Worksheet for identifying proper and improper fractions by selecting the correct value to make statements true.

Let's solve this worksheet step by step.

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🔍 Understanding the Concept

- Proper Fraction: A fraction where the numerator is less than the denominator → value < 1
Example: $ \frac{2}{3} < 1 $

- Improper Fraction: A fraction where the numerator is greater than or equal to the denominator → value ≥ 1
Example: $ \frac{4}{3} > 1 $

We are given statements like:
- $ \frac{a}{b} > 1 $ → we need to choose a number for the blank so that the fraction is greater than 1
- $ \frac{a}{b} < 1 $ → we need a number so that the fraction is less than 1

Each question has two choices (in circles), and we must pick the correct one to make the inequality true.

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Now, let’s go through each part:

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a) $ \frac{7}{\boxed{\phantom{0}}} < 1 $

To make this less than 1, the denominator must be greater than 7.
Options: 8 or 5

- If denominator = 8 → $ \frac{7}{8} < 1 $ ✔
- If denominator = 5 → $ \frac{7}{5} = 1.4 > 1 $ ✘

✔ Answer: 8

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b) $ \frac{\boxed{\phantom{0}}}{3} > 1 $

To make this greater than 1, numerator must be greater than 3
Options: 4 or 2

- 4/3 ≈ 1.33 > 1 ✔
- 2/3 < 1 ✘

✔ Answer: 4

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c) $ \frac{9}{\boxed{\phantom{0}}} < 1 $

Denominator must be greater than 9
Options: 15 or 7

- 9/15 = 0.6 < 1 ✔
- 9/7 ≈ 1.28 > 1 ✘

✔ Answer: 15

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d) $ \frac{14}{\boxed{\phantom{0}}} > 1 $

Numerator > denominator → denominator must be less than 14
Options: 13 or 17

- 14/13 ≈ 1.07 > 1 ✔
- 14/17 < 1 ✘

✔ Answer: 13

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e) $ \frac{\boxed{\phantom{0}}}{19} < 1 $

Numerator must be less than 19
Options: 10 or 20

- 10/19 < 1 ✔
- 20/19 > 1 ✘

✔ Answer: 10

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f) $ \frac{\boxed{\phantom{0}}}{4} > 1 $

Numerator > 4
Options: 6 or 3

- 6/4 = 1.5 > 1 ✔
- 3/4 < 1 ✘

✔ Answer: 6

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g) $ \frac{\boxed{\phantom{0}}}{6} < 1 $

Numerator < 6
Options: 7 or 2

- 7/6 > 1 ✘
- 2/6 = 1/3 < 1 ✔

✔ Answer: 2

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h) $ \frac{11}{\boxed{\phantom{0}}} > 1 $

Denominator < 11
Options: 10 or 12

- 11/10 = 1.1 > 1 ✔
- 11/12 < 1 ✘

✔ Answer: 10

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i) $ \frac{\boxed{\phantom{0}}}{8} > 1 $

Numerator > 8
Options: 11 or 7

- 11/8 = 1.375 > 1 ✔
- 7/8 < 1 ✘

✔ Answer: 11

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j) $ \frac{3}{\boxed{\phantom{0}}} < 1 $

Denominator > 3
Options: 14 or 2

- 3/14 < 1 ✔
- 3/2 = 1.5 > 1 ✘

✔ Answer: 14

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k) $ \frac{9}{\boxed{\phantom{0}}} < 1 $

Denominator > 9
Options: 13 or 8

- 9/13 < 1 ✔
- 9/8 > 1 ✘

✔ Answer: 13

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l) $ \frac{19}{\boxed{\phantom{0}}} > 1 $

Denominator < 19
Options: 7 or 25

- 19/7 ≈ 2.7 > 1 ✔
- 19/25 < 1 ✘

✔ Answer: 7

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m) $ \frac{15}{\boxed{\phantom{0}}} < 1 $

Denominator > 15
Options: 17 or 12

- 15/17 < 1 ✔
- 15/12 = 1.25 > 1 ✘

✔ Answer: 17

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n) $ \frac{\boxed{\phantom{0}}}{17} < 1 $

Numerator < 17
Options: 16 or 25

- 16/17 < 1 ✔
- 25/17 > 1 ✘

✔ Answer: 16

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o) $ \frac{15}{\boxed{\phantom{0}}} > 1 $

Denominator < 15
Options: 16 or 13

- 15/16 < 1 ✘
- 15/13 ≈ 1.15 > 1 ✔

✔ Answer: 13

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p) $ \frac{8}{\boxed{\phantom{0}}} < 1 $

Denominator > 8
Options: 6 or 9

- 8/6 ≈ 1.33 > 1 ✘
- 8/9 < 1 ✔

✔ Answer: 9

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q) $ \frac{3}{\boxed{\phantom{0}}} > 1 $

Denominator < 3
Options: 2 or 6

- 3/2 = 1.5 > 1 ✔
- 3/6 = 0.5 < 1 ✘

✔ Answer: 2

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✔ Final Answers:

| Letter | Answer |
|--------|--------|
| a) | 8 |
| b) | 4 |
| c) | 15 |
| d) | 13 |
| e) | 10 |
| f) | 6 |
| g) | 2 |
| h) | 10 |
| i) | 11 |
| j) | 14 |
| k) | 13 |
| l) | 7 |
| m) | 17 |
| n) | 16 |
| o) | 13 |
| p) | 9 |
| q) | 2 |

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📝 Summary of Strategy:

- For $ \frac{a}{b} < 1 $: Choose denominator > numerator OR numerator < denominator
- For $ \frac{a}{b} > 1 $: Choose numerator > denominator

Always compare the numbers in the options to ensure the inequality holds.

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