Mixed fractions number line worksheet for students to match fractions to positions and compare values.

Problem Overview:

The worksheet involves two main tasks:
1. Placing mixed fractions on a number line and identifying their corresponding letters.
2. Comparing mixed fractions using the symbols `<`, `>`, or `=`.

Let's solve each part step by step.

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Part 1: Placing Mixed Fractions on the Number Line

#### Step 1: Understand the Number Line
The number line ranges from 1 to 3, divided into smaller segments. Each segment represents a fraction of the whole unit. Since there are 8 divisions between each whole number, each division represents \( \frac{1}{8} \).

#### Step 2: Convert Mixed Fractions to Improper Fractions (if needed)
We will compare the given mixed fractions to their positions on the number line.

#### Step 3: Place Each Mixed Fraction

1. \( 1 \frac{1}{4} \)
- Convert to improper fraction: \( 1 \frac{1}{4} = \frac{5}{4} = 1.25 \)
- On the number line, this is halfway between 1 and 1.5. The closest point is b.

2. \( 2 \frac{5}{8} \)
- This is already in mixed form.
- On the number line, it is 5/8 past 2. The closest point is j.

3. \( 2 \frac{3}{4} \)
- Convert to improper fraction: \( 2 \frac{3}{4} = \frac{11}{4} = 2.75 \)
- On the number line, this is 3/4 past 2. The closest point is m.

4. \( 1 \frac{3}{8} \)
- This is already in mixed form.
- On the number line, it is 3/8 past 1. The closest point is c.

5. \( 2 \frac{1}{8} \)
- This is already in mixed form.
- On the number line, it is 1/8 past 2. The closest point is h.

6. \( 1 \frac{7}{8} \)
- This is already in mixed form.
- On the number line, it is 7/8 past 1. The closest point is e.

7. \( 1 \frac{1}{2} \)
- Convert to improper fraction: \( 1 \frac{1}{2} = \frac{3}{2} = 1.5 \)
- On the number line, this is exactly halfway between 1 and 2. The closest point is d.

8. \( 2 \frac{7}{8} \)
- This is already in mixed form.
- On the number line, it is 7/8 past 2. The closest point is n.

9. \( 2 \frac{1}{2} \)
- Convert to improper fraction: \( 2 \frac{1}{2} = \frac{5}{2} = 2.5 \)
- On the number line, this is exactly halfway between 2 and 3. The closest point is l.

10. \( 1 \frac{5}{8} \)
- This is already in mixed form.
- On the number line, it is 5/8 past 1. The closest point is f.

11. \( 2 \frac{1}{4} \)
- Convert to improper fraction: \( 2 \frac{1}{4} = \frac{9}{4} = 2.25 \)
- On the number line, this is 1/4 past 2. The closest point is i.

12. \( 1 \frac{1}{8} \)
- This is already in mixed form.
- On the number line, it is 1/8 past 1. The closest point is a.

#### Final Placement:
- \( 1 \frac{1}{4} \): b
- \( 2 \frac{5}{8} \): j
- \( 2 \frac{3}{4} \): m
- \( 1 \frac{3}{8} \): c
- \( 2 \frac{1}{8} \): h
- \( 1 \frac{7}{8} \): e
- \( 1 \frac{1}{2} \): d
- \( 2 \frac{7}{8} \): n
- \( 2 \frac{1}{2} \): l
- \( 1 \frac{5}{8} \): f
- \( 2 \frac{1}{4} \): i
- \( 1 \frac{1}{8} \): a

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Part 2: Comparing Fractions

#### Step 1: Compare Each Pair of Fractions
We will compare the fractions using the symbols `<`, `>`, or `=`.

1. \( 1 \frac{3}{4} \) vs. \( 1 \frac{6}{8} \)
- Convert both to improper fractions:
- \( 1 \frac{3}{4} = \frac{7}{4} \)
- \( 1 \frac{6}{8} = \frac{14}{8} = \frac{7}{4} \)
- Both are equal: \( 1 \frac{3}{4} = 1 \frac{6}{8} \)

2. \( 2 \frac{1}{8} \) vs. \( 2 \frac{1}{4} \)
- Convert both to improper fractions:
- \( 2 \frac{1}{8} = \frac{17}{8} \)
- \( 2 \frac{1}{4} = \frac{9}{4} = \frac{18}{8} \)
- \( \frac{17}{8} < \frac{18}{8} \): \( 2 \frac{1}{8} < 2 \frac{1}{4} \)

3. \( 1 \frac{7}{8} \) vs. \( 2 \frac{1}{4} \)
- Convert both to improper fractions:
- \( 1 \frac{7}{8} = \frac{15}{8} \)
- \( 2 \frac{1}{4} = \frac{9}{4} = \frac{18}{8} \)
- \( \frac{15}{8} < \frac{18}{8} \): \( 1 \frac{7}{8} < 2 \frac{1}{4} \)

4. \( 2 \frac{5}{8} \) vs. \( 2 \frac{1}{2} \)
- Convert both to improper fractions:
- \( 2 \frac{5}{8} = \frac{21}{8} \)
- \( 2 \frac{1}{2} = \frac{5}{2} = \frac{20}{8} \)
- \( \frac{21}{8} > \frac{20}{8} \): \( 2 \frac{5}{8} > 2 \frac{1}{2} \)

5. \( 1 \frac{3}{8} \) vs. \( 2 \frac{3}{8} \)
- Both have the same fractional part (\( \frac{3}{8} \)):
- \( 1 < 2 \): \( 1 \frac{3}{8} < 2 \frac{3}{8} \)

6. \( 1 \frac{2}{4} \) vs. \( 1 \frac{2}{8} \)
- Simplify \( 1 \frac{2}{4} \):
- \( 1 \frac{2}{4} = 1 \frac{1}{2} = \frac{3}{2} = \frac{12}{8} \)
- \( 1 \frac{2}{8} = \frac{10}{8} \)
- \( \frac{12}{8} > \frac{10}{8} \): \( 1 \frac{2}{4} > 1 \frac{2}{8} \)

7. \( 2 \frac{2}{8} \) vs. \( 2 \frac{1}{4} \)
- Simplify \( 2 \frac{2}{8} \):
- \( 2 \frac{2}{8} = 2 \frac{1}{4} = \frac{9}{4} \)
- Both are equal: \( 2 \frac{2}{8} = 2 \frac{1}{4} \)

8. \( 1 \frac{5}{8} \) vs. \( 1 \frac{3}{4} \)
- Convert both to improper fractions:
- \( 1 \frac{5}{8} = \frac{13}{8} \)
- \( 1 \frac{3}{4} = \frac{7}{4} = \frac{14}{8} \)
- \( \frac{13}{8} < \frac{14}{8} \): \( 1 \frac{5}{8} < 1 \frac{3}{4} \)

9. \( 2 \frac{7}{8} \) vs. \( 1 \frac{7}{8} \)
- Both have the same fractional part (\( \frac{7}{8} \)):
- \( 2 > 1 \): \( 2 \frac{7}{8} > 1 \frac{7}{8} \)

10. \( 1 \frac{3}{4} \) vs. \( 1 \frac{4}{8} \)
- Simplify \( 1 \frac{4}{8} \):
- \( 1 \frac{4}{8} = 1 \frac{1}{2} = \frac{3}{2} = \frac{6}{4} \)
- \( \frac{7}{4} > \frac{6}{4} \): \( 1 \frac{3}{4} > 1 \frac{4}{8} \)

11. \( 2 \frac{2}{4} \) vs. \( 2 \frac{1}{2} \)
- Simplify \( 2 \frac{2}{4} \):
- \( 2 \frac{2}{4} = 2 \frac{1}{2} = \frac{5}{2} \)
- Both are equal: \( 2 \frac{2}{4} = 2 \frac{1}{2} \)

12. \( 1 \frac{6}{8} \) vs. \( 2 \frac{2}{8} \)
- Simplify \( 1 \frac{6}{8} \):
- \( 1 \frac{6}{8} = 1 \frac{3}{4} = \frac{7}{4} = \frac{14}{8} \)
- \( \frac{14}{8} < \frac{18}{8} \): \( 1 \frac{6}{8} < 2 \frac{2}{8} \)

#### Final Comparisons:
1. \( 1 \frac{3}{4} = 1 \frac{6}{8} \)
2. \( 2 \frac{1}{8} < 2 \frac{1}{4} \)
3. \( 1 \frac{7}{8} < 2 \frac{1}{4} \)
4. \( 2 \frac{5}{8} > 2 \frac{1}{2} \)
5. \( 1 \frac{3}{8} < 2 \frac{3}{8} \)
6. \( 1 \frac{2}{4} > 1 \frac{2}{8} \)
7. \( 2 \frac{2}{8} = 2 \frac{1}{4} \)
8. \( 1 \frac{5}{8} < 1 \frac{3}{4} \)
9. \( 2 \frac{7}{8} > 1 \frac{7}{8} \)
10. \( 1 \frac{3}{4} > 1 \frac{4}{8} \)
11. \( 2 \frac{2}{4} = 2 \frac{1}{2} \)
12. \( 1 \frac{6}{8} < 2 \frac{2}{8} \)

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Final Answer:

\[
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{b, j, m, c, h, e, d, n, l, f, i, a} \\
\text{Part 2:} & =, <, <, >, <, >, =, <, >, >, =, <
\end{array}
}
\]