Practice worksheet for multiplying mixed fractions with step-by-step problems.

To solve the problem of multiplying mixed fractions, we need to follow these steps:

Steps to Multiply Mixed Fractions:

1. Convert Mixed Fractions to Improper Fractions:
- A mixed fraction is of the form \( a \frac{b}{c} \), where \( a \) is the whole number, and \( \frac{b}{c} \) is the fractional part.
- To convert it to an improper fraction, use the formula:
\[
\text{Improper Fraction} = \frac{(a \times c) + b}{c}
\]

2. Multiply the Improper Fractions:
- Multiply the numerators together to get the new numerator.
- Multiply the denominators together to get the new denominator.

3. Simplify the Result:
- Simplify the resulting fraction if possible.
- If the result is an improper fraction, convert it back to a mixed fraction by dividing the numerator by the denominator.

Let's solve each problem step by step.

---

Problem 1: \( 1 \frac{1}{3} \times 4 \frac{3}{5} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 1 \frac{1}{3} \):
\[
1 \frac{1}{3} = \frac{(1 \times 3) + 1}{3} = \frac{4}{3}
\]
- For \( 4 \frac{3}{5} \):
\[
4 \frac{3}{5} = \frac{(4 \times 5) + 3}{5} = \frac{23}{5}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{4}{3} \times \frac{23}{5} = \frac{4 \times 23}{3 \times 5} = \frac{92}{15}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- The fraction \( \frac{92}{15} \) is already in simplest form.
- Convert to a mixed fraction:
\[
92 \div 15 = 6 \text{ remainder } 2 \quad \Rightarrow \quad 6 \frac{2}{15}
\]

Answer: \( 6 \frac{2}{15} \)

---

Problem 2: \( 6 \frac{5}{8} \times 3 \frac{7}{8} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 6 \frac{5}{8} \):
\[
6 \frac{5}{8} = \frac{(6 \times 8) + 5}{8} = \frac{53}{8}
\]
- For \( 3 \frac{7}{8} \):
\[
3 \frac{7}{8} = \frac{(3 \times 8) + 7}{8} = \frac{31}{8}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{53}{8} \times \frac{31}{8} = \frac{53 \times 31}{8 \times 8} = \frac{1643}{64}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- The fraction \( \frac{1643}{64} \) is already in simplest form.
- Convert to a mixed fraction:
\[
1643 \div 64 = 25 \text{ remainder } 43 \quad \Rightarrow \quad 25 \frac{43}{64}
\]

Answer: \( 25 \frac{43}{64} \)

---

Problem 3: \( 9 \frac{2}{7} \times 1 \frac{1}{2} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 9 \frac{2}{7} \):
\[
9 \frac{2}{7} = \frac{(9 \times 7) + 2}{7} = \frac{65}{7}
\]
- For \( 1 \frac{1}{2} \):
\[
1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{65}{7} \times \frac{3}{2} = \frac{65 \times 3}{7 \times 2} = \frac{195}{14}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- The fraction \( \frac{195}{14} \) is already in simplest form.
- Convert to a mixed fraction:
\[
195 \div 14 = 13 \text{ remainder } 13 \quad \Rightarrow \quad 13 \frac{13}{14}
\]

Answer: \( 13 \frac{13}{14} \)

---

Problem 4: \( 3 \frac{2}{5} \times 8 \frac{1}{3} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 3 \frac{2}{5} \):
\[
3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{17}{5}
\]
- For \( 8 \frac{1}{3} \):
\[
8 \frac{1}{3} = \frac{(8 \times 3) + 1}{3} = \frac{25}{3}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{17}{5} \times \frac{25}{3} = \frac{17 \times 25}{5 \times 3} = \frac{425}{15}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- Simplify \( \frac{425}{15} \):
\[
\frac{425}{15} = \frac{85}{3} \quad (\text{divide numerator and denominator by } 5)
\]
- Convert to a mixed fraction:
\[
85 \div 3 = 28 \text{ remainder } 1 \quad \Rightarrow \quad 28 \frac{1}{3}
\]

Answer: \( 28 \frac{1}{3} \)

---

Problem 5: \( 6 \frac{2}{3} \times 6 \frac{1}{9} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 6 \frac{2}{3} \):
\[
6 \frac{2}{3} = \frac{(6 \times 3) + 2}{3} = \frac{20}{3}
\]
- For \( 6 \frac{1}{9} \):
\[
6 \frac{1}{9} = \frac{(6 \times 9) + 1}{9} = \frac{55}{9}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{20}{3} \times \frac{55}{9} = \frac{20 \times 55}{3 \times 9} = \frac{1100}{27}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- The fraction \( \frac{1100}{27} \) is already in simplest form.
- Convert to a mixed fraction:
\[
1100 \div 27 = 40 \text{ remainder } 20 \quad \Rightarrow \quad 40 \frac{20}{27}
\]

Answer: \( 40 \frac{20}{27} \)

---

Problem 6: \( 4 \frac{1}{5} \times 9 \frac{1}{2} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 4 \frac{1}{5} \):
\[
4 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{21}{5}
\]
- For \( 9 \frac{1}{2} \):
\[
9 \frac{1}{2} = \frac{(9 \times 2) + 1}{2} = \frac{19}{2}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{21}{5} \times \frac{19}{2} = \frac{21 \times 19}{5 \times 2} = \frac{399}{10}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- The fraction \( \frac{399}{10} \) is already in simplest form.
- Convert to a mixed fraction:
\[
399 \div 10 = 39 \text{ remainder } 9 \quad \Rightarrow \quad 39 \frac{9}{10}
\]

Answer: \( 39 \frac{9}{10} \)

---

Problem 7: \( 1 \frac{1}{4} \times 9 \frac{1}{3} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 1 \frac{1}{4} \):
\[
1 \frac{1}{4} = \frac{(1 \times 4) + 1}{4} = \frac{5}{4}
\]
- For \( 9 \frac{1}{3} \):
\[
9 \frac{1}{3} = \frac{(9 \times 3) + 1}{3} = \frac{28}{3}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{5}{4} \times \frac{28}{3} = \frac{5 \times 28}{4 \times 3} = \frac{140}{12}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- Simplify \( \frac{140}{12} \):
\[
\frac{140}{12} = \frac{35}{3} \quad (\text{divide numerator and denominator by } 4)
\]
- Convert to a mixed fraction:
\[
35 \div 3 = 11 \text{ remainder } 2 \quad \Rightarrow \quad 11 \frac{2}{3}
\]

Answer: \( 11 \frac{2}{3} \)

---

Problem 8: \( 1 \frac{3}{4} \times 5 \frac{1}{5} \)

#### Step 1: Convert Mixed Fractions to Improper Fractions
- For \( 1 \frac{3}{4} \):
\[
1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{7}{4}
\]
- For \( 5 \frac{1}{5} \):
\[
5 \frac{1}{5} = \frac{(5 \times 5) + 1}{5} = \frac{26}{5}
\]

#### Step 2: Multiply the Improper Fractions
\[
\frac{7}{4} \times \frac{26}{5} = \frac{7 \times 26}{4 \times 5} = \frac{182}{20}
\]

#### Step 3: Simplify and Convert to Mixed Fraction
- Simplify \( \frac{182}{20} \):
\[
\frac{182}{20} = \frac{91}{10} \quad (\text{divide numerator and denominator by } 2)
\]
- Convert to a mixed fraction:
\[
91 \div 10 = 9 \text{ remainder } 1 \quad \Rightarrow \quad 9 \frac{1}{10}
\]

Answer: \( 9 \frac{1}{10} \)

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 6 \frac{2}{15} \\
2. & \ 25 \frac{43}{64} \\
3. & \ 13 \frac{13}{14} \\
4. & \ 28 \frac{1}{3} \\
5. & \ 40 \frac{20}{27} \\
6. & \ 39 \frac{9}{10} \\
7. & \ 11 \frac{2}{3} \\
8. & \ 9 \frac{1}{10}
\end{aligned}
}
\]