This worksheet challenges students to find missing numbers in division equations involving whole numbers and unit fractions.

Let's solve each problem step by step.

We are dividing whole numbers by unit fractions (fractions with numerator 1), or solving for missing values in such equations.

Key Concept:

Dividing by a unit fraction is the same as multiplying by its reciprocal.

For example:
$$
a \div \frac{1}{b} = a \times b
$$

So, if we have:
$$
x \div \frac{1}{b} = c
\quad \Rightarrow \quad x = c \times \frac{1}{b} = \frac{c}{b}
$$
or
$$
a \div \frac{1}{b} = ?
\quad \Rightarrow \quad a \times b
$$

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Let’s go through each one:

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1) ___ ÷ 1/4 = 8

Let $ x \div \frac{1}{4} = 8 $
Then $ x = 8 \times \frac{1}{4} = 2 $

✔ Answer: 2

---

2) 5 ÷ 1/3 = ___

$ 5 \div \frac{1}{3} = 5 \times 3 = 15 $

✔ Answer: 15

---

3) ___ ÷ 1/2 = 14

Let $ x \div \frac{1}{2} = 14 $
Then $ x = 14 \times \frac{1}{2} = 7 $

✔ Answer: 7

---

4) 7 ÷ 1/5 = ___

$ 7 \div \frac{1}{5} = 7 \times 5 = 35 $

✔ Answer: 35

---

5) ___ ÷ 1/4 = 12

$ x = 12 \times \frac{1}{4} = 3 $

✔ Answer: 3

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6) 4 ÷ ___ = 8

Let $ 4 \div x = 8 $ → $ x = \frac{4}{8} = \frac{1}{2} $

But since it's a unit fraction, check: $ 4 \div \frac{1}{2} = 8 $? Yes!

✔ Answer: 1/2

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7) 5 ÷ ___ = 20

$ 5 \div x = 20 $ → $ x = \frac{5}{20} = \frac{1}{4} $

Check: $ 5 \div \frac{1}{4} = 5 \times 4 = 20 $ ✔

✔ Answer: 1/4

---

8) 7 ÷ 1/3 = ___

$ 7 \times 3 = 21 $

✔ Answer: 21

---

9) ___ ÷ 1/4 = 16

$ x = 16 \times \frac{1}{4} = 4 $

✔ Answer: 4

---

10) 6 ÷ ___ = 18

$ x = \frac{6}{18} = \frac{1}{3} $

Check: $ 6 \div \frac{1}{3} = 6 \times 3 = 18 $ ✔

✔ Answer: 1/3

---

11) 3 ÷ 1/9 = ___

$ 3 \times 9 = 27 $

✔ Answer: 27

---

12) ___ ÷ 1/3 = 21

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

✔ Answer: 7

---

13) ___ ÷ 1/5 = 25

$ x = 25 \times \frac{1}{5} = 5 $

✔ Answer: 5

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14) 4 ÷ ___ = 36

$ x = \frac{4}{36} = \frac{1}{9} $

Check: $ 4 \div \frac{1}{9} = 4 \times 9 = 36 $ ✔

✔ Answer: 1/9

---

15) 10 ÷ 1/4 = ___

$ 10 \times 4 = 40 $

✔ Answer: 40

---

16) ___ ÷ 1/6 = 6

$ x = 6 \times \frac{1}{6} = 1 $

✔ Answer: 1

---

17) 4 ÷ ___ = 32

$ x = \frac{4}{32} = \frac{1}{8} $

Check: $ 4 \div \frac{1}{8} = 4 \times 8 = 32 $ ✔

✔ Answer: 1/8

---

18) 4 ÷ 1/7 = ___

$ 4 \times 7 = 28 $

✔ Answer: 28

---

19) ___ ÷ 1/2 = 24

$ x = 24 \times \frac{1}{2} = 12 $

✔ Answer: 12

---

20) 7 ÷ 1/4 = ___

$ 7 \times 4 = 28 $

✔ Answer: 28

---

21) 3 ÷ ___ = 24

$ x = \frac{3}{24} = \frac{1}{8} $

Check: $ 3 \div \frac{1}{8} = 3 \times 8 = 24 $ ✔

✔ Answer: 1/8

---

22) 8 ÷ ___ = 56

$ x = \frac{8}{56} = \frac{1}{7} $

Check: $ 8 \div \frac{1}{7} = 8 \times 7 = 56 $ ✔

✔ Answer: 1/7

---

23) 4 ÷ 1/11 = ___

$ 4 \times 11 = 44 $

✔ Answer: 44

---

24) ___ ÷ 1/5 = 35

$ x = 35 \times \frac{1}{5} = 7 $

✔ Answer: 7

---

25) 10 ÷ ___ = 40

$ x = \frac{10}{40} = \frac{1}{4} $

Check: $ 10 \div \frac{1}{4} = 10 \times 4 = 40 $ ✔

✔ Answer: 1/4

---

26) 8 ÷ ___ = 48

$ x = \frac{8}{48} = \frac{1}{6} $

Check: $ 8 \div \frac{1}{6} = 8 \times 6 = 48 $ ✔

✔ Answer: 1/6

---

27) ___ ÷ 1/6 = 30

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

✔ Answer: 5

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28) ___ ÷ 1/5 = 60

$ x = 60 \times \frac{1}{5} = 12 $

✔ Answer: 12

---

29) 9 ÷ 1/6 = ___

$ 9 \times 6 = 54 $

✔ Answer: 54

---

30) 7 ÷ ___ = 63

$ x = \frac{7}{63} = \frac{1}{9} $

Check: $ 7 \div \frac{1}{9} = 7 \times 9 = 63 $ ✔

✔ Answer: 1/9

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1) | 2 |
| 2) | 15 |
| 3) | 7 |
| 4) | 35 |
| 5) | 3 |
| 6) | 1/2 |
| 7) | 1/4 |
| 8) | 21 |
| 9) | 4 |
| 10) | 1/3 |
| 11) | 27 |
| 12) | 7 |
| 13) | 5 |
| 14) | 1/9 |
| 15) | 40 |
| 16) | 1 |
| 17) | 1/8 |
| 18) | 28 |
| 19) | 12 |
| 20) | 28 |
| 21) | 1/8 |
| 22) | 1/7 |
| 23) | 44 |
| 24) | 7 |
| 25) | 1/4 |
| 26) | 1/6 |
| 27) | 5 |
| 28) | 12 |
| 29) | 54 |
| 30) | 1/9 |

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🔍 Summary Tip:

When you divide a whole number by a unit fraction $ \frac{1}{n} $, just multiply the whole number by $ n $.
And when solving for the missing divisor, divide the dividend by the result to get the fraction.

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