Chapter R.14, Problem 1DE

To determine

To calculate: The expression equivalent to the algebraic expression $\frac{7}{8}$ by the use of multiply by 1 to make the denominator as $8x$.

Answer to Problem 1DE

Solution:

The equivalent expression to the algebraic expression $\frac{7}{8}$ with the denominator $8x$ is $\underset{\_}{\frac{7x}{8x}}$.

Explanation of Solution

Given information:

The provided expression and denominator are $\frac{7}{8}$ and $8x$ respectively.

Formula used:

The identity property of 1 or the multiplying by 1 property is as stated below:

$a\cdot 1=1\cdot a=a$

The above expression states that 1 is the multiplicative identity and a can be any number.

Calculation:

Consider the expression $\frac{7}{8}$.

To make the denominator $8x$, use the multiplying by 1 property as below:

$\frac{7}{8}=\frac{7}{8}\cdot 1$

Now, replace 1 by $\frac{x}{x}$,

$\begin{array}{c}\frac{7}{8}=\frac{7}{8}\cdot 1\\ =\frac{7}{8}\cdot \frac{x}{x}\\ =\frac{7x}{8x}\end{array}$

Hence, the equivalent expression to the algebraic expression $\frac{7}{8}$ with the denominator $8x$ is $\frac{7x}{8x}$.