Fraction practice worksheet with addition, subtraction, comparison, number line placement, and conversion exercises.

Let's solve each part of the worksheet step by step.

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Part 1: Add and subtract fractions with the same denominator

When adding or subtracting fractions with the same denominator, you simply add or subtract the numerators and keep the denominator the same.

#### 1. $\frac{5}{12} + \frac{5}{12} = \frac{5+5}{12} = \frac{10}{12}$
Simplify: $\frac{10}{12} = \frac{5}{6}$
✔ Answer: $\boxed{\frac{5}{6}}$

#### 2. $\frac{7}{10} + \frac{2}{10} = \frac{7+2}{10} = \frac{9}{10}$
✔ Answer: $\boxed{\frac{9}{10}}$

#### 3. $\frac{4}{5} - \frac{1}{5} = \frac{4-1}{5} = \frac{3}{5}$
✔ Answer: $\boxed{\frac{3}{5}}$

#### 4. $\frac{7}{9} - \frac{3}{9} = \frac{7-3}{9} = \frac{4}{9}$
✔ Answer: $\boxed{\frac{4}{9}}$

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Part 2: Compare fractions using < and >

We’ll compare each pair by converting to decimals or finding a common denominator.

#### 1. $\frac{1}{2} \quad \square \quad \frac{2}{5}$

- $\frac{1}{2} = 0.5$
- $\frac{2}{5} = 0.4$
- $0.5 > 0.4$ → So, $\frac{1}{2} > \frac{2}{5}$
✔ Answer: $\boxed{>}$

#### 2. $\frac{1}{2} \quad \square \quad \frac{5}{8}$

- $\frac{1}{2} = 0.5$
- $\frac{5}{8} = 0.625$
- $0.5 < 0.625$ → So, $\frac{1}{2} < \frac{5}{8}$
✔ Answer: $\boxed{<}$

#### 3. $\frac{3}{8} \quad \square \quad \frac{2}{5}$

- $\frac{3}{8} = 0.375$
- $\frac{2}{5} = 0.4$
- $0.375 < 0.4$ → So, $\frac{3}{8} < \frac{2}{5}$
✔ Answer: $\boxed{<}$

#### 4. $\frac{7}{10} \quad \square \quad \frac{5}{8}$

- $\frac{7}{10} = 0.7$
- $\frac{5}{8} = 0.625$
- $0.7 > 0.625$ → So, $\frac{7}{10} > \frac{5}{8}$
✔ Answer: $\boxed{>}$

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Part 3: Place fractions on the number line

We have two sets:

#### First set: $\frac{5}{8}, \frac{1}{8}, \frac{4}{8}, \frac{3}{8}$

These are all eighths. The number line from 0 to 1 is divided into 8 equal parts (each part = $\frac{1}{8}$).

So:
- $\frac{1}{8}$ → 1st tick
- $\frac{3}{8}$ → 3rd tick
- $\frac{4}{8} = \frac{1}{2}$ → 4th tick (middle)
- $\frac{5}{8}$ → 5th tick

Label them accordingly on the number line.

#### Second set: $\frac{9}{10}, \frac{2}{10}, \frac{7}{10}, \frac{6}{10}$

All tenths. Number line from 0 to 1, divided into 10 parts.

- $\frac{2}{10} = 0.2$ → 2nd tick
- $\frac{6}{10} = 0.6$ → 6th tick
- $\frac{7}{10} = 0.7$ → 7th tick
- $\frac{9}{10} = 0.9$ → 9th tick

Place them accordingly.

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Part 4: Complete the table — Mixed and Improper Fractions

#### Figure (a): Triangles

Each triangle is divided into 3 parts. Each shaded part is $\frac{1}{3}$.

There are 3 triangles, each fully shaded.

- Each triangle = 1 whole = $\frac{3}{3}$
- Total = $3 \times 1 = 3$ wholes

So:
- Mixed fraction: $3$
- Improper fraction: $\frac{9}{3}$

But since it’s exactly 3, we can write:
- Mixed: $3$
- Improper: $\frac{9}{3}$ or just $3$, but usually improper is written as $\frac{9}{3}$

✔ So:
- Mixed fraction: $\boxed{3}$
- Improper fraction: $\boxed{\frac{9}{3}}$

But wait — let’s check if only parts are shaded.

Looking at the image description: It says "three triangles", each seems fully shaded (since it shows full gray shading). So yes, each represents 1 whole.

So total = 3 wholes.

✔ Final answer for (a):
- Mixed: $3$
- Improper: $\frac{9}{3}$

#### Figure (b): Hexagons

Each hexagon is divided into 6 parts.

There are 5 hexagons.

- First four: fully shaded → each = 1 whole
- Fifth: partially shaded? Let’s see.

The image shows: 4 full hexagons and 1 hexagon with only 1 part shaded.

Wait — the last one has 1/6 shaded?

But in your text, it says: "five hexagons" — and they're shown as:
- Four completely shaded
- One with only one section shaded

So total shaded = $4 + \frac{1}{6} = 4\frac{1}{6}$

So:
- Mixed fraction: $\boxed{4\frac{1}{6}}$
- Improper fraction: Convert $4\frac{1}{6} = \frac{4 \times 6 + 1}{6} = \frac{24 + 1}{6} = \frac{25}{6}$

✔ So:
- Mixed: $4\frac{1}{6}$
- Improper: $\frac{25}{6}$

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✔ Final Answers Summary:

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#### Addition/Subtraction:
- $\frac{5}{12} + \frac{5}{12} = \boxed{\frac{5}{6}}$
- $\frac{7}{10} + \frac{2}{10} = \boxed{\frac{9}{10}}$
- $\frac{4}{5} - \frac{1}{5} = \boxed{\frac{3}{5}}$
- $\frac{7}{9} - \frac{3}{9} = \boxed{\frac{4}{9}}$

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#### Comparison:
- $\frac{1}{2} \boxed{>} \frac{2}{5}$
- $\frac{1}{2} \boxed{<} \frac{5}{8}$
- $\frac{3}{8} \boxed{<} \frac{2}{5}$
- $\frac{7}{10} \boxed{>} \frac{5}{8}$

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#### Number Line:
- For eighths: place $\frac{1}{8}, \frac{3}{8}, \frac{4}{8}, \frac{5}{8}$ at their respective positions.
- For tenths: place $\frac{2}{10}, \frac{6}{10}, \frac{7}{10}, \frac{9}{10}$ at correct ticks.

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#### Table:

| Figures | Mixed Fraction | Improper Fraction |
|--------|----------------|--------------------|
| (a) | $3$ | $\frac{9}{3}$ |
| (b) | $4\frac{1}{6}$ | $\frac{25}{6}$ |

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Let me know if you'd like a visual sketch of the number lines or figures!