Chapter 0.5, Problem 32E

To determine

The quotient of the expression $\frac{16}{9}÷\frac{4}{9}$ .

Answer to Problem 32E

The quotient of the expression $\frac{16}{9}÷\frac{4}{9}$ is $4$ .

Explanation of Solution

Given information:

The expression $\frac{16}{9}÷\frac{4}{9}$ .

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 $\left(\right),\times \text{ or }\cdot$ .

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 $\frac{16}{9}÷\frac{4}{9}$ .

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,

  $\frac{16}{9}÷\frac{4}{9}=\frac{16}{9}\cdot \left(\frac{9}{4}\right)$

16 can be expressed as the product of 4 and 4.

So, $\frac{16}{9}÷\frac{4}{9}$ can be written as,

  $\frac{16}{9}÷\frac{4}{9}=\frac{4\cdot 4\cdot 9}{9\cdot 4}$

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,

  $\frac{16}{9}÷\frac{4}{9}=\frac{4\cdot 4\cdot 9}{9\cdot 4}$

Striking off the common terms, we get,

  $\frac{16}{9}÷\frac{4}{9}=4$

Thus, the quotient of the expression $\frac{16}{9}÷\frac{4}{9}$ is $4$ .