Chapter 11.1, Problem 8WE

To determine

The proper sign to make given statement correct.

Answer to Problem 8WE

The correct statement is $-\frac{214}{14}>-15\frac{2}{3}$ .

Explanation of Solution

Given statement:

  $-\frac{214}{14}\_\_\_\_-15\frac{2}{3}$

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,

  $\begin{array}{l}-\frac{214}{14}\_\_\_\_-15\frac{2}{3}\\ -\frac{214}{14}\_\_\_\_-\frac{47}{3}\\ -214\times 3\_?\_-47\times 14\\ -642>-658\end{array}$

Therefore,

  $-\frac{214}{14}>-15\frac{2}{3}$

The correct statement is $-\frac{214}{14}>-15\frac{2}{3}$ .