Multiply Mixed Numbers Worksheet (examples, answers, videos ... - Free Printable

Let's solve each problem step by step. The goal is to convert mixed numbers to improper fractions, multiply them, and simplify using cancellation when possible.

---

🔹 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{20 + 2}{5} = \frac{22}{5} $
- $ 2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} $

Step 2: Multiply
$$
\frac{22}{5} \times \frac{5}{2}
$$

Step 3: Cancel common factors
- 5 in numerator and denominator cancels:
$$
\frac{22}{\cancel{5}} \times \frac{\cancel{5}}{2} = \frac{22}{2} = 11
$$

✔ Answer: $ 11 $

---

🔹 2. $ 2\frac{1}{4} \times 3\frac{1}{3} $

Convert:
- $ 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4} $
- $ 3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3} $

Multiply:
$$
\frac{9}{4} \times \frac{10}{3}
$$

Cancel:
- 9 and 3 → $ \frac{9}{3} = 3 $, so $ \frac{3}{1} $
- 10 and 4 → both divisible by 2 → $ \frac{5}{2} $

So:
$$
\frac{9}{4} \times \frac{10}{3} = \frac{3}{2} \times \frac{5}{1} = \frac{15}{2}
$$

Convert to mixed number: $ \frac{15}{2} = 7\frac{1}{2} $

✔ Answer: $ 7\frac{1}{2} $

---

🔹 3. $ 4\frac{2}{5} \times 4\frac{3}{4} $

Convert:
- $ 4\frac{2}{5} = \frac{22}{5} $ (from earlier)
- $ 4\frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{19}{4} $

Multiply:
$$
\frac{22}{5} \times \frac{19}{4}
$$

No common factors to cancel.

$$
= \frac{22 \times 19}{5 \times 4} = \frac{418}{20}
$$

Simplify:
- Divide numerator and denominator by 2: $ \frac{209}{10} $

Convert to mixed number: $ 20\frac{9}{10} $

✔ Answer: $ 20\frac{9}{10} $

---

🔹 4. $ 4\frac{1}{3} \times 2\frac{1}{2} $

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

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

Convert to mixed number: $ 10\frac{5}{6} $

✔ Answer: $ 10\frac{5}{6} $

---

🔹 5. $ 2\frac{2}{5} \times 3\frac{1}{3} $

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

Multiply:
$$
\frac{12}{5} \times \frac{10}{3}
$$

Cancel:
- 12 and 3 → $ \frac{12}{3} = 4 $, so $ \frac{4}{1} $
- 10 and 5 → $ \frac{10}{5} = 2 $, so $ \frac{2}{1} $

So:
$$
\frac{4}{1} \times \frac{2}{1} = 8
$$

✔ Answer: $ 8 $

---

🔹 6. $ 2\frac{1}{2} \times 2\frac{2}{3} $

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

Multiply:
$$
\frac{5}{2} \times \frac{8}{3}
$$

Cancel:
- 8 and 2 → $ \frac{8}{2} = 4 $, so $ \frac{4}{1} $
- So: $ \frac{5}{1} \times \frac{4}{3} = \frac{20}{3} $

Convert: $ 6\frac{2}{3} $

✔ Answer: $ 6\frac{2}{3} $

---

🔹 7. $ 2\frac{2}{5} \times 2\frac{1}{3} $

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

Multiply:
$$
\frac{12}{5} \times \frac{7}{3}
$$

Cancel:
- 12 and 3 → $ \frac{12}{3} = 4 $, so $ \frac{4}{1} $
- So: $ \frac{4}{5} \times \frac{7}{1} = \frac{28}{5} $

Convert: $ 5\frac{3}{5} $

✔ Answer: $ 5\frac{3}{5} $

---

🔹 8. $ 4\frac{3}{4} \times 4\frac{2}{3} $

Convert:
- $ 4\frac{3}{4} = \frac{19}{4} $
- $ 4\frac{2}{3} = \frac{14}{3} $

Multiply:
$$
\frac{19}{4} \times \frac{14}{3}
$$

Cancel:
- 14 and 4 → both divisible by 2 → $ \frac{7}{2} $
- So: $ \frac{19}{2} \times \frac{7}{3} = \frac{133}{6} $

Convert: $ 22\frac{1}{6} $

✔ Answer: $ 22\frac{1}{6} $

---

✔ Final Answers:

1. $ 4\frac{2}{5} \times 2\frac{1}{2} = 11 $
2. $ 2\frac{1}{4} \times 3\frac{1}{3} = 7\frac{1}{2} $
3. $ 4\frac{2}{5} \times 4\frac{3}{4} = 20\frac{9}{10} $
4. $ 4\frac{1}{3} \times 2\frac{1}{2} = 10\frac{5}{6} $
5. $ 2\frac{2}{5} \times 3\frac{1}{3} = 8 $
6. $ 2\frac{1}{2} \times 2\frac{2}{3} = 6\frac{2}{3} $
7. $ 2\frac{2}{5} \times 2\frac{1}{3} = 5\frac{3}{5} $
8. $ 4\frac{3}{4} \times 4\frac{2}{3} = 22\frac{1}{6} $

---

Let me know if you'd like a printable version or visual explanation!