Dividing Fractions Worksheet with Ten Practice Problems

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

To divide fractions, we use the "keep, change, flip" method:

- Keep the first fraction as it is.
- Change the division sign to multiplication.
- Flip (or take the reciprocal of) the second fraction.

Then multiply the two fractions and simplify if needed.

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1) $ \frac{6}{9} \div \frac{1}{10} $

- Keep: $ \frac{6}{9} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{10} $ → $ \frac{10}{1} $

Now multiply:
$$
\frac{6}{9} \times \frac{10}{1} = \frac{60}{9}
$$

Simplify:
$$
\frac{60}{9} = \frac{20}{3} = 6\frac{2}{3}
$$

✔ Answer: $ \boxed{\frac{20}{3}} $ or $ \boxed{6\frac{2}{3}} $

---

2) $ \frac{5}{6} \div \frac{1}{10} $

- Keep: $ \frac{5}{6} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{10} $ → $ \frac{10}{1} $

$$
\frac{5}{6} \times \frac{10}{1} = \frac{50}{6}
$$

Simplify:
$$
\frac{50}{6} = \frac{25}{3} = 8\frac{1}{3}
$$

✔ Answer: $ \boxed{\frac{25}{3}} $ or $ \boxed{8\frac{1}{3}} $

---

3) $ \frac{1}{3} \div \frac{1}{2} $

- Keep: $ \frac{1}{3} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{2} $ → $ \frac{2}{1} $

$$
\frac{1}{3} \times \frac{2}{1} = \frac{2}{3}
$$

✔ Answer: $ \boxed{\frac{2}{3}} $

---

4) $ \frac{9}{10} \div \frac{2}{6} $

First, simplify $ \frac{2}{6} = \frac{1}{3} $

Now:
- Keep: $ \frac{9}{10} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{3} $ → $ \frac{3}{1} $

$$
\frac{9}{10} \times \frac{3}{1} = \frac{27}{10} = 2\frac{7}{10}
$$

✔ Answer: $ \boxed{\frac{27}{10}} $ or $ \boxed{2\frac{7}{10}} $

---

5) $ \frac{4}{6} \div \frac{1}{4} $

Simplify $ \frac{4}{6} = \frac{2}{3} $

Now:
- Keep: $ \frac{2}{3} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{4} $ → $ \frac{4}{1} $

$$
\frac{2}{3} \times \frac{4}{1} = \frac{8}{3} = 2\frac{2}{3}
$$

✔ Answer: $ \boxed{\frac{8}{3}} $ or $ \boxed{2\frac{2}{3}} $

---

6) $ \frac{4}{10} \div \frac{1}{3} $

Simplify $ \frac{4}{10} = \frac{2}{5} $

- Keep: $ \frac{2}{5} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{3} $ → $ \frac{3}{1} $

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

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

---

7) $ \frac{3}{6} \div \frac{2}{3} $

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

- Keep: $ \frac{1}{2} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{2}{3} $ → $ \frac{3}{2} $

$$
\frac{1}{2} \times \frac{3}{2} = \frac{3}{4}
$$

✔ Answer: $ \boxed{\frac{3}{4}} $

---

8) $ \frac{1}{3} \div \frac{7}{9} $

- Keep: $ \frac{1}{3} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{7}{9} $ → $ \frac{9}{7} $

$$
\frac{1}{3} \times \frac{9}{7} = \frac{9}{21} = \frac{3}{7}
$$

✔ Answer: $ \boxed{\frac{3}{7}} $

---

9) $ \frac{1}{2} \div \frac{5}{6} $

- Keep: $ \frac{1}{2} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{5}{6} $ → $ \frac{6}{5} $

$$
\frac{1}{2} \times \frac{6}{5} = \frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \boxed{\frac{3}{5}} $

---

10) $ \frac{7}{10} \div \frac{1}{3} $

- Keep: $ \frac{7}{10} $
- Change: $ \div $ → $ \times $
- Flip: $ \frac{1}{3} $ → $ \frac{3}{1} $

$$
\frac{7}{10} \times \frac{3}{1} = \frac{21}{10} = 2\frac{1}{10}
$$

✔ Answer: $ \boxed{\frac{21}{10}} $ or $ \boxed{2\frac{1}{10}} $

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✔ Final Answers:

1) $ \frac{20}{3} $
2) $ \frac{25}{3} $
3) $ \frac{2}{3} $
4) $ \frac{27}{10} $
5) $ \frac{8}{3} $
6) $ \frac{6}{5} $
7) $ \frac{3}{4} $
8) $ \frac{3}{7} $
9) $ \frac{3}{5} $
10) $ \frac{21}{10} $

Let me know if you'd like this in a printable format or with steps shown for each!