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These five rational numbers are plotted on a horizontal number line. \newline53-\frac{5}{3}, 55\frac{5}{5}, 12-\frac{1}{2}, 710\frac{7}{10}, 43-\frac{4}{3} \newlineWhich statement about the locations on the number line of the rational numbers is true? \newlineA. 23\frac{2}{3} is farthest to the left, and 78\frac{7}{8} is farthest to the right. \newlineB. 13-\frac{1}{3} is farthest to the left, and 78\frac{7}{8} is farthest to the right. \newlineC. 23-\frac{2}{3} is farthest to the left, and 710\frac{7}{10} is farthest to the right. \newlineD. 43-\frac{4}{3} is farthest to the left, and 710\frac{7}{10} is farthest to the right.

Full solution

Q. These five rational numbers are plotted on a horizontal number line. \newline53-\frac{5}{3}, 55\frac{5}{5}, 12-\frac{1}{2}, 710\frac{7}{10}, 43-\frac{4}{3} \newlineWhich statement about the locations on the number line of the rational numbers is true? \newlineA. 23\frac{2}{3} is farthest to the left, and 78\frac{7}{8} is farthest to the right. \newlineB. 13-\frac{1}{3} is farthest to the left, and 78\frac{7}{8} is farthest to the right. \newlineC. 23-\frac{2}{3} is farthest to the left, and 710\frac{7}{10} is farthest to the right. \newlineD. 43-\frac{4}{3} is farthest to the left, and 710\frac{7}{10} is farthest to the right.
  1. Convert to decimal: Convert all the given rational numbers to decimal form for easier comparison on the number line.\newline- 55=1 \frac{5}{5} = 1 \newline- 710=0.7 \frac{7}{10} = 0.7 \newline- 12=0.5 \frac{-1}{2} = -0.5 \newline- 531.67 \frac{-5}{3} \approx -1.67 \newline- 431.33 \frac{-4}{3} \approx -1.33
  2. Identify extremes: Identify the rational numbers farthest to the left and right on the number line.\newlineFarthest left: 53 \frac{-5}{3} (approximately 1-1.6767)\newlineFarthest right: 710 \frac{7}{10} (00.77)
  3. Match with choices: Match the findings with the given choices.\newlineA. 23 \frac{2}{3} is farthest to the left, and 78 \frac{7}{8} is farthest to the right. (Incorrect)\newlineB. 13 \frac{-1}{3} is farthest to the lett, and 78 \frac{7}{8} is farthest to the right. (Incorrect)\newlineC. 23 \frac{-2}{3} is farthest to the left, and 710 \frac{7}{10} is farthest to the right. (Incorrect)\newlineD. 43 \frac{-4}{3} is tarthest to the left, and 710 \frac{7}{10} is farthest to the right. (Incorrect, should be 53 \frac{-5}{3} )