Convert mixed numbers to improper fractions with this math worksheet.

To solve the problem of converting mixed numbers to improper fractions, we follow a systematic approach. Here's how it works:

Steps to Convert a Mixed Number to an Improper Fraction:

1. Multiply the whole number part by the denominator of the fractional part.
2. Add the result to the numerator of the fractional part.
3. Write the sum as the new numerator, keeping the original denominator.

Let's solve each problem step by step.

---

Problem 1: $ 2 \frac{2}{3} $

- Whole number: $ 2 $
- Fraction: $ \frac{2}{3} $
- Denominator: $ 3 $

#### Step 1: Multiply the whole number by the denominator.
$$
2 \times 3 = 6
$$

#### Step 2: Add the result to the numerator.
$$
6 + 2 = 8
$$

#### Step 3: Write the new fraction.
$$
\frac{8}{3}
$$

Answer: $ \frac{8}{3} $

---

Problem 2: $ 3 \frac{1}{4} $

- Whole number: $ 3 $
- Fraction: $ \frac{1}{4} $
- Denominator: $ 4 $

#### Step 1: Multiply the whole number by the denominator.
$$
3 \times 4 = 12
$$

#### Step 2: Add the result to the numerator.
$$
12 + 1 = 13
$$

#### Step 3: Write the new fraction.
$$
\frac{13}{4}
$$

Answer: $ \frac{13}{4} $

---

Problem 3: $ 4 \frac{2}{5} $

- Whole number: $ 4 $
- Fraction: $ \frac{2}{5} $
- Denominator: $ 5 $

#### Step 1: Multiply the whole number by the denominator.
$$
4 \times 5 = 20
$$

#### Step 2: Add the result to the numerator.
$$
20 + 2 = 22
$$

#### Step 3: Write the new fraction.
$$
\frac{22}{5}
$$

Answer: $ \frac{22}{5} $

---

Problem 4: $ 2 \frac{3}{5} $

- Whole number: $ 2 $
- Fraction: $ \frac{3}{5} $
- Denominator: $ 5 $

#### Step 1: Multiply the whole number by the denominator.
$$
2 \times 5 = 10
$$

#### Step 2: Add the result to the numerator.
$$
10 + 3 = 13
$$

#### Step 3: Write the new fraction.
$$
\frac{13}{5}
$$

Answer: $ \frac{13}{5} $

---

Problem 5: $ 1 \frac{3}{2} $

- Whole number: $ 1 $
- Fraction: $ \frac{3}{2} $
- Denominator: $ 2 $

#### Step 1: Multiply the whole number by the denominator.
$$
1 \times 2 = 2
$$

#### Step 2: Add the result to the numerator.
$$
2 + 3 = 5
$$

#### Step 3: Write the new fraction.
$$
\frac{5}{2}
$$

Answer: $ \frac{5}{2} $

---

Problem 6: $ 3 \frac{3}{4} $

- Whole number: $ 3 $
- Fraction: $ \frac{3}{4} $
- Denominator: $ 4 $

#### Step 1: Multiply the whole number by the denominator.
$$
3 \times 4 = 12
$$

#### Step 2: Add the result to the numerator.
$$
12 + 3 = 15
$$

#### Step 3: Write the new fraction.
$$
\frac{15}{4}
$$

Answer: $ \frac{15}{4} $

---

Problem 7: $ 1 \frac{2}{4} $

- Whole number: $ 1 $
- Fraction: $ \frac{2}{4} $
- Denominator: $ 4 $

#### Step 1: Multiply the whole number by the denominator.
$$
1 \times 4 = 4
$$

#### Step 2: Add the result to the numerator.
$$
4 + 2 = 6
$$

#### Step 3: Write the new fraction.
$$
\frac{6}{4}
$$

Simplify the fraction (if possible):
$$
\frac{6}{4} = \frac{3}{2}
$$

Answer: $ \frac{3}{2} $

---

Problem 8: $ 3 \frac{4}{7} $

- Whole number: $ 3 $
- Fraction: $ \frac{4}{7} $
- Denominator: $ 7 $

#### Step 1: Multiply the whole number by the denominator.
$$
3 \times 7 = 21
$$

#### Step 2: Add the result to the numerator.
$$
21 + 4 = 25
$$

#### Step 3: Write the new fraction.
$$
\frac{25}{7}
$$

Answer: $ \frac{25}{7} $

---

Problem 9: $ 2 \frac{5}{7} $

- Whole number: $ 2 $
- Fraction: $ \frac{5}{7} $
- Denominator: $ 7 $

#### Step 1: Multiply the whole number by the denominator.
$$
2 \times 7 = 14
$$

#### Step 2: Add the result to the numerator.
$$
14 + 5 = 19
$$

#### Step 3: Write the new fraction.
$$
\frac{19}{7}
$$

Answer: $ \frac{19}{7} $

---

Problem 10: $ 1 \frac{3}{6} $

- Whole number: $ 1 $
- Fraction: $ \frac{3}{6} $
- Denominator: $ 6 $

#### Step 1: Multiply the whole number by the denominator.
$$
1 \times 6 = 6
$$

#### Step 2: Add the result to the numerator.
$$
6 + 3 = 9
$$

#### Step 3: Write the new fraction.
$$
\frac{9}{6}
$$

Simplify the fraction (if possible):
$$
\frac{9}{6} = \frac{3}{2}
$$

Answer: $ \frac{3}{2} $

---

Final Answers:

1. $ \frac{8}{3} $
2. $ \frac{13}{4} $
3. $ \frac{22}{5} $
4. $ \frac{13}{5} $
5. $ \frac{5}{2} $
6. $ \frac{15}{4} $
7. $ \frac{3}{2} $
8. $ \frac{25}{7} $
9. $ \frac{19}{7} $
10. $ \frac{3}{2} $

$$
\boxed{\frac{8}{3}, \frac{13}{4}, \frac{22}{5}, \frac{13}{5}, \frac{5}{2}, \frac{15}{4}, \frac{3}{2}, \frac{25}{7}, \frac{19}{7}, \frac{3}{2}}
$$