Fractions Worksheets: Find Missing Numbers in Multiplication of Fractions

Here's the complete solution to the worksheet “Find missing number in Multiplication of Fractions”, with explanations for each problem.

---

🔢 Basic Rule for Multiplying Fractions:

To multiply two fractions:
Numerator × Numerator / Denominator × Denominator

If you’re solving for a missing factor, use:
> Missing Factor = Product ÷ Known Factor

Which is the same as:
> Missing Factor = Product × Reciprocal of Known Factor

---

## ✔ Solutions:

---

1) $\frac{2}{5} \times \frac{1}{5} = \boxed{\frac{2}{25}}$

Explanation:
Multiply numerators: $2 \times 1 = 2$
Multiply denominators: $5 \times 5 = 25$
→ $\frac{2}{25}$

---

2) $\frac{4}{5} \times \frac{1}{3} = \boxed{\frac{4}{15}}$

Explanation:
$4 \times 1 = 4$, $5 \times 3 = 15$ → $\frac{4}{15}$

---

3) $\frac{4}{15} \times \frac{2}{3} = \boxed{\frac{8}{45}}$

Explanation:
$4 \times 2 = 8$, $15 \times 3 = 45$ → $\frac{8}{45}$

---

4) $\boxed{\frac{2}{5}} \times \frac{15}{8} = \frac{3}{4}$

Explanation:
Let missing number = $x$.
Then: $x \times \frac{15}{8} = \frac{3}{4}$
→ $x = \frac{3}{4} \div \frac{15}{8} = \frac{3}{4} \times \frac{8}{15} = \frac{24}{60} = \frac{2}{5}$ (simplified)

---

5) $\boxed{\frac{5}{12}} \times \frac{9}{4} = \frac{15}{16}$

Explanation:
$x \times \frac{9}{4} = \frac{15}{16}$
→ $x = \frac{15}{16} \div \frac{9}{4} = \frac{15}{16} \times \frac{4}{9} = \frac{60}{144} = \frac{5}{12}$ (simplified)

---

6) $\boxed{\frac{8}{27}} \times \frac{21}{16} = \frac{7}{18}$

Explanation:
$x \times \frac{21}{16} = \frac{7}{18}$
→ $x = \frac{7}{18} \div \frac{21}{16} = \frac{7}{18} \times \frac{16}{21} = \frac{112}{378}$
Simplify: divide numerator and denominator by 14 → $\frac{8}{27}$

---

7) $\frac{2}{7} \times \boxed{\frac{3}{4}} = \frac{3}{14}$

Explanation:
$x = \frac{3}{14} \div \frac{2}{7} = \frac{3}{14} \times \frac{7}{2} = \frac{21}{28} = \frac{3}{4}$

---

8) $\frac{3}{8} \times \boxed{\frac{7}{6}} = \frac{7}{16}$

Explanation:
$x = \frac{7}{16} \div \frac{3}{8} = \frac{7}{16} \times \frac{8}{3} = \frac{56}{48} = \frac{7}{6}$ (simplified)

---

9) $\frac{9}{7} \times \boxed{\frac{1}{18}} = \frac{1}{14}$

Explanation:
$x = \frac{1}{14} \div \frac{9}{7} = \frac{1}{14} \times \frac{7}{9} = \frac{7}{126} = \frac{1}{18}$

---

10) $\boxed{\frac{4}{9}} \times \frac{3}{5} = \frac{4}{15}$

Explanation:
$x = \frac{4}{15} \div \frac{3}{5} = \frac{4}{15} \times \frac{5}{3} = \frac{20}{45} = \frac{4}{9}$

---

11) $\boxed{\frac{11}{14}} \times \frac{7}{10} = \frac{11}{20}$

Explanation:
$x = \frac{11}{20} \div \frac{7}{10} = \frac{11}{20} \times \frac{10}{7} = \frac{110}{140} = \frac{11}{14}$

---

12) $\boxed{6} \times \frac{3}{10} = \frac{9}{5}$

Explanation:
$x = \frac{9}{5} \div \frac{3}{10} = \frac{9}{5} \times \frac{10}{3} = \frac{90}{15} = 6$

---

## 📝 Final Answers Summary:

| Problem | Answer |
|---------|--------------|
| 1 | $\frac{2}{25}$ |
| 2 | $\frac{4}{15}$ |
| 3 | $\frac{8}{45}$ |
| 4 | $\frac{2}{5}$ |
| 5 | $\frac{5}{12}$ |
| 6 | $\frac{8}{27}$ |
| 7 | $\frac{3}{4}$ |
| 8 | $\frac{7}{6}$ |
| 9 | $\frac{1}{18}$ |
| 10 | $\frac{4}{9}$ |
| 11 | $\frac{11}{14}$|
| 12 | $6$ |

✔ All answers are simplified to lowest terms.

Let me know if you’d like a printable version or step-by-step video-style breakdown!