Worksheet for multiplying mixed fractions with step-by-step examples and practice problems.

The image shows a worksheet titled "Multiplying Mixed Fractions Sheet 6." The task involves multiplying mixed fractions and expressing the answers in simplest form. Below, I will solve each problem step by step.

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Problem 1:

$$
2 \frac{3}{4} \times \frac{5}{8}
$$

#### Step 1: Convert the mixed fraction to an improper fraction.
$$
2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}
$$

#### Step 2: Multiply the improper fraction by the given fraction.
$$
\frac{11}{4} \times \frac{5}{8} = \frac{11 \times 5}{4 \times 8} = \frac{55}{32}
$$

#### Step 3: Simplify the result (if possible).
The fraction $\frac{55}{32}$ is already in simplest form. Since it is an improper fraction, convert it back to a mixed number:
$$
\frac{55}{32} = 1 \frac{23}{32}
$$

#### Final Answer:
$$
\boxed{1 \frac{23}{32}}
$$

---

Problem 2:

$$
\frac{7}{9} \times 2 \frac{1}{3}
$$

#### Step 1: Convert the mixed fraction to an improper fraction.
$$
2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}
$$

#### Step 2: Multiply the fractions.
$$
\frac{7}{9} \times \frac{7}{3} = \frac{7 \times 7}{9 \times 3} = \frac{49}{27}
$$

#### Step 3: Simplify the result (if possible).
The fraction $\frac{49}{27}$ is already in simplest form. Convert it to a mixed number:
$$
\frac{49}{27} = 1 \frac{22}{27}
$$

#### Final Answer:
$$
\boxed{1 \frac{22}{27}}
$$

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Problem 3:

$$
1 \frac{2}{5} \times \frac{10}{11}
$$

#### Step 1: Convert the mixed fraction to an improper fraction.
$$
1 \frac{2}{5} = 1 + \frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5}
$$

#### Step 2: Multiply the fractions.
$$
\frac{7}{5} \times \frac{10}{11} = \frac{7 \times 10}{5 \times 11} = \frac{70}{55}
$$

#### Step 3: Simplify the result.
Both 70 and 55 are divisible by 5:
$$
\frac{70}{55} = \frac{70 \div 5}{55 \div 5} = \frac{14}{11}
$$

Convert to a mixed number:
$$
\frac{14}{11} = 1 \frac{3}{11}
$$

#### Final Answer:
$$
\boxed{1 \frac{3}{11}}
$$

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Problem 4:

$$
1 \frac{1}{2} \times 1 \frac{1}{2}
$$

#### Step 1: Convert both mixed fractions to improper fractions.
$$
1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
$$

#### Step 2: Multiply the fractions.
$$
\frac{3}{2} \times \frac{3}{2} = \frac{3 \times 3}{2 \times 2} = \frac{9}{4}
$$

#### Step 3: Simplify the result (if possible).
The fraction $\frac{9}{4}$ is already in simplest form. Convert it to a mixed number:
$$
\frac{9}{4} = 2 \frac{1}{4}
$$

#### Final Answer:
$$
\boxed{2 \frac{1}{4}}
$$

---

Problem 5:

$$
7 \frac{1}{2} \times 1 \frac{1}{3}
$$

#### Step 1: Convert both mixed fractions to improper fractions.
$$
7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2}
$$
$$
1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}
$$

#### Step 2: Multiply the fractions.
$$
\frac{15}{2} \times \frac{4}{3} = \frac{15 \times 4}{2 \times 3} = \frac{60}{6}
$$

#### Step 3: Simplify the result.
$$
\frac{60}{6} = 10
$$

#### Final Answer:
$$
\boxed{10}
$$

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Problem 6:

$$
1 \frac{1}{3} \times 1 \frac{1}{3}
$$

#### Step 1: Convert the mixed fraction to an improper fraction.
$$
1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3}
$$

#### Step 2: Multiply the fractions.
$$
\frac{4}{3} \times \frac{4}{3} = \frac{4 \times 4}{3 \times 3} = \frac{16}{9}
$$

#### Step 3: Simplify the result (if possible).
The fraction $\frac{16}{9}$ is already in simplest form. Convert it to a mixed number:
$$
\frac{16}{9} = 1 \frac{7}{9}
$$

#### Final Answer:
$$
\boxed{1 \frac{7}{9}}
$$

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Final Answers:

1. $\boxed{1 \frac{23}{32}}$
2. $\boxed{1 \frac{22}{27}}$
3. $\boxed{1 \frac{3}{11}}$
4. $\boxed{2 \frac{1}{4}}$
5. $\boxed{10}$
6. $\boxed{1 \frac{7}{9}}$