Chapter 0.5, Problem 26E

To determine

To find: The reciprocal of the number $\frac{1}{22}$ .

Answer to Problem 26E

The reciprocal of the number $\frac{1}{22}$ is $\frac{22}{1}$ .

Explanation of Solution

Given information:

The number $\frac{1}{22}$ .

Formula used:

Reciprocal of any real number (except 0) is obtained when 1 is divided by the number.

  $\begin{array}{c}\frac{a}{b}=1÷\frac{a}{b}\\ =1\cdot \frac{b}{a}\\ =\frac{b}{a}\end{array}$

Here, $\frac{b}{a}$ is called the multiplicative inverse of $\frac{a}{b}$ .

When a number is multiplied with its reciprocal, then the result is always 1.

  $\frac{a}{b}\cdot \frac{b}{a}=1$

Calculation:

Consider the expression $\frac{1}{22}$ .

Reciprocal of any real number (except 0) is obtained when 1 is divided by the number.

  $\begin{array}{c}\frac{a}{b}=1÷\frac{a}{b}\\ =1\cdot \frac{b}{a}\\ =\frac{b}{a}\end{array}$

Here, $\frac{b}{a}$ is called the multiplicative inverse of $\frac{a}{b}$ .

So, the reciprocal of $\frac{1}{22}$ is evaluated as,

  $\begin{array}{c}\frac{1}{22}=1÷\frac{1}{22}\\ =1\cdot \frac{22}{1}\\ =\frac{22}{1}\\ =22\end{array}$

Recall when a number is multiplied with its reciprocal, then the result is always 1.

  $\frac{a}{b}\cdot \frac{b}{a}=1$

So, when $\frac{1}{22}$ is multiplied by $\frac{22}{1}$ , the result should be 1.

  $\frac{1}{22}\cdot \frac{22}{1}=1$

Thus, the reciprocal of the number $\frac{1}{22}$ is $22$ .