Set of eight multiplication problems involving mixed numbers for students to solve.

Let’s solve each problem step by step.

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Problem 1: $4 \frac{2}{5} \times 2 \frac{1}{2}$

Step 1: Convert to improper fractions.
$4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{22}{5}$
$2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$

Step 2: Multiply the fractions.
$\frac{22}{5} \times \frac{5}{2} = \frac{22 \times 5}{5 \times 2}$

Step 3: Cancel common factors.
The 5 in numerator and denominator cancels out.
$\frac{22}{1} \times \frac{1}{2} = \frac{22}{2} = 11$

✔ Answer: 11

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

Step 1: Convert to improper fractions.
$2 \frac{1}{4} = \frac{9}{4}$
$3 \frac{1}{3} = \frac{10}{3}$

Step 2: Multiply.
$\frac{9}{4} \times \frac{10}{3} = \frac{90}{12}$

Step 3: Simplify.
Divide numerator and denominator by 6:
$\frac{90 ÷ 6}{12 ÷ 6} = \frac{15}{2} = 7 \frac{1}{2}$

✔ Answer: 7½

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

Step 1: Convert.
$4 \frac{2}{5} = \frac{22}{5}$
$4 \frac{3}{4} = \frac{19}{4}$

Step 2: Multiply.
$\frac{22}{5} \times \frac{19}{4} = \frac{418}{20}$

Step 3: Simplify.
Divide numerator and denominator by 2:
$\frac{209}{10} = 20 \frac{9}{10}$

✔ Answer: 20⁹⁄₁₀

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

Step 1: Convert.
$4 \frac{1}{3} = \frac{13}{3}$
$2 \frac{1}{2} = \frac{5}{2}$

Step 2: Multiply.
$\frac{13}{3} \times \frac{5}{2} = \frac{65}{6}$

Step 3: Convert to mixed number.
$65 ÷ 6 = 10$ remainder 5 → $10 \frac{5}{6}$

✔ Answer: 10⁵⁄₆

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

Step 1: Convert.
$2 \frac{2}{5} = \frac{12}{5}$
$3 \frac{1}{3} = \frac{10}{3}$

Step 2: Multiply.
$\frac{12}{5} \times \frac{10}{3} = \frac{120}{15}$

Step 3: Simplify.
$120 ÷ 15 = 8$

✔ Answer: 8

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Problem 6: $2 \frac{1}{2} \times 2 \frac{2}{3}$

Step 1: Convert.
$2 \frac{1}{2} = \frac{5}{2}$
$2 \frac{2}{3} = \frac{8}{3}$

Step 2: Multiply.
$\frac{5}{2} \times \frac{8}{3} = \frac{40}{6}$

Step 3: Simplify.
Divide by 2: $\frac{20}{3} = 6 \frac{2}{3}$

✔ Answer: 6⅔

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Problem 7: $2 \frac{2}{5} \times 2 \frac{1}{3}$

Step 1: Convert.
$2 \frac{2}{5} = \frac{12}{5}$
$2 \frac{1}{3} = \frac{7}{3}$

Step 2: Multiply.
$\frac{12}{5} \times \frac{7}{3} = \frac{84}{15}$

Step 3: Simplify.
Divide by 3: $\frac{28}{5} = 5 \frac{3}{5}$

✔ Answer: 5⅗

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Problem 8: $4 \frac{3}{4} \times 4 \frac{2}{3}$

Step 1: Convert.
$4 \frac{3}{4} = \frac{19}{4}$
$4 \frac{2}{3} = \frac{14}{3}$

Step 2: Multiply.
$\frac{19}{4} \times \frac{14}{3} = \frac{266}{12}$

Step 3: Simplify.
Divide numerator and denominator by 2: $\frac{133}{6}$

Convert to mixed number:
$133 ÷ 6 = 22$ remainder 1 → $22 \frac{1}{6}$

✔ Answer: 22⅙

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Final Answer:
11, 7½, 20⁹⁄₁₀, 10⁵⁄₆, 8, 6⅔, 5⅗, 22⅙