Fractions Greater than One (solutions, examples, videos ... - Free Printable

The task involves analyzing the given diagrams and determining the unit fraction, the total number of units shaded, and the total shaded area as a fraction. Let's solve each part step by step.

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Part (a) - Sample

- Diagram: Three diamonds, each divided into two equal parts, with one part shaded in each diamond.
- Unit Fraction: Each diamond is divided into 2 equal parts, so the unit fraction is \( \frac{1}{2} \).
- Total Number of Units Shaded: There are 5 shaded parts in total.
- Total Shaded Area: The total shaded area is calculated as:
\[
\text{Total Shaded Area} = \text{Unit Fraction} \times \text{Total Number of Units Shaded} = \frac{1}{2} \times 5 = \frac{5}{2}
\]

This part is already completed correctly in the image.

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Part (b)

- Diagram: Three rectangles, each divided into 8 equal parts, with all parts shaded.
- Unit Fraction: Each rectangle is divided into 8 equal parts, so the unit fraction is \( \frac{1}{8} \).
- Total Number of Units Shaded: There are 15 shaded parts in total.
- Total Shaded Area: The total shaded area is calculated as:
\[
\text{Total Shaded Area} = \text{Unit Fraction} \times \text{Total Number of Units Shaded} = \frac{1}{8} \times 15 = \frac{15}{8}
\]

This part is already completed correctly in the image.

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Part (c)

- Diagram: Three rectangles, each divided into 6 equal parts, with 2 parts shaded in each rectangle.
- Unit Fraction: Each rectangle is divided into 6 equal parts, so the unit fraction is \( \frac{1}{6} \).
- Total Number of Units Shaded: There are 2 shaded parts in each rectangle, and there are 3 rectangles, so the total number of shaded parts is:
\[
2 \times 3 = 6
\]
- Total Shaded Area: The total shaded area is calculated as:
\[
\text{Total Shaded Area} = \text{Unit Fraction} \times \text{Total Number of Units Shaded} = \frac{1}{6} \times 6 = \frac{6}{6} = 1
\]

The total shaded area should be \( 1 \), not \( \frac{2}{6} \). The correct answer for this part is:
\[
\boxed{\frac{6}{6} = 1}
\]

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Part (d)

- Diagram: Two rectangles, each divided into 4 equal parts, with 3 parts shaded in each rectangle.
- Unit Fraction: Each rectangle is divided into 4 equal parts, so the unit fraction is \( \frac{1}{4} \).
- Total Number of Units Shaded: There are 3 shaded parts in each rectangle, and there are 2 rectangles, so the total number of shaded parts is:
\[
3 \times 2 = 6
\]
- Total Shaded Area: The total shaded area is calculated as:
\[
\text{Total Shaded Area} = \text{Unit Fraction} \times \text{Total Number of Units Shaded} = \frac{1}{4} \times 6 = \frac{6}{4} = \frac{3}{2}
\]

The total shaded area is \( \frac{3}{2} \).

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Final Answers

- Part (c): The total shaded area is \( \boxed{1} \).
- Part (d): The total shaded area is \( \boxed{\frac{3}{2}} \).

The completed table should look like this:

| Part | Unit Fraction | Total Number of Units Shaded | Total Shaded Area |
|------|---------------|------------------------------|-------------------|
| a | \( \frac{1}{2} \) | 5 | \( \frac{5}{2} \) |
| b | \( \frac{1}{8} \) | 15 | \( \frac{15}{8} \) |
| c | \( \frac{1}{6} \) | 6 | \( 1 \) |
| d | \( \frac{1}{4} \) | 6 | \( \frac{3}{2} \) |