Fractions on Number Lines worksheet for students to practice placing fractions on a number line.

Problem Description:

The task involves labeling fractions on number lines. The fractions to be labeled are provided for each number line, and the goal is to correctly place these fractions on the respective number lines.

Solution Explanation:

#### Step 1: Understand the structure of a number line
- A number line is a visual representation of numbers as points on a straight line.
- Fractions represent parts of a whole, and their placement on a number line depends on how many equal parts the unit interval (from 0 to 1) is divided into.

#### Step 2: Label the fractions on each number line

##### Number Line 1: Label $\frac{1}{3}$, $\frac{2}{3}$, and $\frac{4}{3}$.
- The denominator is 3, so the unit interval from 0 to 1 is divided into 3 equal parts.
- Each part represents $\frac{1}{3}$.
- Place $\frac{1}{3}$ at the first division mark after 0.
- Place $\frac{2}{3}$ at the second division mark after 0.
- Place $\frac{4}{3}$ at the first division mark after 1 (since $\frac{4}{3} = 1 + \frac{1}{3}$).

##### Number Line 2: Label $\frac{1}{6}$, $\frac{3}{6}$, and $\frac{5}{6}$.
- The denominator is 6, so the unit interval from 0 to 1 is divided into 6 equal parts.
- Each part represents $\frac{1}{6}$.
- Place $\frac{1}{6}$ at the first division mark after 0.
- Place $\frac{3}{6}$ at the third division mark after 0.
- Place $\frac{5}{6}$ at the fifth division mark after 0.

##### Number Line 3: Label $\frac{3}{10}$, $\frac{7}{10}$, and $\frac{9}{10}$.
- The denominator is 10, so the unit interval from 0 to 1 is divided into 10 equal parts.
- Each part represents $\frac{1}{10}$.
- Place $\frac{3}{10}$ at the third division mark after 0.
- Place $\frac{7}{10}$ at the seventh division mark after 0.
- Place $\frac{9}{10}$ at the ninth division mark after 0.

##### Number Line 4: Label $\frac{3}{8}$, $\frac{5}{8}$, and $\frac{7}{8}$.
- The denominator is 8, so the unit interval from 0 to 1 is divided into 8 equal parts.
- Each part represents $\frac{1}{8}$.
- Place $\frac{3}{8}$ at the third division mark after 0.
- Place $\frac{5}{8}$ at the fifth division mark after 0.
- Place $\frac{7}{8}$ at the seventh division mark after 0.

#### Step 3: Verify the placements
- Ensure that the fractions are placed at the correct division marks based on their numerators.
- Double-check that the divisions are evenly spaced.

Final Answer:

The fractions are labeled as follows:

1. Number Line 1:
- $\frac{1}{3}$: First division mark after 0.
- $\frac{2}{3}$: Second division mark after 0.
- $\frac{4}{3}$: First division mark after 1.

2. Number Line 2:
- $\frac{1}{6}$: First division mark after 0.
- $\frac{3}{6}$: Third division mark after 0.
- $\frac{5}{6}$: Fifth division mark after 0.

3. Number Line 3:
- $\frac{3}{10}$: Third division mark after 0.
- $\frac{7}{10}$: Seventh division mark after 0.
- $\frac{9}{10}$: Ninth division mark after 0.

4. Number Line 4:
- $\frac{3}{8}$: Third division mark after 0.
- $\frac{5}{8}$: Fifth division mark after 0.
- $\frac{7}{8}$: Seventh division mark after 0.

$$
\boxed{\text{Fractions labeled as described above.}}
$$