Chapter 0.5, Problem 40E

To determine

To find: The quotient of the expression $4÷\left(-\frac{2}{7}\right)$ .

Answer to Problem 40E

The quotient of the expression $4÷\left(-\frac{2}{7}\right)$ is $-14$ .

Explanation of Solution

Given information:

The expression $4÷\left(-\frac{2}{7}\right)$ .

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 $4÷\left(-\frac{2}{7}\right)$ .

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,

  $4÷\left(-\frac{2}{7}\right)=4\cdot \left(-\frac{7}{2}\right)$

4 can be written as the product of 2 and 2.

Simplify further it as,

  $\begin{array}{c}4÷\left(-\frac{2}{7}\right)=4\cdot \left(-\frac{7}{2}\right)\\ =-\frac{2\cdot 2\cdot 7}{2}\end{array}$

Striking off the common terms, we get,

  $4÷\left(-\frac{2}{7}\right)=-7\cdot 2$

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,

  $4÷\left(-\frac{2}{7}\right)=-14$

Thus, the quotient of the expression $4÷\left(-\frac{2}{7}\right)$ is $-14$ .