Rational Numbers on a Number Line Worksheets - Math Monks - Free Printable

To solve the problem of plotting the given rational numbers on the number lines, we need to carefully determine the position of each number relative to the scale provided on each number line. Let's go through each number step by step.

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1. Plot \( -\frac{3}{5} \)

- The number line ranges from \(-1\) to \(1\).
- \( -\frac{3}{5} \) is a negative number, so it lies to the left of \(0\).
- To plot \( -\frac{3}{5} \):
- Divide the distance between \(-1\) and \(0\) into 5 equal parts.
- \( -\frac{3}{5} \) is 3 parts away from \(0\) towards \(-1\).

Plot: Mark the point 3/5 of the way from \(0\) to \(-1\).

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2. Plot \( 3\frac{1}{4} \)

- The number line ranges from \(1\) to \(5\).
- \( 3\frac{1}{4} = 3 + \frac{1}{4} = 3.25 \).
- To plot \( 3\frac{1}{4} \):
- Locate \(3\) on the number line.
- Divide the distance between \(3\) and \(4\) into 4 equal parts.
- \( 3\frac{1}{4} \) is 1 part away from \(3\) towards \(4\).

Plot: Mark the point 1/4 of the way from \(3\) to \(4\).

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3. Plot \( \frac{11}{6} \)

- The number line ranges from \(-1\) to \(3\).
- \( \frac{11}{6} \approx 1.833 \).
- To plot \( \frac{11}{6} \):
- Divide the distance between \(1\) and \(2\) into 6 equal parts.
- \( \frac{11}{6} \) is 5 parts away from \(1\) towards \(2\) (since \( \frac{11}{6} = 1 + \frac{5}{6} \)).

Plot: Mark the point 5/6 of the way from \(1\) to \(2\).

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4. Plot \( -2\frac{2}{7} \)

- The number line ranges from \(-3\) to \(0\).
- \( -2\frac{2}{7} = -2 - \frac{2}{7} \).
- To plot \( -2\frac{2}{7} \):
- Locate \(-2\) on the number line.
- Divide the distance between \(-2\) and \(-3\) into 7 equal parts.
- \( -2\frac{2}{7} \) is 2 parts away from \(-2\) towards \(-3\).

Plot: Mark the point 2/7 of the way from \(-2\) to \(-3\).

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5. Plot \( \frac{3}{8} \)

- The number line ranges from \(-2\) to \(1\).
- \( \frac{3}{8} \) is a positive number, so it lies to the right of \(0\).
- To plot \( \frac{3}{8} \):
- Divide the distance between \(0\) and \(1\) into 8 equal parts.
- \( \frac{3}{8} \) is 3 parts away from \(0\) towards \(1\).

Plot: Mark the point 3/8 of the way from \(0\) to \(1\).

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6. Plot \( \frac{21}{9} \)

- Simplify \( \frac{21}{9} \):
\[
\frac{21}{9} = \frac{7}{3} \approx 2.333
\]
- The number line ranges from \(0\) to \(3\).
- To plot \( \frac{7}{3} \):
- Locate \(2\) on the number line.
- Divide the distance between \(2\) and \(3\) into 3 equal parts.
- \( \frac{7}{3} \) is 1 part away from \(2\) towards \(3\).

Plot: Mark the point 1/3 of the way from \(2\) to \(3\).

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7. Plot \( 6\frac{1}{3} \)

- The number line ranges from \(3\) to \(8\).
- \( 6\frac{1}{3} = 6 + \frac{1}{3} = 6.333 \).
- To plot \( 6\frac{1}{3} \):
- Locate \(6\) on the number line.
- Divide the distance between \(6\) and \(7\) into 3 equal parts.
- \( 6\frac{1}{3} \) is 1 part away from \(6\) towards \(7\).

Plot: Mark the point 1/3 of the way from \(6\) to \(7\).

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8. Plot \( -4\frac{4}{5} \)

- The number line ranges from \(-6\) to \(-2\).
- \( -4\frac{4}{5} = -4 - \frac{4}{5} \).
- To plot \( -4\frac{4}{5} \):
- Locate \(-4\) on the number line.
- Divide the distance between \(-4\) and \(-5\) into 5 equal parts.
- \( -4\frac{4}{5} \) is 4 parts away from \(-4\) towards \(-5\).

Plot: Mark the point 4/5 of the way from \(-4\) to \(-5\).

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Final Answer

The points are plotted as described above. The final answer is:

\[
\boxed{
\begin{array}{l}
1. \text{Mark } -\frac{3}{5} \text{ at } 3/5 \text{ of the way from } 0 \text{ to } -1. \\
2. \text{Mark } 3\frac{1}{4} \text{ at } 1/4 \text{ of the way from } 3 \text{ to } 4. \\
3. \text{Mark } \frac{11}{6} \text{ at } 5/6 \text{ of the way from } 1 \text{ to } 2. \\
4. \text{Mark } -2\frac{2}{7} \text{ at } 2/7 \text{ of the way from } -2 \text{ to } -3. \\
5. \text{Mark } \frac{3}{8} \text{ at } 3/8 \text{ of the way from } 0 \text{ to } 1. \\
6. \text{Mark } \frac{21}{9} \text{ at } 1/3 \text{ of the way from } 2 \text{ to } 3. \\
7. \text{Mark } 6\frac{1}{3} \text{ at } 1/3 \text{ of the way from } 6 \text{ to } 7. \\
8. \text{Mark } -4\frac{4}{5} \text{ at } 4/5 \text{ of the way from } -4 \text{ to } -5.
\end{array}
}
\]