Multiplying Mixed Numbers worksheet with ten problems for practice.

Problem: Multiplying Mixed Numbers

The task involves multiplying mixed numbers. To solve these problems, we will follow these steps:
1. Convert each mixed number to an improper fraction.
2. Multiply the numerators together and the denominators together.
3. Simplify the resulting fraction if possible.
4. Convert the result back to a mixed number if necessary.

Let's solve each problem step by step.

---

Problem 1: \( 4 \frac{9}{10} \times 4 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{9}{10} = \frac{(4 \times 10) + 9}{10} = \frac{40 + 9}{10} = \frac{49}{10} \)
- \( 4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \)

#### Step 2: Multiply the fractions.
\[
\frac{49}{10} \times \frac{9}{2} = \frac{49 \times 9}{10 \times 2} = \frac{441}{20}
\]

#### Step 3: Convert the result to a mixed number.
- Divide 441 by 20: \( 441 \div 20 = 22 \) remainder \( 1 \).
- So, \( \frac{441}{20} = 22 \frac{1}{20} \).

#### Final Answer:
\[
\boxed{22 \frac{1}{20}}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)
- \( 3 \frac{3}{5} = \frac{(3 \times 5) + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5} \)

#### Step 2: Multiply the fractions.
\[
\frac{5}{2} \times \frac{18}{5} = \frac{5 \times 18}{2 \times 5} = \frac{90}{10} = 9
\]

#### Final Answer:
\[
\boxed{9}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)
- \( 4 \frac{1}{3} = \frac{(4 \times 3) + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \)

#### Step 2: Multiply the fractions.
\[
\frac{5}{2} \times \frac{13}{3} = \frac{5 \times 13}{2 \times 3} = \frac{65}{6}
\]

#### Step 3: Convert the result to a mixed number.
- Divide 65 by 6: \( 65 \div 6 = 10 \) remainder \( 5 \).
- So, \( \frac{65}{6} = 10 \frac{5}{6} \).

#### Final Answer:
\[
\boxed{10 \frac{5}{6}}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \)
- \( 3 \frac{2}{3} = \frac{(3 \times 3) + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3} \)

#### Step 2: Multiply the fractions.
\[
\frac{7}{2} \times \frac{11}{3} = \frac{7 \times 11}{2 \times 3} = \frac{77}{6}
\]

#### Step 3: Convert the result to a mixed number.
- Divide 77 by 6: \( 77 \div 6 = 12 \) remainder \( 5 \).
- So, \( \frac{77}{6} = 12 \frac{5}{6} \).

#### Final Answer:
\[
\boxed{12 \frac{5}{6}}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \)
- \( 2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \)

#### Step 2: Multiply the fractions.
\[
\frac{7}{2} \times \frac{8}{3} = \frac{7 \times 8}{2 \times 3} = \frac{56}{6}
\]

#### Step 3: Simplify the fraction.
- Simplify \( \frac{56}{6} \) by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{56 \div 2}{6 \div 2} = \frac{28}{3}
\]

#### Step 4: Convert the result to a mixed number.
- Divide 28 by 3: \( 28 \div 3 = 9 \) remainder \( 1 \).
- So, \( \frac{28}{3} = 9 \frac{1}{3} \).

#### Final Answer:
\[
\boxed{9 \frac{1}{3}}
\]

---

Problem 6: \( 2 \frac{7}{10} \times 4 \frac{3}{4} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{7}{10} = \frac{(2 \times 10) + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10} \)
- \( 4 \frac{3}{4} = \frac{(4 \times 4) + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \)

#### Step 2: Multiply the fractions.
\[
\frac{27}{10} \times \frac{19}{4} = \frac{27 \times 19}{10 \times 4} = \frac{513}{40}
\]

#### Step 3: Convert the result to a mixed number.
- Divide 513 by 40: \( 513 \div 40 = 12 \) remainder \( 33 \).
- So, \( \frac{513}{40} = 12 \frac{33}{40} \).

#### Final Answer:
\[
\boxed{12 \frac{33}{40}}
\]

---

Problem 7: \( 2 \frac{1}{2} \times 4 \frac{4}{5} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)
- \( 4 \frac{4}{5} = \frac{(4 \times 5) + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5} \)

#### Step 2: Multiply the fractions.
\[
\frac{5}{2} \times \frac{24}{5} = \frac{5 \times 24}{2 \times 5} = \frac{120}{10} = 12
\]

#### Final Answer:
\[
\boxed{12}
\]

---

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

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{4}{5} = \frac{(4 \times 5) + 4}{5} = \frac{20 + 4}{5} = \frac{24}{5} \)
- \( 4 \frac{1}{3} = \frac{(4 \times 3) + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \)

#### Step 2: Multiply the fractions.
\[
\frac{24}{5} \times \frac{13}{3} = \frac{24 \times 13}{5 \times 3} = \frac{312}{15}
\]

#### Step 3: Simplify the fraction.
- Simplify \( \frac{312}{15} \) by dividing numerator and denominator by their greatest common divisor (GCD), which is 3:
\[
\frac{312 \div 3}{15 \div 3} = \frac{104}{5}
\]

#### Step 4: Convert the result to a mixed number.
- Divide 104 by 5: \( 104 \div 5 = 20 \) remainder \( 4 \).
- So, \( \frac{104}{5} = 20 \frac{4}{5} \).

#### Final Answer:
\[
\boxed{20 \frac{4}{5}}
\]

---

Problem 9: \( 4 \frac{1}{2} \times 3 \frac{1}{5} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2} \)
- \( 3 \frac{1}{5} = \frac{(3 \times 5) + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5} \)

#### Step 2: Multiply the fractions.
\[
\frac{9}{2} \times \frac{16}{5} = \frac{9 \times 16}{2 \times 5} = \frac{144}{10}
\]

#### Step 3: Simplify the fraction.
- Simplify \( \frac{144}{10} \) by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{144 \div 2}{10 \div 2} = \frac{72}{5}
\]

#### Step 4: Convert the result to a mixed number.
- Divide 72 by 5: \( 72 \div 5 = 14 \) remainder \( 2 \).
- So, \( \frac{72}{5} = 14 \frac{2}{5} \).

#### Final Answer:
\[
\boxed{14 \frac{2}{5}}
\]

---

Problem 10: \( 2 \frac{1}{2} \times 2 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions.
- \( 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \)
- \( 2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \)

#### Step 2: Multiply the fractions.
\[
\frac{5}{2} \times \frac{9}{4} = \frac{5 \times 9}{2 \times 4} = \frac{45}{8}
\]

#### Step 3: Convert the result to a mixed number.
- Divide 45 by 8: \( 45 \div 8 = 5 \) remainder \( 5 \).
- So, \( \frac{45}{8} = 5 \frac{5}{8} \).

#### Final Answer:
\[
\boxed{5 \frac{5}{8}}
\]

---

Final Answers:

1. \( \boxed{22 \frac{1}{20}} \)
2. \( \boxed{9} \)
3. \( \boxed{10 \frac{5}{6}} \)
4. \( \boxed{12 \frac{5}{6}} \)
5. \( \boxed{9 \frac{1}{3}} \)
6. \( \boxed{12 \frac{33}{40}} \)
7. \( \boxed{12} \)
8. \( \boxed{20 \frac{4}{5}} \)
9. \( \boxed{14 \frac{2}{5}} \)
10. \( \boxed{5 \frac{5}{8}} \)