Ordering and Comparing Rational Numbers - Free Printable

To solve the problem of positioning rational numbers on the number lines, we need to carefully evaluate each number and place it correctly on the given number line. Let's go through each part step by step.

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Part A

Numbers: \( |-1 \frac{1}{2}| \), \( \frac{5}{2} \), \( -1.2 \), \( -3 \frac{3}{4} \)

1. Evaluate \( |-1 \frac{1}{2}| \):
\[
-1 \frac{1}{2} = -1.5 \quad \text{(mixed number to decimal)}
\]
The absolute value is:
\[
|-1.5| = 1.5
\]

2. Evaluate \( \frac{5}{2} \):
\[
\frac{5}{2} = 2.5
\]

3. Evaluate \( -1.2 \):
\[
-1.2 \quad \text{(already in decimal form)}
\]

4. Evaluate \( -3 \frac{3}{4} \):
\[
-3 \frac{3}{4} = -3.75 \quad \text{(mixed number to decimal)}
\]

Number Line Placement:
- \( |-1 \frac{1}{2}| = 1.5 \) is placed at 1.5.
- \( \frac{5}{2} = 2.5 \) is placed at 2.5.
- \( -1.2 \) is placed at -1.2.
- \( -3 \frac{3}{4} = -3.75 \) is placed at -3.75.

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Part B

Numbers: \( -\frac{7}{2} \), \( |-2.3| \), \( 4 \frac{1}{3} \), \( -0.8 \)

1. Evaluate \( -\frac{7}{2} \):
\[
-\frac{7}{2} = -3.5
\]

2. Evaluate \( |-2.3| \):
\[
|-2.3| = 2.3
\]

3. Evaluate \( 4 \frac{1}{3} \):
\[
4 \frac{1}{3} = 4 + \frac{1}{3} = 4.333\ldots \approx 4.33
\]

4. Evaluate \( -0.8 \):
\[
-0.8 \quad \text{(already in decimal form)}
\]

Number Line Placement:
- \( -\frac{7}{2} = -3.5 \) is placed at -3.5.
- \( |-2.3| = 2.3 \) is placed at 2.3.
- \( 4 \frac{1}{3} \approx 4.33 \) is placed at 4.33.
- \( -0.8 \) is placed at -0.8.

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Part C

Numbers: \( |-0.6| \), \( -\frac{5}{2} \), \( 1 \frac{2}{3} \), \( |-3.2| \), \( -\frac{3}{4} \)

1. Evaluate \( |-0.6| \):
\[
|-0.6| = 0.6
\]

2. Evaluate \( -\frac{5}{2} \):
\[
-\frac{5}{2} = -2.5
\]

3. Evaluate \( 1 \frac{2}{3} \):
\[
1 \frac{2}{3} = 1 + \frac{2}{3} = 1.666\ldots \approx 1.67
\]

4. Evaluate \( |-3.2| \):
\[
|-3.2| = 3.2
\]

5. Evaluate \( -\frac{3}{4} \):
\[
-\frac{3}{4} = -0.75
\]

Number Line Placement:
- \( |-0.6| = 0.6 \) is placed at 0.6.
- \( -\frac{5}{2} = -2.5 \) is placed at -2.5.
- \( 1 \frac{2}{3} \approx 1.67 \) is placed at 1.67.
- \( |-3.2| = 3.2 \) is placed at 3.2.
- \( -\frac{3}{4} = -0.75 \) is placed at -0.75.

---

Part D

Numbers: \( |-4.3| \), \( -0.7 \), \( |-0.2| \), \( -\frac{9}{4} \), \( -3.6 \)

1. Evaluate \( |-4.3| \):
\[
|-4.3| = 4.3
\]

2. Evaluate \( -0.7 \):
\[
-0.7 \quad \text{(already in decimal form)}
\]

3. Evaluate \( |-0.2| \):
\[
|-0.2| = 0.2
\]

4. Evaluate \( -\frac{9}{4} \):
\[
-\frac{9}{4} = -2.25
\]

5. Evaluate \( -3.6 \):
\[
-3.6 \quad \text{(already in decimal form)}
\]

Number Line Placement:
- \( |-4.3| = 4.3 \) is placed at 4.3.
- \( -0.7 \) is placed at -0.7.
- \( |-0.2| = 0.2 \) is placed at 0.2.
- \( -\frac{9}{4} = -2.25 \) is placed at -2.25.
- \( -3.6 \) is placed at -3.6.

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Part E

Numbers: \( |-3 \frac{3}{4}| \), \( -4.2 \), \( -\frac{7}{3} \), \( 0.5 \), \( -\frac{3}{5} \)

1. Evaluate \( |-3 \frac{3}{4}| \):
\[
-3 \frac{3}{4} = -3.75 \quad \text{(mixed number to decimal)}
\]
The absolute value is:
\[
|-3.75| = 3.75
\]

2. Evaluate \( -4.2 \):
\[
-4.2 \quad \text{(already in decimal form)}
\]

3. Evaluate \( -\frac{7}{3} \):
\[
-\frac{7}{3} = -2.333\ldots \approx -2.33
\]

4. Evaluate \( 0.5 \):
\[
0.5 \quad \text{(already in decimal form)}
\]

5. Evaluate \( -\frac{3}{5} \):
\[
-\frac{3}{5} = -0.6
\]

Number Line Placement:
- \( |-3 \frac{3}{4}| = 3.75 \) is placed at 3.75.
- \( -4.2 \) is placed at -4.2.
- \( -\frac{7}{3} \approx -2.33 \) is placed at -2.33.
- \( 0.5 \) is placed at 0.5.
- \( -\frac{3}{5} = -0.6 \) is placed at -0.6.

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Final Answer

\[
\boxed{
\begin{array}{l}
\text{A: } 1.5, 2.5, -1.2, -3.75 \\
\text{B: } -3.5, 2.3, 4.33, -0.8 \\
\text{C: } 0.6, -2.5, 1.67, 3.2, -0.75 \\
\text{D: } 4.3, -0.7, 0.2, -2.25, -3.6 \\
\text{E: } 3.75, -4.2, -2.33, 0.5, -0.6 \\
\end{array}
}
\]