? Converting between Mixed Number and Improper Fractions - Free Printable

Problem Description:

The task involves converting mixed numbers to improper fractions and vice versa. The right-hand page provides instructions on how to perform these conversions, while the left-hand page contains exercises for practice.

Solution Explanation:

#### Converting a Mixed Number to an Improper Fraction:
1. Step 1: Multiply the whole number by the denominator.
2. Step 2: Add the result to the numerator.
3. Step 3: Write the sum as the new numerator, keeping the original denominator.

#### Converting an Improper Fraction to a Mixed Number:
1. Step 1: Divide the numerator by the denominator.
2. Step 2: Write down the quotient as the whole number.
3. Step 3: Write the remainder as the numerator of the new fraction, with the original denominator.

Exercise Solutions:

#### Part 1: Convert each mixed number to an improper fraction.

1. \( 2 \frac{1}{4} \)
- Step 1: Multiply the whole number (2) by the denominator (4): \( 2 \times 4 = 8 \).
- Step 2: Add the numerator (1) to the result: \( 8 + 1 = 9 \).
- Step 3: Write the new fraction: \( \frac{9}{4} \).
- Answer: \( \frac{9}{4} \)

2. \( 1 \frac{3}{5} \)
- 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 new fraction: \( \frac{8}{5} \).
- Answer: \( \frac{8}{5} \)

3. \( 3 \frac{2}{7} \)
- Step 1: Multiply the whole number (3) by the denominator (7): \( 3 \times 7 = 21 \).
- Step 2: Add the numerator (2) to the result: \( 21 + 2 = 23 \).
- Step 3: Write the new fraction: \( \frac{23}{7} \).
- Answer: \( \frac{23}{7} \)

4. \( 4 \frac{1}{6} \)
- Step 1: Multiply the whole number (4) by the denominator (6): \( 4 \times 6 = 24 \).
- Step 2: Add the numerator (1) to the result: \( 24 + 1 = 25 \).
- Step 3: Write the new fraction: \( \frac{25}{6} \).
- Answer: \( \frac{25}{6} \)

#### Part 2: Convert each fraction to a mixed number.

5. \( \frac{11}{3} \)
- Step 1: Divide the numerator (11) by the denominator (3): \( 11 \div 3 = 3 \) remainder \( 2 \).
- Step 2: Write the quotient (3) as the whole number.
- Step 3: Write the remainder (2) as the numerator of the new fraction, with the original denominator (3).
- Answer: \( 3 \frac{2}{3} \)

6. \( \frac{17}{4} \)
- Step 1: Divide the numerator (17) by the denominator (4): \( 17 \div 4 = 4 \) remainder \( 1 \).
- Step 2: Write the quotient (4) as the whole number.
- Step 3: Write the remainder (1) as the numerator of the new fraction, with the original denominator (4).
- Answer: \( 4 \frac{1}{4} \)

7. \( \frac{20}{7} \)
- Step 1: Divide the numerator (20) by the denominator (7): \( 20 \div 7 = 2 \) remainder \( 6 \).
- Step 2: Write the quotient (2) as the whole number.
- Step 3: Write the remainder (6) as the numerator of the new fraction, with the original denominator (7).
- Answer: \( 2 \frac{6}{7} \)

8. \( \frac{29}{8} \)
- Step 1: Divide the numerator (29) by the denominator (8): \( 29 \div 8 = 3 \) remainder \( 5 \).
- Step 2: Write the quotient (3) as the whole number.
- Step 3: Write the remainder (5) as the numerator of the new fraction, with the original denominator (8).
- Answer: \( 3 \frac{5}{8} \)

Final Answers:

1. \( \frac{9}{4} \)
2. \( \frac{8}{5} \)
3. \( \frac{23}{7} \)
4. \( \frac{25}{6} \)
5. \( 3 \frac{2}{3} \)
6. \( 4 \frac{1}{4} \)
7. \( 2 \frac{6}{7} \)
8. \( 3 \frac{5}{8} \)

\[
\boxed{
\begin{array}{l}
1. \frac{9}{4} \\
2. \frac{8}{5} \\
3. \frac{23}{7} \\
4. \frac{25}{6} \\
5. 3 \frac{2}{3} \\
6. 4 \frac{1}{4} \\
7. 2 \frac{6}{7} \\
8. 3 \frac{5}{8}
\end{array}
}
\]