Chapter 3.3, Problem 75SR

To determine

The find: the larger group.

Answer to Problem 75SR

The fraction $\frac{26}{100}\text{or}\frac{13}{50}$ of teenagers is larger than $\frac{25}{100}\text{or}\frac{1}{4}$ teenagers.

Explanation of Solution

Given:

The fractions of teenagers go to sleep between 9 and 10 PM is $\frac{1}{4}$ .

The fraction of teenagers goes to sleep between 12 AM and later is $\frac{13}{50}$ .

Calculation:

Take LCM of the denominators of the fractions $\frac{1}{4}$ and $\frac{13}{50}$ as follows:

  $\begin{array}{l}4=2^2\\ 50=2\times 5^2\\ \text{LCM}=2^2\times 5^2=100\end{array}$

Multiply numerator and denominator by 25 in fraction $\frac{1}{4}$ as follows:

  $\begin{array}{l}\Rightarrow \frac{1\times 25}{4\times 25}\\ \Rightarrow \frac{25}{100}\end{array}$

Multiply numerator and denominator by 2 in fraction $\frac{13}{50}$ as follows:

  $\begin{array}{l}\Rightarrow \frac{13\times 2}{50\times 2}\\ \Rightarrow \frac{26}{100}\end{array}$

Thus, the fraction $\frac{26}{100}\text{or}\frac{13}{50}$ of teenagers is larger than $\frac{25}{100}\text{or}\frac{1}{4}$ teenagers.