Grade 6 math worksheet on dividing fractions, with eight problems to find the quotient.

Let's solve each of the fraction division problems step by step.

---

🔷 Rule for Dividing Fractions:

To divide two fractions, multiply the first fraction by the reciprocal (flip) of the second fraction.

That is:
$$
\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
$$

---

Now, let’s solve each one:

---

i. $ \frac{3}{4} \div \frac{2}{4} $

Step 1: Flip the second fraction and multiply:
$$
\frac{3}{4} \times \frac{4}{2}
$$

Step 2: Simplify:
- Cancel out the 4s: $ \frac{3}{1} \times \frac{1}{2} = \frac{3}{2} $

✔ Answer: $ \boxed{\frac{3}{2}} $ or $ 1\frac{1}{2} $

---

ii. $ \frac{5}{6} \div \frac{1}{7} $

Flip the second fraction:
$$
\frac{5}{6} \times \frac{7}{1} = \frac{35}{6}
$$

✔ Answer: $ \boxed{\frac{35}{6}} $ or $ 5\frac{5}{6} $

---

iii. $ \frac{1}{7} \div \frac{5}{8} $

Flip the second fraction:
$$
\frac{1}{7} \times \frac{8}{5} = \frac{8}{35}
$$

✔ Answer: $ \boxed{\frac{8}{35}} $

---

iv. $ \frac{5}{6} \div \frac{1}{5} $

Flip the second fraction:
$$
\frac{5}{6} \times \frac{5}{1} = \frac{25}{6}
$$

✔ Answer: $ \boxed{\frac{25}{6}} $ or $ 4\frac{1}{6} $

---

v. $ \frac{1}{7} \div \frac{2}{3} $

Flip the second fraction:
$$
\frac{1}{7} \times \frac{3}{2} = \frac{3}{14}
$$

✔ Answer: $ \boxed{\frac{3}{14}} $

---

vi. $ \frac{1}{6} \div \frac{1}{8} $

Flip the second fraction:
$$
\frac{1}{6} \times \frac{8}{1} = \frac{8}{6} = \frac{4}{3}
$$

✔ Answer: $ \boxed{\frac{4}{3}} $ or $ 1\frac{1}{3} $

---

vii. $ \frac{2}{7} \div \frac{1}{9} $

Flip the second fraction:
$$
\frac{2}{7} \times \frac{9}{1} = \frac{18}{7}
$$

✔ Answer: $ \boxed{\frac{18}{7}} $ or $ 2\frac{4}{7} $

---

viii. $ \frac{1}{6} \div \frac{4}{9} $

Flip the second fraction:
$$
\frac{1}{6} \times \frac{9}{4} = \frac{9}{24} = \frac{3}{8}
$$

(Simplify $ \frac{9}{24} $ by dividing numerator and denominator by 3)

✔ Answer: $ \boxed{\frac{3}{8}} $

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| i. | $ \frac{3}{2} $ |
| ii. | $ \frac{35}{6} $ |
| iii. | $ \frac{8}{35} $ |
| iv. | $ \frac{25}{6} $ |
| v. | $ \frac{3}{14} $ |
| vi. | $ \frac{4}{3} $ |
| vii. | $ \frac{18}{7} $ |
| viii. | $ \frac{3}{8} $ |

---

Let me know if you'd like these answers as mixed numbers or decimals!