Chapter 1.6, Problem 3STP

For Exercises $1-5,$ choose the correct letter.

Which expression has the same value as $-\frac{1}{7}÷\left(-\frac{2}{3}\right)?$

A. $\frac{1}{7}\times \frac{3}{2}$

B. $-\left(\frac{1}{7}\times \frac{3}{2}\right)$

�. $\frac{7}{1}\times \frac{2}{3}$

D. $-\left(\frac{7}{1}\times \frac{2}{3}\right)$

To determine

To find: the expression which has same value as given expression.

Answer to Problem 3STP

The option (a) is correct answer.

Explanation of Solution

Given information: $-\frac{1}{7}÷\left(-\frac{2}{3}\right)$

Here, find the value which is equal to which of the given option,

First simplify given value and then simplify the option value and match with them,

  $\begin{array}{l}-\frac{1}{7}÷\left(-\frac{2}{3}\right)=\frac{-\frac{1}{7}}{-\frac{2}{3}}\\ =\frac{1}{7}\times \frac{3}{2}\\ =\frac{3}{14}\end{array}$

Now simplify all option one by one.

  (a)$\frac{1}{7}\times \frac{3}{2}=\frac{3}{14}$

Which are equals to given value,

  (b)$-\left(\frac{1}{7}\times \frac{3}{2}\right)=-\frac{3}{14}$

Which are not equals to given value,

  (c)$\frac{7}{1}\times \frac{2}{3}=\frac{14}{3}$

Which are not equals to given value,

  (d)$-\left(\frac{7}{1}\times \frac{2}{3}\right)=-\frac{14}{3}$

Which are not equals to given value,

Therefore option (a) is correct answer.