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

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

\newline

-\frac{5}{3}

\frac{5}{5}

-\frac{1}{2}

\frac{7}{10}

-\frac{4}{3}

\newline

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

\newline

\frac{2}{3}

is farthest to the left, and

\frac{7}{8}

is farthest to the right.

\newline

-\frac{1}{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.

Convert to decimal: Convert all the given rational numbers to decimal form for easier comparison on the number line. $\newline$ - $\frac{5}{5} = 1$ $\newline$ - $\frac{7}{10} = 0.7$ $\newline$ - $\frac{-1}{2} = -0.5$ $\newline$ - $\frac{-5}{3} \approx -1.67$ $\newline$ - $\frac{-4}{3} \approx -1.33$
Identify extremes: Identify the rational numbers farthest to the left and right on the number line. $\newline$ Farthest left: $\frac{-5}{3}$ (approximately $-1$ . $67$ ) $\newline$ Farthest right: $\frac{7}{10}$ ( $0$ . $7$ )
Match with choices: Match the findings with the given choices. $\newline$ A. $\frac{2}{3}$ is farthest to the left, and $\frac{7}{8}$ is farthest to the right. (Incorrect) $\newline$ B. $\frac{-1}{3}$ is farthest to the lett, and $\frac{7}{8}$ is farthest to the right. (Incorrect) $\newline$ C. $\frac{-2}{3}$ is farthest to the left, and $\frac{7}{10}$ is farthest to the right. (Incorrect) $\newline$ D. $\frac{-4}{3}$ is tarthest to the left, and $\frac{7}{10}$ is farthest to the right. (Incorrect, should be $\frac{-5}{3}$ )