Chapter 1.9, Problem 38STP

To determine

Find the required number.

Answer to Problem 38STP

  $-\frac{1}{12}$

Explanation of Solution

Given:

Two thirds equals negative eight times a number.

Concept Used:

Convert the phrase ‘Two thirds equals $\text{N}$ negative eight times a number’ into equation.

Calculation:

Let the number be $\text{N}$

Negative eight times a number: $-8\text{N}$

Two − thirds equals $\text{N}$ negative eight times a number: $\frac{2}{3}=-8\text{N}$

Equation: $\frac{2}{3}=-8\text{N}$

Solve : Multiply each term of the equation by 3, the denominator of left side

  $\begin{array}{l}\frac{2}{3}=-8\text{N}\\ 3·\frac{2}{3}=3·-8\text{N[}\text{Multiply}\text{both}\text{sides}\text{by}\text{3}\text{]}\\ \text{2}\text{=}-\text{24N}\\ \frac{2}{-24}=\frac{-24\text{N}}{-24}\text{[}\text{Divide}\text{both}\text{sides}\text{by}-24\text{]}\\ -\frac{1}{12}=\text{N}\end{array}$

The required number is $-\frac{1}{12}$

Thus, the required number is $-\frac{1}{12}$