Question
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Plot the numbers \( -\frac{5}{6} \) and \( \frac{13}{6} \) on the number line below.

Ask by Romero Floyd. in the United States
Mar 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Plot \( -\frac{5}{6} \) between \(-1\) and \(0\) and \( \frac{13}{6} \) between \(2\) and \(3\) on the number line.

Solution

1. First, convert the fractions to decimals (approximately) to understand their positions: - \( -\frac{5}{6} \approx -0.8333 \) - \( \frac{13}{6} \approx 2.1667 \) 2. Notice that: - \( -\frac{5}{6} \) lies between \(-1\) and \(0\), closer to \(-1\). - \( \frac{13}{6} \) lies between \(2\) and \(3\), closer to \(2\). 3. To plot these on a number line, follow these steps: - Draw a horizontal line. - Mark the integers, for example, \(-2\), \(-1\), \(0\), \(1\), \(2\), \(3\). - Identify the position of \( -\frac{5}{6} \) between \(-1\) and \(0\). - Identify the position of \( \frac{13}{6} \) between \(2\) and \(3\). 4. A simple representation of the number line is shown below: \[ \begin{array}{ccccccccccc} & -2 & & -1 & & 0 & & 1 & & 2 & & 3 \\ & \quad & \quad & \bullet & \quad & \quad & \quad & \quad & \quad & \bullet & \quad \\ & \quad & \quad & -\frac{5}{6} & \quad & \quad & \quad & \quad & \quad & \frac{13}{6} & \quad \\ \end{array} \] 5. In this diagram: - The bullet at \(-\frac{5}{6}\) is placed between \(-1\) and \(0\). - The bullet at \(\frac{13}{6}\) is placed between \(2\) and \(3\). This completes the plot of the numbers on the number line.

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The Deep Dive

To plot the numbers \(-\frac{5}{6}\) and \(\frac{13}{6}\) on a number line, first, identify that \(-\frac{5}{6}\) is slightly less than \(-1\) (since \(-\frac{6}{6} = -1\)), and \(\frac{13}{6}\) is a little more than \(2\) (since \(\frac{12}{6} = 2\)). On the number line: 1. Locate \( -1 \) on the left side of the number line, and mark a point just before it to represent \(-\frac{5}{6}\). 2. For \( \frac{13}{6} \), find \( 2 \) on the right side of the number line, and mark a point just after it to represent \(\frac{13}{6}\). Now both points are clearly represented on the number line! This results in: - A point labeled \(-\frac{5}{6}\) to the left of \(-1\) - A point labeled \(\frac{13}{6}\) to the right of \(2\) Now you have plotted both fractions accurately!

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