Math Quiz online exercise for Grade 5 - Free Printable

Let's solve this Fifth Grade Math Quiz step by step, explaining each part clearly.

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Part I: Multiple Choice – Identify the Fraction Represented by the Shaded Part

We are given shapes divided into equal parts, and we must identify what fraction of the whole is shaded.

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#### 1.
- Shape: 2 rows × 2 columns = 4 total squares
- Shaded: 2 squares
- So, $ \frac{2}{4} $
✔ Correct answer: $ \frac{2}{4} $ (already circled)

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#### 2.
- Shape: 3 rows × 2 columns = 6 total squares
- Shaded: 4 squares
- So, $ \frac{4}{6} $
✔ Answer: $ \frac{4}{6} $

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#### 3.
- Shape: 3 rows × 3 columns = 9 total squares
- Shaded: 5 squares
- So, $ \frac{5}{9} $
✔ Answer: $ \frac{5}{9} $

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#### 4.
- Shape: 3 rows × 3 columns = 9 total squares
- Shaded: 6 squares
- So, $ \frac{6}{9} $
✔ Answer: $ \frac{6}{9} $

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#### 5.
- Shape: 3 rows × 3 columns = 9 total squares
- Shaded: 8 squares
- So, $ \frac{8}{9} $
✔ Answer: $ \frac{8}{9} $

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#### 6.
- Triangle divided into 3 equal parts
- Shaded: 1 part
- So, $ \frac{1}{3} $
✔ Answer: $ \frac{1}{3} $

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#### 7.
- Circle divided into 5 equal parts
- Shaded: 3 parts
- So, $ \frac{3}{5} $
✔ Answer: $ \frac{3}{5} $

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#### 8.
- Circle divided into 6 equal parts
- Shaded: 4 parts
- So, $ \frac{4}{6} $
✔ Answer: $ \frac{4}{6} $

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#### 9.
- Circle divided into 8 equal parts
- Shaded: 5 parts
- So, $ \frac{5}{8} $
✔ Answer: $ \frac{5}{8} $

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#### 10.
- Circle divided into 8 equal parts
- Shaded: 3 parts
- So, $ \frac{3}{8} $
✔ Answer: $ \frac{3}{8} $

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✔ Part I Answers Summary:

| Q | Answer |
|---|--------|
| 1 | $ \frac{2}{4} $ |
| 2 | $ \frac{4}{6} $ |
| 3 | $ \frac{5}{9} $ |
| 4 | $ \frac{6}{9} $ |
| 5 | $ \frac{8}{9} $ |
| 6 | $ \frac{1}{3} $ |
| 7 | $ \frac{3}{5} $ |
| 8 | $ \frac{4}{6} $ |
| 9 | $ \frac{5}{8} $ |
|10 | $ \frac{3}{8} $ |

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Part II: Adding with Fractions – Use Area Model

We need to:
1. Add fractions using area models (drawings).
2. Write equivalent fractions with common denominators.
3. Add them.

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#### 1. $ \frac{2}{3} + \frac{1}{4} $

Step 1: Find a common denominator
- LCM of 3 and 4 is 12

Convert:
- $ \frac{2}{3} = \frac{8}{12} $
- $ \frac{1}{4} = \frac{3}{12} $

So:
$$
\frac{2}{3} + \frac{1}{4} = \frac{8}{12} + \frac{3}{12} = \frac{11}{12}
$$

Area Model:
- Draw two rectangles (each representing 1 whole)
- Divide first rectangle into 12 parts → shade 8 (for $ \frac{8}{12} $)
- Divide second rectangle into 12 parts → shade 3 (for $ \frac{3}{12} $)
- Total shaded: 11 out of 12 → $ \frac{11}{12} $

✔ Answer: $ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} $

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#### 2. $ \frac{1}{4} + \frac{1}{6} $

Common denominator: LCM of 4 and 6 = 12

Convert:
- $ \frac{1}{4} = \frac{3}{12} $
- $ \frac{1}{6} = \frac{2}{12} $

So:
$$
\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}
$$

Area Model:
- First rectangle: divide into 12 parts → shade 3
- Second rectangle: divide into 12 parts → shade 2
- Total: 5/12

✔ Answer: $ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $

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#### 3. $ \frac{1}{8} + \frac{3}{4} $

Common denominator: LCM of 8 and 4 = 8

Convert:
- $ \frac{1}{8} = \frac{1}{8} $
- $ \frac{3}{4} = \frac{6}{8} $

So:
$$
\frac{1}{8} + \frac{3}{4} = \frac{1}{8} + \frac{6}{8} = \frac{7}{8}
$$

Area Model:
- First rectangle: divide into 8 parts → shade 1
- Second rectangle: divide into 8 parts → shade 6
- Total: 7/8

✔ Answer: $ \frac{1}{8} + \frac{6}{8} = \frac{7}{8} $

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#### 4. $ \frac{2}{10} + \frac{1}{2} $

Simplify $ \frac{2}{10} = \frac{1}{5} $

But let’s use common denominator:

LCM of 10 and 2 = 10

Convert:
- $ \frac{2}{10} = \frac{2}{10} $
- $ \frac{1}{2} = \frac{5}{10} $

So:
$$
\frac{2}{10} + \frac{1}{2} = \frac{2}{10} + \frac{5}{10} = \frac{7}{10}
$$

Area Model:
- First rectangle: divide into 10 parts → shade 2
- Second rectangle: divide into 10 parts → shade 5
- Total: 7/10

✔ Answer: $ \frac{2}{10} + \frac{5}{10} = \frac{7}{10} $

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✔ Part II Answers Summary:

| Q | Expression | Equivalent Fractions | Sum |
|---|------------|-----------------------|-----|
| 1 | $ \frac{2}{3} + \frac{1}{4} $ | $ \frac{8}{12} + \frac{3}{12} $ | $ \frac{11}{12} $ |
| 2 | $ \frac{1}{4} + \frac{1}{6} $ | $ \frac{3}{12} + \frac{2}{12} $ | $ \frac{5}{12} $ |
| 3 | $ \frac{1}{8} + \frac{3}{4} $ | $ \frac{1}{8} + \frac{6}{8} $ | $ \frac{7}{8} $ |
| 4 | $ \frac{2}{10} + \frac{1}{2} $ | $ \frac{2}{10} + \frac{5}{10} $ | $ \frac{7}{10} $ |

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✔ Final Answer Key:

#### Part I (Multiple Choice):
1. $ \frac{2}{4} $
2. $ \frac{4}{6} $
3. $ \frac{5}{9} $
4. $ \frac{6}{9} $
5. $ \frac{8}{9} $
6. $ \frac{1}{3} $
7. $ \frac{3}{5} $
8. $ \frac{4}{6} $
9. $ \frac{5}{8} $
10. $ \frac{3}{8} $

#### Part II (Addition with Area Models):
1. $ \frac{8}{12} + \frac{3}{12} = \frac{11}{12} $
2. $ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $
3. $ \frac{1}{8} + \frac{6}{8} = \frac{7}{8} $
4. $ \frac{2}{10} + \frac{5}{10} = \frac{7}{10} $

> 📌 Note: For the area model drawings, you would draw two rectangles for each problem:
> - One divided into the common denominator parts (e.g., 12 for #1), shaded accordingly.
> - The other similarly, then combine.

Let me know if you'd like visual diagrams drawn in text form!