Grade 5 math worksheet on dividing fractions by fractions with space to write answers.

Let's solve each problem on the "Dividing fractions by fractions" worksheet step by step. The key rule for dividing fractions is:

> To divide by a fraction, multiply by its reciprocal.

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

We'll apply this rule to each problem.

---

1. $ \frac{1}{4} \div \frac{9}{10} $

$$
= \frac{1}{4} \times \frac{10}{9} = \frac{10}{36} = \frac{5}{18}
$$

✔ Answer: $ \frac{5}{18} $

---

2. $ \frac{5}{9} \div \frac{1}{2} $

$$
= \frac{5}{9} \times \frac{2}{1} = \frac{10}{9} = 1\frac{1}{9}
$$

✔ Answer: $ \frac{10}{9} $ or $ 1\frac{1}{9} $

---

3. $ \frac{1}{3} \div \frac{6}{5} $

$$
= \frac{1}{3} \times \frac{5}{6} = \frac{5}{18}
$$

✔ Answer: $ \frac{5}{18} $

---

4. $ \frac{8}{10} \div \frac{2}{5} $

First simplify $ \frac{8}{10} = \frac{4}{5} $

$$
= \frac{4}{5} \div \frac{2}{5} = \frac{4}{5} \times \frac{5}{2} = \frac{20}{10} = 2
$$

✔ Answer: $ 2 $

---

5. $ \frac{3}{5} \div \frac{7}{7} $

Note: $ \frac{7}{7} = 1 $

$$
= \frac{3}{5} \div 1 = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $

---

6. $ \frac{5}{6} \div \frac{1}{3} $

$$
= \frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2}
$$

✔ Answer: $ \frac{5}{2} $ or $ 2\frac{1}{2} $

---

7. $ \frac{5}{10} \div \frac{5}{12} $

Simplify $ \frac{5}{10} = \frac{1}{2} $

$$
= \frac{1}{2} \div \frac{5}{12} = \frac{1}{2} \times \frac{12}{5} = \frac{12}{10} = \frac{6}{5} = 1\frac{1}{5}
$$

✔ Answer: $ \frac{6}{5} $ or $ 1\frac{1}{5} $

---

8. $ \frac{7}{11} \div \frac{1}{4} $

$$
= \frac{7}{11} \times \frac{4}{1} = \frac{28}{11} = 2\frac{6}{11}
$$

✔ Answer: $ \frac{28}{11} $ or $ 2\frac{6}{11} $

---

9. $ \frac{5}{6} \div \frac{5}{6} $

Any number divided by itself is 1:

$$
= \frac{5}{6} \times \frac{6}{5} = \frac{30}{30} = 1
$$

✔ Answer: $ 1 $

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10. $ \frac{1}{4} \div \frac{1}{3} $

$$
= \frac{1}{4} \times \frac{3}{1} = \frac{3}{4}
$$

✔ Answer: $ \frac{3}{4} $

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✔ Final Answers:

1. $ \frac{5}{18} $
2. $ \frac{10}{9} $ or $ 1\frac{1}{9} $
3. $ \frac{5}{18} $
4. $ 2 $
5. $ \frac{3}{5} $
6. $ \frac{5}{2} $ or $ 2\frac{1}{2} $
7. $ \frac{6}{5} $ or $ 1\frac{1}{5} $
8. $ \frac{28}{11} $ or $ 2\frac{6}{11} $
9. $ 1 $
10. $ \frac{3}{4} $

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📝 Summary of Key Steps:

- Always multiply by the reciprocal of the divisor.
- Simplify fractions before multiplying if possible.
- Convert improper fractions to mixed numbers if needed (as per instructions).

Let me know if you'd like this as a printable answer sheet!