Fraction multiplication worksheet for students to solve and reduce to lowest terms.

Let's solve each problem on Worksheet #2: Be a Fraction Wizard! step by step. The task is to multiply the mixed numbers and reduce the result to lowest terms.

---

🔧 Step-by-step Strategy:

1. Convert each mixed number to an improper fraction.
2. Multiply the two improper fractions.
3. Simplify the result (reduce to lowest terms).
4. Convert back to a mixed number if needed.

---

We'll go through each problem:

---

1. $ 2\frac{5}{7} \times 6\frac{2}{5} $

Convert:
- $ 2\frac{5}{7} = \frac{2 \times 7 + 5}{7} = \frac{14 + 5}{7} = \frac{19}{7} $
- $ 6\frac{2}{5} = \frac{6 \times 5 + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5} $

Multiply:
- $ \frac{19}{7} \times \frac{32}{5} = \frac{19 \times 32}{7 \times 5} = \frac{608}{35} $

Simplify:
- $ \frac{608}{35} $ → divide 608 ÷ 35 = 17 with remainder 13 → $ 17\frac{13}{35} $

✔ Answer: $ 17\frac{13}{35} $

---

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

Convert:
- $ 2\frac{1}{5} = \frac{11}{5} $
- $ 7\frac{1}{2} = \frac{15}{2} $

Multiply:
- $ \frac{11}{5} \times \frac{15}{2} = \frac{165}{10} $

Simplify:
- $ \frac{165}{10} = \frac{33}{2} = 16\frac{1}{2} $

✔ Answer: $ 16\frac{1}{2} $

---

3. $ 4\frac{3}{4} \times 9\frac{8}{9} $

Convert:
- $ 4\frac{3}{4} = \frac{19}{4} $
- $ 9\frac{8}{9} = \frac{89}{9} $

Multiply:
- $ \frac{19}{4} \times \frac{89}{9} = \frac{1691}{36} $

Simplify:
- $ 1691 ÷ 36 = 46 $ remainder $ 35 $ → $ 46\frac{35}{36} $

✔ Answer: $ 46\frac{35}{36} $

---

4. $ 3\frac{3}{6} \times 1\frac{1}{6} $

Note: $ 3\frac{3}{6} = 3\frac{1}{2} $, simplify first.

Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 1\frac{1}{6} = \frac{7}{6} $

Multiply:
- $ \frac{7}{2} \times \frac{7}{6} = \frac{49}{12} $

Simplify:
- $ \frac{49}{12} = 4\frac{1}{12} $

✔ Answer: $ 4\frac{1}{12} $

---

5. $ 4\frac{2}{3} \times 4\frac{5}{9} $

Convert:
- $ 4\frac{2}{3} = \frac{14}{3} $
- $ 4\frac{5}{9} = \frac{41}{9} $

Multiply:
- $ \frac{14}{3} \times \frac{41}{9} = \frac{574}{27} $

Simplify:
- $ 574 ÷ 27 = 21 $ remainder $ 7 $ → $ 21\frac{7}{27} $

✔ Answer: $ 21\frac{7}{27} $

---

6. $ 1\frac{1}{8} \times 6\frac{5}{6} $

Convert:
- $ 1\frac{1}{8} = \frac{9}{8} $
- $ 6\frac{5}{6} = \frac{41}{6} $

Multiply:
- $ \frac{9}{8} \times \frac{41}{6} = \frac{369}{48} $

Simplify:
- Divide numerator and denominator by 3: $ \frac{123}{16} $
- $ 123 ÷ 16 = 7 $ remainder $ 11 $ → $ 7\frac{11}{16} $

✔ Answer: $ 7\frac{11}{16} $

---

7. $ 2\frac{6}{7} \times 2\frac{3}{5} $

Convert:
- $ 2\frac{6}{7} = \frac{20}{7} $
- $ 2\frac{3}{5} = \frac{13}{5} $

Multiply:
- $ \frac{20}{7} \times \frac{13}{5} = \frac{260}{35} $

Simplify:
- $ \frac{260}{35} = \frac{52}{7} = 7\frac{3}{7} $

✔ Answer: $ 7\frac{3}{7} $

---

8. $ 4\frac{5}{8} \times 6\frac{5}{8} $

Convert:
- $ 4\frac{5}{8} = \frac{37}{8} $
- $ 6\frac{5}{8} = \frac{53}{8} $

Multiply:
- $ \frac{37}{8} \times \frac{53}{8} = \frac{1961}{64} $

Simplify:
- $ 1961 ÷ 64 = 30 $ remainder $ 41 $ → $ 30\frac{41}{64} $

✔ Answer: $ 30\frac{41}{64} $

---

9. $ 5\frac{1}{9} \times 7\frac{3}{5} $

Convert:
- $ 5\frac{1}{9} = \frac{46}{9} $
- $ 7\frac{3}{5} = \frac{38}{5} $

Multiply:
- $ \frac{46}{9} \times \frac{38}{5} = \frac{1748}{45} $

Simplify:
- $ 1748 ÷ 45 = 38 $ remainder $ 38 $ → $ 38\frac{38}{45} $

✔ Answer: $ 38\frac{38}{45} $

---

10. $ 3\frac{2}{3} \times 7\frac{1}{3} $

Convert:
- $ 3\frac{2}{3} = \frac{11}{3} $
- $ 7\frac{1}{3} = \frac{22}{3} $

Multiply:
- $ \frac{11}{3} \times \frac{22}{3} = \frac{242}{9} $

Simplify:
- $ 242 ÷ 9 = 26 $ remainder $ 8 $ → $ 26\frac{8}{9} $

✔ Answer: $ 26\frac{8}{9} $

---

11. $ 6\frac{7}{8} \times 8\frac{1}{3} $

Convert:
- $ 6\frac{7}{8} = \frac{55}{8} $
- $ 8\frac{1}{3} = \frac{25}{3} $

Multiply:
- $ \frac{55}{8} \times \frac{25}{3} = \frac{1375}{24} $

Simplify:
- $ 1375 ÷ 24 = 57 $ remainder $ 7 $ → $ 57\frac{7}{24} $

✔ Answer: $ 57\frac{7}{24} $

---

12. $ 7\frac{1}{6} \times 9\frac{2}{4} $

Note: $ 9\frac{2}{4} = 9\frac{1}{2} $

Convert:
- $ 7\frac{1}{6} = \frac{43}{6} $
- $ 9\frac{1}{2} = \frac{19}{2} $

Multiply:
- $ \frac{43}{6} \times \frac{19}{2} = \frac{817}{12} $

Simplify:
- $ 817 ÷ 12 = 68 $ remainder $ 1 $ → $ 68\frac{1}{12} $

✔ Answer: $ 68\frac{1}{12} $

---

13. $ 4\frac{3}{4} \times 6\frac{1}{2} $

Convert:
- $ 4\frac{3}{4} = \frac{19}{4} $
- $ 6\frac{1}{2} = \frac{13}{2} $

Multiply:
- $ \frac{19}{4} \times \frac{13}{2} = \frac{247}{8} $

Simplify:
- $ 247 ÷ 8 = 30 $ remainder $ 7 $ → $ 30\frac{7}{8} $

✔ Answer: $ 30\frac{7}{8} $

---

14. $ 3\frac{3}{4} \times 7\frac{2}{3} $

Convert:
- $ 3\frac{3}{4} = \frac{15}{4} $
- $ 7\frac{2}{3} = \frac{23}{3} $

Multiply:
- $ \frac{15}{4} \times \frac{23}{3} = \frac{345}{12} $

Simplify:
- $ \frac{345}{12} = \frac{115}{4} = 28\frac{3}{4} $

✔ Answer: $ 28\frac{3}{4} $

---

15. $ 5\frac{2}{6} \times 2\frac{1}{4} $

Simplify $ 5\frac{2}{6} = 5\frac{1}{3} $

Convert:
- $ 5\frac{1}{3} = \frac{16}{3} $
- $ 2\frac{1}{4} = \frac{9}{4} $

Multiply:
- $ \frac{16}{3} \times \frac{9}{4} = \frac{144}{12} = 12 $

✔ Answer: $ 12 $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 17\frac{13}{35} $ |
| 2 | $ 16\frac{1}{2} $ |
| 3 | $ 46\frac{35}{36} $ |
| 4 | $ 4\frac{1}{12} $ |
| 5 | $ 21\frac{7}{27} $ |
| 6 | $ 7\frac{11}{16} $ |
| 7 | $ 7\frac{3}{7} $ |
| 8 | $ 30\frac{41}{64} $ |
| 9 | $ 38\frac{38}{45} $ |
| 10 | $ 26\frac{8}{9} $ |
| 11 | $ 57\frac{7}{24} $ |
| 12 | $ 68\frac{1}{12} $ |
| 13 | $ 30\frac{7}{8} $ |
| 14 | $ 28\frac{3}{4} $ |
| 15 | $ 12 $ |

---

Let me know if you'd like this in a printable format or need help checking any specific one! 🧙‍♂️✨