Multiplying Mixed Fractions Worksheet - Practice multiplying mixed numbers with step-by-step examples.

Problem: Multiplying Mixed Fractions

The task is to multiply the given mixed fractions and express the answers as improper fractions in their simplest form. Let's solve each problem step by step.

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#### Step 1: Convert Mixed Fractions to Improper Fractions
To multiply mixed fractions, first convert them into improper fractions. The formula to convert a mixed fraction \( a \frac{b}{c} \) to an improper fraction is:
\[
a \frac{b}{c} = \frac{(a \times c) + b}{c}
\]

#### Step 2: Multiply the Fractions
Once both fractions are in improper form, multiply the numerators together and the denominators together:
\[
\frac{p}{q} \times \frac{r}{s} = \frac{p \times r}{q \times s}
\]

#### Step 3: Simplify the Result
Simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

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Solutions

#### 1. \( 2 \frac{1}{2} \times \frac{4}{5} \)

1. Convert \( 2 \frac{1}{2} \) to an improper fraction:
\[
2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{2}
\]

2. Multiply the fractions:
\[
\frac{5}{2} \times \frac{4}{5} = \frac{5 \times 4}{2 \times 5} = \frac{20}{10}
\]

3. Simplify the result:
\[
\frac{20}{10} = 2
\]

Answer: \( \boxed{\frac{20}{10}} \) or \( \boxed{2} \)

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#### 2. \( 1 \frac{3}{4} \times \frac{3}{5} \)

1. Convert \( 1 \frac{3}{4} \) to an improper fraction:
\[
1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{7}{4}
\]

2. Multiply the fractions:
\[
\frac{7}{4} \times \frac{3}{5} = \frac{7 \times 3}{4 \times 5} = \frac{21}{20}
\]

3. Simplify the result (already in simplest form):
\[
\frac{21}{20}
\]

Answer: \( \boxed{\frac{21}{20}} \)

---

#### 3. \( 4 \frac{1}{2} \times \frac{5}{6} \)

1. Convert \( 4 \frac{1}{2} \) to an improper fraction:
\[
4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{9}{2}
\]

2. Multiply the fractions:
\[
\frac{9}{2} \times \frac{5}{6} = \frac{9 \times 5}{2 \times 6} = \frac{45}{12}
\]

3. Simplify the result:
\[
\frac{45}{12} = \frac{15}{4} \quad (\text{dividing numerator and denominator by } 3)
\]

Answer: \( \boxed{\frac{45}{12}} \) or \( \boxed{\frac{15}{4}} \)

---

#### 4. \( 2 \frac{2}{7} \times 3 \)

1. Convert \( 2 \frac{2}{7} \) to an improper fraction:
\[
2 \frac{2}{7} = \frac{(2 \times 7) + 2}{7} = \frac{16}{7}
\]

2. Write \( 3 \) as a fraction:
\[
3 = \frac{3}{1}
\]

3. Multiply the fractions:
\[
\frac{16}{7} \times \frac{3}{1} = \frac{16 \times 3}{7 \times 1} = \frac{48}{7}
\]

4. Simplify the result (already in simplest form):
\[
\frac{48}{7}
\]

Answer: \( \boxed{\frac{48}{7}} \)

---

#### 5. \( \frac{2}{7} \times 3 \frac{1}{5} \)

1. Convert \( 3 \frac{1}{5} \) to an improper fraction:
\[
3 \frac{1}{5} = \frac{(3 \times 5) + 1}{5} = \frac{16}{5}
\]

2. Multiply the fractions:
\[
\frac{2}{7} \times \frac{16}{5} = \frac{2 \times 16}{7 \times 5} = \frac{32}{35}
\]

3. Simplify the result (already in simplest form):
\[
\frac{32}{35}
\]

Answer: \( \boxed{\frac{32}{35}} \)

---

#### 6. \( 8 \frac{1}{2} \times \frac{2}{11} \)

1. Convert \( 8 \frac{1}{2} \) to an improper fraction:
\[
8 \frac{1}{2} = \frac{(8 \times 2) + 1}{2} = \frac{17}{2}
\]

2. Multiply the fractions:
\[
\frac{17}{2} \times \frac{2}{11} = \frac{17 \times 2}{2 \times 11} = \frac{34}{22}
\]

3. Simplify the result:
\[
\frac{34}{22} = \frac{17}{11} \quad (\text{dividing numerator and denominator by } 2)
\]

Answer: \( \boxed{\frac{34}{22}} \) or \( \boxed{\frac{17}{11}} \)

---

#### 7. \( \frac{5}{12} \times 4 \frac{2}{3} \)

1. Convert \( 4 \frac{2}{3} \) to an improper fraction:
\[
4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{14}{3}
\]

2. Multiply the fractions:
\[
\frac{5}{12} \times \frac{14}{3} = \frac{5 \times 14}{12 \times 3} = \frac{70}{36}
\]

3. Simplify the result:
\[
\frac{70}{36} = \frac{35}{18} \quad (\text{dividing numerator and denominator by } 2)
\]

Answer: \( \boxed{\frac{70}{36}} \) or \( \boxed{\frac{35}{18}} \)

---

#### 8. \( 2 \frac{1}{5} \times 5 \frac{1}{2} \)

1. Convert \( 2 \frac{1}{5} \) to an improper fraction:
\[
2 \frac{1}{5} = \frac{(2 \times 5) + 1}{5} = \frac{11}{5}
\]

2. Convert \( 5 \frac{1}{2} \) to an improper fraction:
\[
5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{11}{2}
\]

3. Multiply the fractions:
\[
\frac{11}{5} \times \frac{11}{2} = \frac{11 \times 11}{5 \times 2} = \frac{121}{10}
\]

4. Simplify the result (already in simplest form):
\[
\frac{121}{10}
\]

Answer: \( \boxed{\frac{121}{10}} \)

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Final Answers

1. \( \boxed{\frac{20}{10}} \) or \( \boxed{2} \)
2. \( \boxed{\frac{21}{20}} \)
3. \( \boxed{\frac{45}{12}} \) or \( \boxed{\frac{15}{4}} \)
4. \( \boxed{\frac{48}{7}} \)
5. \( \boxed{\frac{32}{35}} \)
6. \( \boxed{\frac{34}{22}} \) or \( \boxed{\frac{17}{11}} \)
7. \( \boxed{\frac{70}{36}} \) or \( \boxed{\frac{35}{18}} \)
8. \( \boxed{\frac{121}{10}} \)

---

Boxed Final Answer:
\[
\boxed{
\begin{aligned}
1. & \ \frac{20}{10} \text{ or } 2 \\
2. & \ \frac{21}{20} \\
3. & \ \frac{45}{12} \text{ or } \frac{15}{4} \\
4. & \ \frac{48}{7} \\
5. & \ \frac{32}{35} \\
6. & \ \frac{34}{22} \text{ or } \frac{17}{11} \\
7. & \ \frac{70}{36} \text{ or } \frac{35}{18} \\
8. & \ \frac{121}{10} \\
\end{aligned}
}
\]