$\newline$ These five rational numbers are plotted on a horizontal number line. $\newline$ $-\frac{3}{3}, \frac{5}{5},-\frac{1}{5}, \frac{7}{10},-\frac{1}{3}$ $\newline$ Which statement about the locations on the number line of the rational numbers is true? $\newline$ A. $\frac{2}{3}$ is faithest to the left, and $\frac{7}{8}$ is farthest to the right. $\newline$ B. $-\frac{4}{3}$ is farthest to the left, and $\frac{7}{8}$ is farthest to the right. $\newline$ C. $-\frac{2}{3}$ is farthest to the left, and $\frac{7}{10}$ is farthest to the right. $\newline$ D. $\frac{4}{3}$ is farthest to the left, and $\frac{7}{10}$ is farthest to the right.

Full solution

\newline

These five rational numbers are plotted on a horizontal number line.

\newline

-\frac{3}{3}, \frac{5}{5},-\frac{1}{5}, \frac{7}{10},-\frac{1}{3}

\newline

Which statement about the locations on the number line of the rational numbers is true?

\newline

\frac{2}{3}

is faithest to the left, and

\frac{7}{8}

is farthest to the right.

\newline

-\frac{4}{3}

is farthest to the left, and

\frac{7}{8}

is farthest to the right.

\newline

-\frac{2}{3}

is farthest to the left, and

\frac{7}{10}

is farthest to the right.

\newline

\frac{4}{3}

is farthest to the left, and

\frac{7}{10}

is farthest to the right.

List Given Rational Numbers: Step $1$ : List the given rational numbers and simplify them if possible. $\newline$ $-1 ext{, } 1 ext{, } -0.2 ext{, } 0.7 ext{, } -0.333\ldots$
Compare and Determine Order: Step $2$ : Compare the simplified numbers to determine their order on the number line. $\newline$ From left to right: $-1 ext{,} -0.333\ldots ext{,} -0.2 ext{,} 0.7 ext{,} 1$
Analyze Answer Choices: Step $3$ : Analyze each answer choice to see which matches the farthest left and right positions. $\newline$ A. $(\frac{2}{3})$ is farthest left, and $(\frac{7}{8})$ is farthest right - Incorrect. $\newline$ B. $-(\frac{4}{3})$ is farthest left, and $(\frac{7}{8})$ is farthest right - Incorrect. $\newline$ C. $-(\frac{2}{3})$ is farthest left, and $(\frac{7}{10})$ is farthest right - Incorrect. $\newline$ D. $(\frac{4}{3})$ is farthest left, and $(\frac{7}{10})$ is farthest right - Incorrect.