Chapter 11.1, Problem 1WE

To determine

The proper sign to make given statement correct.

Answer to Problem 1WE

The correct statement is $\frac{1}{4}>\frac{4}{27}$ .

Explanation of Solution

Given statement:

  $\frac{1}{4}\_\_\_\_\frac{4}{27}$

Calculation:

From the given statement, we have to identify the first number is <,=,> the second number.

Formula:

  $\begin{array}{l}\frac{a}{c}>\frac{b}{d},\left(\text{if }ad>bd\right),\\ \frac{a}{c}<\frac{b}{d},\left(\text{if }ad<bd\right)\end{array}$

Now,

  $\begin{array}{l}\frac{1}{4}\_\_\_\_\frac{4}{27}\\ 1\times 27\_\_4\times 4\\ 27>16\end{array}$

Therefore,

  $\frac{1}{4}>\frac{4}{27}$

The correct statement is $\frac{1}{4}>\frac{4}{27}$ .