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Which shows a rational number plotted correctly on a number line?

A number line going from negative 8 to positive 4 in increments of 2. There are 4 equal spaces between each number. Negative 3.5 is plotted on the mark 1 space to the left of 4.
A number line going from negative 20 to negative 10 in increments of 2. There are 4 equal spaces between each number. Negative StartFraction 21 Over 2 EndFraction is plotted on the mark 1 space to the left of negative 10.
A number line going from negative 10 to positive 4 in increments of 2. There are 4 equal spaces between each number. Negative StartFraction 7 Over 2 EndFraction is plotted on the mark labeled negative 6.
A number line going from negative 2 to positive 8 in increments of 2. StartFraction 9 Over 2 EndFraction is plotted on the mark 1 space to the left of 4.

1 answer

To determine which of the provided options shows a rational number plotted correctly on a number line, let's analyze each one step-by-step.

  1. Option 1: A number line from -8 to 4, increments of 2.

    • The numbers are: -8, -6, -4, -2, 0, 2, 4.
    • Between -4 and -2, we can find -3.5 by recognizing that it is halfway between -4 and -3.
    • However, it is incorrectly stated that -3.5 is one space left of 4 (which is not true; it should be between -4 and -2). So this option is incorrect.

  2. Option 2: A number line from -20 to -10, increments of 2.

    • The numbers are: -20, -18, -16, -14, -12, -10.
    • The rational number \(-\frac{21}{2}\) or -10.5 lies between -12 and -10.
    • It is correctly stated as being one space to the left of -10 (note that there are four equal spaces between each number, confirming this position). So this option is correct.

  3. Option 3: A number line from -10 to 4, increments of 2.

    • The numbers are: -10, -8, -6, -4, -2, 0, 2, 4.
    • \(-\frac{7}{2}\) or -3.5 is not at -6 but rather between -4 and -2, hence it is incorrectly placed if plotted at -6. So this option is incorrect.

  4. Option 4: A number line from -2 to 8, increments of 2.

    • The numbers are: -2, 0, 2, 4, 6, 8.
    • \(\frac{9}{2}\) or 4.5 is indeed located halfway between 4 and 5, which is not indicated correctly as one space to the left of 4. Hence, this option is incorrect.

Thus, the only option that correctly shows a rational number plotted on the number line is Option 2.