Chapter 0.5, Problem 34E

To determine

To find: The quotient of the expression $\frac{3}{7}÷\left(-\frac{1}{5}\right)$ .

Answer to Problem 34E

The quotient of the expression $\frac{3}{7}÷\left(-\frac{1}{5}\right)$ is $-\frac{15}{7}$ .

Explanation of Solution

Given information:

The expression $\frac{3}{7}÷\left(-\frac{1}{5}\right)$ .

Formula used:

Product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Product of a negative and a positive integer is always negative.

Division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Calculation:

Consider the expression $\frac{3}{7}÷\left(-\frac{1}{5}\right)$ .

Recall that division in real numbers is multiplication by reciprocal. If $b\ne 0$ , then,

  $\begin{array}{c}a÷b=a\left(\frac{1}{b}\right)\\ =\frac{a}{b}\end{array}$

Here, $\frac{1}{b}$ is the multiplicative inverse.

Apply it,

  $\begin{array}{c}\frac{3}{7}÷\left(-\frac{1}{5}\right)=\frac{3}{7}\cdot \left(-\frac{1}{\frac{1}{5}}\right)\\ =\frac{3}{7}\cdot -\frac{5}{1}\end{array}$

Recall that product of two real numbers is obtained when they are multiplied together. That is two or more numbers are separated by multiplication signs $\left(\right),\times \text{ or }\cdot$ .

Simplify it,

  $\begin{array}{c}\frac{3}{7}÷\left(-\frac{1}{5}\right)=\frac{3}{7}\cdot \left(-\frac{1}{\frac{1}{5}}\right)\\ =\frac{3}{7}\cdot -\frac{5}{1}\\ =-\frac{3\cdot 5}{7\cdot 1}\\ =-\frac{15}{7}\end{array}$

Thus, the quotient of the expression $\frac{3}{7}÷\left(-\frac{1}{5}\right)$ is $-\frac{15}{7}$ .