4th Grade Math Worksheets PDF | Printable Math Worksheets - Free Printable

Problem Overview:

The task involves identifying fractions that are equivalent to \( \frac{1}{2} \) by analyzing shaded shapes. Equivalent fractions represent the same value but have different numerators and denominators.

Step-by-Step Solution:

#### Section A: Write down what fraction of each shape is shaded. Then check any that are equivalent to \( \frac{1}{2} \).

We will analyze each shape, determine the fraction of the shaded area, and check if it is equivalent to \( \frac{1}{2} \).

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#### Row 1: Squares
1. Shape 1 (Example):
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Simplify: \( \frac{2}{4} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

2. Shape 2:
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Simplify: \( \frac{2}{4} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

3. Shape 3:
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Simplify: \( \frac{2}{4} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

4. Shape 4:
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Simplify: \( \frac{2}{4} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

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#### Row 2: Squares
5. Shape 5:
- Total parts: 9
- Shaded parts: 4
- Fraction: \( \frac{4}{9} \)
- Not equivalent to \( \frac{1}{2} \)

6. Shape 6:
- Total parts: 6
- Shaded parts: 3
- Fraction: \( \frac{3}{6} \)
- Simplify: \( \frac{3}{6} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

7. Shape 7:
- Total parts: 8
- Shaded parts: 3
- Fraction: \( \frac{3}{8} \)
- Not equivalent to \( \frac{1}{2} \)

8. Shape 8:
- Total parts: 4
- Shaded parts: 2
- Fraction: \( \frac{2}{4} \)
- Simplify: \( \frac{2}{4} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

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#### Row 3: Hexagons
9. Shape 9:
- Total parts: 6
- Shaded parts: 3
- Fraction: \( \frac{3}{6} \)
- Simplify: \( \frac{3}{6} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

10. Shape 10:
- Total parts: 6
- Shaded parts: 3
- Fraction: \( \frac{3}{6} \)
- Simplify: \( \frac{3}{6} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

11. Shape 11:
- Total parts: 6
- Shaded parts: 2
- Fraction: \( \frac{2}{6} \)
- Simplify: \( \frac{2}{6} = \frac{1}{3} \)
- Not equivalent to \( \frac{1}{2} \)

12. Shape 12:
- Total parts: 8
- Shaded parts: 4
- Fraction: \( \frac{4}{8} \)
- Simplify: \( \frac{4}{8} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

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#### Row 4: Circles
13. Shape 13:
- Total parts: 8
- Shaded parts: 3
- Fraction: \( \frac{3}{8} \)
- Not equivalent to \( \frac{1}{2} \)

14. Shape 14:
- Total parts: 8
- Shaded parts: 4
- Fraction: \( \frac{4}{8} \)
- Simplify: \( \frac{4}{8} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

15. Shape 15:
- Total parts: 10
- Shaded parts: 3
- Fraction: \( \frac{3}{10} \)
- Not equivalent to \( \frac{1}{2} \)

16. Shape 16:
- Total parts: 10
- Shaded parts: 5
- Fraction: \( \frac{5}{10} \)
- Simplify: \( \frac{5}{10} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

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#### Row 5: Octagons
17. Shape 17:
- Total parts: 8
- Shaded parts: 4
- Fraction: \( \frac{4}{8} \)
- Simplify: \( \frac{4}{8} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

18. Shape 18:
- Total parts: 10
- Shaded parts: 4
- Fraction: \( \frac{4}{10} \)
- Simplify: \( \frac{4}{10} = \frac{2}{5} \)
- Not equivalent to \( \frac{1}{2} \)

19. Shape 19:
- Total parts: 12
- Shaded parts: 6
- Fraction: \( \frac{6}{12} \)
- Simplify: \( \frac{6}{12} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

20. Shape 20:
- Total parts: 16
- Shaded parts: 8
- Fraction: \( \frac{8}{16} \)
- Simplify: \( \frac{8}{16} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

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#### Row 6: Grids
21. Shape 21:
- Total parts: 9
- Shaded parts: 4
- Fraction: \( \frac{4}{9} \)
- Not equivalent to \( \frac{1}{2} \)

22. Shape 22:
- Total parts: 16
- Shaded parts: 8
- Fraction: \( \frac{8}{16} \)
- Simplify: \( \frac{8}{16} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

23. Shape 23:
- Total parts: 12
- Shaded parts: 6
- Fraction: \( \frac{6}{12} \)
- Simplify: \( \frac{6}{12} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

24. Shape 24:
- Total parts: 16
- Shaded parts: 8
- Fraction: \( \frac{8}{16} \)
- Simplify: \( \frac{8}{16} = \frac{1}{2} \)
- Equivalent to \( \frac{1}{2} \)

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Fractions Equivalent to \( \frac{1}{2} \):

From the analysis above, the fractions equivalent to \( \frac{1}{2} \) are:
\[
\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}, \frac{6}{12}, \frac{8}{16}
\]

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What do you notice?

- All the fractions equivalent to \( \frac{1}{2} \) can be simplified to \( \frac{1}{2} \).
- The numerator is always half of the denominator.
- The shaded area in each shape represents exactly half of the total area.

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Final Answer:

\[
\boxed{\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}, \frac{6}{12}, \frac{8}{16}}
\]