Fraction sequences math worksheet for practicing mixed number patterns.

Problem Analysis:

The task involves completing fraction sequences and identifying patterns in each sequence. The instructions specify that fractions do not need to be simplified. Additionally, there is a question about identifying an error in a counting sequence.

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Solution:

#### 1. Sequence: \( 5 \frac{3}{5}, 5 \frac{1}{5}, 4 \frac{4}{5}, \_\_, \_\_, \_\_ \)

- Step 1: Identify the pattern.
- From \( 5 \frac{3}{5} \) to \( 5 \frac{1}{5} \): Subtract \( \frac{2}{5} \).
- From \( 5 \frac{1}{5} \) to \( 4 \frac{4}{5} \): Subtract \( \frac{2}{5} \).

- Step 2: Continue the pattern.
- \( 4 \frac{4}{5} - \frac{2}{5} = 4 \frac{2}{5} \)
- \( 4 \frac{2}{5} - \frac{2}{5} = 4 \frac{0}{5} = 4 \)
- \( 4 - \frac{2}{5} = 3 \frac{3}{5} \)

- Answer: \( 4 \frac{2}{5}, 4, 3 \frac{3}{5} \)

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#### 2. Sequence: \( 6 \frac{1}{10}, 5 \frac{8}{10}, 5 \frac{5}{10}, \_\_, \_\_, \_\_ \)

- Step 1: Identify the pattern.
- From \( 6 \frac{1}{10} \) to \( 5 \frac{8}{10} \): Subtract \( \frac{3}{10} \).
- From \( 5 \frac{8}{10} \) to \( 5 \frac{5}{10} \): Subtract \( \frac{3}{10} \).

- Step 2: Continue the pattern.
- \( 5 \frac{5}{10} - \frac{3}{10} = 5 \frac{2}{10} \)
- \( 5 \frac{2}{10} - \frac{3}{10} = 4 \frac{9}{10} \)
- \( 4 \frac{9}{10} - \frac{3}{10} = 4 \frac{6}{10} \)

- Answer: \( 5 \frac{2}{10}, 4 \frac{9}{10}, 4 \frac{6}{10} \)

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#### 3. Sequence: \( 9 \frac{2}{6}, 8 \frac{3}{6}, 7 \frac{4}{6}, \_\_, \_\_, \_\_ \)

- Step 1: Identify the pattern.
- From \( 9 \frac{2}{6} \) to \( 8 \frac{3}{6} \): Subtract \( 1 \frac{1}{6} \).
- From \( 8 \frac{3}{6} \) to \( 7 \frac{4}{6} \): Subtract \( 1 \frac{1}{6} \).

- Step 2: Continue the pattern.
- \( 7 \frac{4}{6} - 1 \frac{1}{6} = 6 \frac{5}{6} \)
- \( 6 \frac{5}{6} - 1 \frac{1}{6} = 5 \frac{4}{6} \)
- \( 5 \frac{4}{6} - 1 \frac{1}{6} = 4 \frac{3}{6} \)

- Answer: \( 6 \frac{5}{6}, 5 \frac{4}{6}, 4 \frac{3}{6} \)

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#### 4. Sequence: \( 10 \frac{3}{7}, 9 \frac{6}{7}, 9 \frac{2}{7}, \_\_, \_\_, \_\_ \)

- Step 1: Identify the pattern.
- From \( 10 \frac{3}{7} \) to \( 9 \frac{6}{7} \): Subtract \( \frac{4}{7} \).
- From \( 9 \frac{6}{7} \) to \( 9 \frac{2}{7} \): Subtract \( \frac{4}{7} \).

- Step 2: Continue the pattern.
- \( 9 \frac{2}{7} - \frac{4}{7} = 8 \frac{5}{7} \)
- \( 8 \frac{5}{7} - \frac{4}{7} = 8 \frac{1}{7} \)
- \( 8 \frac{1}{7} - \frac{4}{7} = 7 \frac{4}{7} \)

- Answer: \( 8 \frac{5}{7}, 8 \frac{1}{7}, 7 \frac{4}{7} \)

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#### 5. Sequence: \( 9, 8 \frac{4}{9}, 7 \frac{8}{9}, \_\_, \_\_, \_\_ \)

- Step 1: Identify the pattern.
- From \( 9 \) to \( 8 \frac{4}{9} \): Subtract \( \frac{5}{9} \).
- From \( 8 \frac{4}{9} \) to \( 7 \frac{8}{9} \): Subtract \( \frac{5}{9} \).

- Step 2: Continue the pattern.
- \( 7 \frac{8}{9} - \frac{5}{9} = 7 \frac{3}{9} \)
- \( 7 \frac{3}{9} - \frac{5}{9} = 6 \frac{7}{9} \)
- \( 6 \frac{7}{9} - \frac{5}{9} = 6 \frac{2}{9} \)

- Answer: \( 7 \frac{3}{9}, 6 \frac{7}{9}, 6 \frac{2}{9} \)

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#### 6. Zara counted down from 8 in steps of seven eighths, but she made a mistake. Circle the first number she made incorrectly.

- Step 1: Understand the sequence.
- Start at \( 8 \).
- Subtract \( \frac{7}{8} \) each time.

- Step 2: Calculate each step.
- \( 8 - \frac{7}{8} = 7 \frac{1}{8} \) (Correct)
- \( 7 \frac{1}{8} - \frac{7}{8} = 6 \frac{2}{8} \) (Correct)
- \( 6 \frac{2}{8} - \frac{7}{8} = 5 \frac{3}{8} \) (Correct)
- \( 5 \frac{3}{8} - \frac{7}{8} = 4 \frac{4}{8} \) (Incorrect, should be \( 4 \frac{4}{8} \))

- Step 3: Identify the mistake.
- The first incorrect number is \( 4 \frac{5}{8} \).

- Answer: Circle \( 4 \frac{5}{8} \).

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Final Answers:

1. \( 4 \frac{2}{5}, 4, 3 \frac{3}{5} \)
2. \( 5 \frac{2}{10}, 4 \frac{9}{10}, 4 \frac{6}{10} \)
3. \( 6 \frac{5}{6}, 5 \frac{4}{6}, 4 \frac{3}{6} \)
4. \( 8 \frac{5}{7}, 8 \frac{1}{7}, 7 \frac{4}{7} \)
5. \( 7 \frac{3}{9}, 6 \frac{7}{9}, 6 \frac{2}{9} \)
6. Circle \( 4 \frac{5}{8} \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \ 4 \frac{2}{5}, 4, 3 \frac{3}{5} \\
2. \ 5 \frac{2}{10}, 4 \frac{9}{10}, 4 \frac{6}{10} \\
3. \ 6 \frac{5}{6}, 5 \frac{4}{6}, 4 \frac{3}{6} \\
4. \ 8 \frac{5}{7}, 8 \frac{1}{7}, 7 \frac{4}{7} \\
5. \ 7 \frac{3}{9}, 6 \frac{7}{9}, 6 \frac{2}{9} \\
6. \ 4 \frac{5}{8}
\end{array}
}
\]