the fraction with a denominator of $100$ is the same as the percent.