Number Line Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Plot and label the following on a number line: −3-3, −12-\dfrac{1}{2}, 00, 1.751.75, 73\dfrac{7}{3}. Then find the distance between −3-3 and 73\dfrac{7}{3}.

Solution

  1. 1
    Convert to decimals for placement: −3=−3-3 = -3, −12=−0.5-\dfrac{1}{2} = -0.5, 0=00 = 0, 1.75=1.751.75 = 1.75, 73≈2.33\dfrac{7}{3} \approx 2.33.
  2. 2
    Order from left to right: −3,  −0.5,  0,  1.75,  2.33-3,\; -0.5,\; 0,\; 1.75,\; 2.33.
  3. 3
    Distance from −3-3 to 73\dfrac{7}{3}: ∣73−(−3)∣=∣73+3∣=∣163∣=163≈5.33\left|\dfrac{7}{3} - (-3)\right| = \left|\dfrac{7}{3} + 3\right| = \left|\dfrac{16}{3}\right| = \dfrac{16}{3} \approx 5.33.

Answer

Distance =163≈5.33= \dfrac{16}{3} \approx 5.33.
The number line provides a geometric model for all real numbers. Distance between two points is the absolute value of their difference, so direction does not matter — only the magnitude of the gap. Converting to decimals makes ordering visual and intuitive.

About Number Line

A straight line where each point represents a number, with equal spacing giving a visual model of all real numbers. The number line extends infinitely in both directions, with negative numbers to the left of zero and positive numbers to the right, providing a geometric representation of order and distance.

Learn more about Number Line →

More Number Line Examples

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