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Expert-verified Found in: Page 226 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Let a and b represent non zero integers. Find a rational number in the form $\frac{a}{b}$ so that $-1.7<\frac{a}{b}$ and $\frac{a}{b}>-\frac{5}{3}$. Explain how you found the number.

The rational number lying between $-1.7and-\frac{5}{3}$ is $-\frac{33}{20}$.

See the step by step solution

## Step 1. Given information

The numbers are $-1.7and-\frac{5}{3}$.

## Step 2. Calculation

Let $xandy$be the two rational number such that $x

Then, $\frac{1}{2}\left(x+y\right)$ is a rational number lying between $xandy$.

Let $x=-1.7$ and

$\begin{array}{c}y=-\frac{5}{3}\\ =-1.6\end{array}$

Then, clearly

$\begin{array}{c}-1.7<-1.6\\ x

Therefore, a rational number lying between $xandy$

$\begin{array}{c}\frac{1}{2}\left(x+y\right)=\frac{1}{2}\left(-1.7+-\frac{5}{3}\right)\\ =-\frac{33}{20}\end{array}$

Thus, the rational number lying between $-1.7and-\frac{5}{3}$ is $-\frac{33}{20}$. ### Want to see more solutions like these? 