12+ Free Comparing Fractions on a Number Line Worksheet Pages - Free Printable

Problem Analysis:

The task involves comparing fractions using a number line. The goal is to determine whether one fraction is greater than, less than, or equal to another fraction. The provided number line helps visualize the relative positions of the fractions.

Given Fractions and Comparisons:

1. Compare \( \frac{1}{2} \) with \( \frac{1}{5} \)
2. Compare \( \frac{1}{2} \) with \( \frac{2}{4} \)
3. Compare \( \frac{1}{2} \) with \( \frac{9}{10} \)

Solution:

#### Step 1: Understand the Number Line
The number line is divided into segments, and the fractions are marked at specific points. The fractions from left to right are:
- \( \frac{1}{5} \)
- \( \frac{1}{3} \)
- \( \frac{3}{7} \)
- \( \frac{3}{5} \)
- \( \frac{3}{4} \)
- \( \frac{9}{10} \)

#### Step 2: Locate \( \frac{1}{2} \) on the Number Line
The fraction \( \frac{1}{2} \) is not explicitly marked on the number line, but we know its position. Since \( \frac{1}{2} = 0.5 \), it lies exactly in the middle of the number line between 0 and 1.

#### Step 3: Compare Each Fraction

##### Comparison 1: \( \frac{1}{2} \) vs. \( \frac{1}{5} \)
- \( \frac{1}{5} \) is located to the left of \( \frac{1}{2} \) on the number line.
- This means \( \frac{1}{5} \) is smaller than \( \frac{1}{2} \).
- Therefore, \( \frac{1}{2} > \frac{1}{5} \).

##### Comparison 2: \( \frac{1}{2} \) vs. \( \frac{2}{4} \)
- Simplify \( \frac{2}{4} \): \( \frac{2}{4} = \frac{1}{2} \).
- Both fractions are equal.
- Therefore, \( \frac{1}{2} = \frac{2}{4} \).

##### Comparison 3: \( \frac{1}{2} \) vs. \( \frac{9}{10} \)
- \( \frac{9}{10} \) is located to the right of \( \frac{1}{2} \) on the number line.
- This means \( \frac{9}{10} \) is larger than \( \frac{1}{2} \).
- Therefore, \( \frac{1}{2} < \frac{9}{10} \).

Final Answers:

1. \( \frac{1}{2} > \frac{1}{5} \)
2. \( \frac{1}{2} = \frac{2}{4} \)
3. \( \frac{1}{2} < \frac{9}{10} \)

Boxed Answer:

\[
\boxed{
\begin{aligned}
1) & \quad \frac{1}{2} > \frac{1}{5} \\
2) & \quad \frac{1}{2} = \frac{2}{4} \\
3) & \quad \frac{1}{2} < \frac{9}{10}
\end{aligned}
}
\]