Math worksheet for converting improper fractions to mixed numbers and vice versa, designed for educational practice.

Problem: Converting between Improper Fractions and Mixed Numbers

The task involves two parts:
1. Converting improper fractions to mixed numbers.
2. Rewriting mixed numbers as improper fractions.

Let's solve each part step by step.

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Part A: Convert each improper fraction to a mixed number.

#### 1) $\frac{9}{5}$
- Step 1: Divide the numerator (9) by the denominator (5).
- $ 9 \div 5 = 1 $ remainder $ 4 $.
- Step 2: Write the result as a mixed number.
- The quotient (1) becomes the whole number, and the remainder (4) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 1 \frac{4}{5} $.

Answer: $ 1 \frac{4}{5} $

#### 2) $\frac{53}{12}$
- Step 1: Divide the numerator (53) by the denominator (12).
- $ 53 \div 12 = 4 $ remainder $ 5 $.
- Step 2: Write the result as a mixed number.
- The quotient (4) becomes the whole number, and the remainder (5) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 4 \frac{5}{12} $.

Answer: $ 4 \frac{5}{12} $

#### 3) $\frac{10}{3}$
- Step 1: Divide the numerator (10) by the denominator (3).
- $ 10 \div 3 = 3 $ remainder $ 1 $.
- Step 2: Write the result as a mixed number.
- The quotient (3) becomes the whole number, and the remainder (1) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 3 \frac{1}{3} $.

Answer: $ 3 \frac{1}{3} $

#### 4) $\frac{8}{7}$
- Step 1: Divide the numerator (8) by the denominator (7).
- $ 8 \div 7 = 1 $ remainder $ 1 $.
- Step 2: Write the result as a mixed number.
- The quotient (1) becomes the whole number, and the remainder (1) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 1 \frac{1}{7} $.

Answer: $ 1 \frac{1}{7} $

#### 5) $\frac{65}{11}$
- Step 1: Divide the numerator (65) by the denominator (11).
- $ 65 \div 11 = 5 $ remainder $ 10 $.
- Step 2: Write the result as a mixed number.
- The quotient (5) becomes the whole number, and the remainder (10) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 5 \frac{10}{11} $.

Answer: $ 5 \frac{10}{11} $

#### 6) $\frac{31}{4}$
- Step 1: Divide the numerator (31) by the denominator (4).
- $ 31 \div 4 = 7 $ remainder $ 3 $.
- Step 2: Write the result as a mixed number.
- The quotient (7) becomes the whole number, and the remainder (3) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 7 \frac{3}{4} $.

Answer: $ 7 \frac{3}{4} $

#### 7) $\frac{29}{6}$
- Step 1: Divide the numerator (29) by the denominator (6).
- $ 29 \div 6 = 4 $ remainder $ 5 $.
- Step 2: Write the result as a mixed number.
- The quotient (4) becomes the whole number, and the remainder (5) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 4 \frac{5}{6} $.

Answer: $ 4 \frac{5}{6} $

#### 8) $\frac{74}{9}$
- Step 1: Divide the numerator (74) by the denominator (9).
- $ 74 \div 9 = 8 $ remainder $ 2 $.
- Step 2: Write the result as a mixed number.
- The quotient (8) becomes the whole number, and the remainder (2) becomes the numerator of the fractional part. The denominator remains the same.
- Mixed number: $ 8 \frac{2}{9} $.

Answer: $ 8 \frac{2}{9} $

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Part B: Rewrite each mixed number as an improper fraction.

#### 1) $ 9 \frac{3}{10} $
- Step 1: Multiply the whole number (9) by the denominator (10).
- $ 9 \times 10 = 90 $.
- Step 2: Add the numerator (3) to the result.
- $ 90 + 3 = 93 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 93, and the denominator remains the same.
- Improper fraction: $ \frac{93}{10} $.

Answer: $ \frac{93}{10} $

#### 2) $ 7 \frac{1}{2} $
- Step 1: Multiply the whole number (7) by the denominator (2).
- $ 7 \times 2 = 14 $.
- Step 2: Add the numerator (1) to the result.
- $ 14 + 1 = 15 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 15, and the denominator remains the same.
- Improper fraction: $ \frac{15}{2} $.

Answer: $ \frac{15}{2} $

#### 3) $ 1 \frac{1}{6} $
- Step 1: Multiply the whole number (1) by the denominator (6).
- $ 1 \times 6 = 6 $.
- Step 2: Add the numerator (1) to the result.
- $ 6 + 1 = 7 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 7, and the denominator remains the same.
- Improper fraction: $ \frac{7}{6} $.

Answer: $ \frac{7}{6} $

#### 4) $ 2 \frac{6}{11} $
- Step 1: Multiply the whole number (2) by the denominator (11).
- $ 2 \times 11 = 22 $.
- Step 2: Add the numerator (6) to the result.
- $ 22 + 6 = 28 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 28, and the denominator remains the same.
- Improper fraction: $ \frac{28}{11} $.

Answer: $ \frac{28}{11} $

#### 5) $ 4 \frac{5}{8} $
- Step 1: Multiply the whole number (4) by the denominator (8).
- $ 4 \times 8 = 32 $.
- Step 2: Add the numerator (5) to the result.
- $ 32 + 5 = 37 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 37, and the denominator remains the same.
- Improper fraction: $ \frac{37}{8} $.

Answer: $ \frac{37}{8} $

#### 6) $ 1 \frac{3}{5} $
- Step 1: Multiply the whole number (1) by the denominator (5).
- $ 1 \times 5 = 5 $.
- Step 2: Add the numerator (3) to the result.
- $ 5 + 3 = 8 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 8, and the denominator remains the same.
- Improper fraction: $ \frac{8}{5} $.

Answer: $ \frac{8}{5} $

#### 7) $ 6 \frac{2}{7} $
- Step 1: Multiply the whole number (6) by the denominator (7).
- $ 6 \times 7 = 42 $.
- Step 2: Add the numerator (2) to the result.
- $ 42 + 2 = 44 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 44, and the denominator remains the same.
- Improper fraction: $ \frac{44}{7} $.

Answer: $ \frac{44}{7} $

#### 8) $ 5 \frac{8}{9} $
- Step 1: Multiply the whole number (5) by the denominator (9).
- $ 5 \times 9 = 45 $.
- Step 2: Add the numerator (8) to the result.
- $ 45 + 8 = 53 $.
- Step 3: Write the result as an improper fraction.
- The new numerator is 53, and the denominator remains the same.
- Improper fraction: $ \frac{53}{9} $.

Answer: $ \frac{53}{9} $

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Final Answers:

#### Part A:
1. $ 1 \frac{4}{5} $
2. $ 4 \frac{5}{12} $
3. $ 3 \frac{1}{3} $
4. $ 1 \frac{1}{7} $
5. $ 5 \frac{10}{11} $
6. $ 7 \frac{3}{4} $
7. $ 4 \frac{5}{6} $
8. $ 8 \frac{2}{9} $

#### Part B:
1. $ \frac{93}{10} $
2. $ \frac{15}{2} $
3. $ \frac{7}{6} $
4. $ \frac{28}{11} $
5. $ \frac{37}{8} $
6. $ \frac{8}{5} $
7. $ \frac{44}{7} $
8. $ \frac{53}{9} $

Boxed Final Answer:

$$
\boxed{
\begin{array}{ll}
\text{Part A:} & 1) \, 1 \frac{4}{5}, \, 2) \, 4 \frac{5}{12}, \, 3) \, 3 \frac{1}{3}, \, 4) \, 1 \frac{1}{7}, \, 5) \, 5 \frac{10}{11}, \, 6) \, 7 \frac{3}{4}, \, 7) \, 4 \frac{5}{6}, \, 8) \, 8 \frac{2}{9} \\
\text{Part B:} & 1) \, \frac{93}{10}, \, 2) \, \frac{15}{2}, \, 3) \, \frac{7}{6}, \, 4) \, \frac{28}{11}, \, 5) \, \frac{37}{8}, \, 6) \, \frac{8}{5}, \, 7) \, \frac{44}{7}, \, 8) \, \frac{53}{9}
\end{array}
}
$$