Identifying Proper and Improper Fractions worksheet for educational practice.

Let's solve the problem step by step.

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Understanding Proper and Improper Fractions

- A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number).
Example: $ \frac{3}{4} $ → 3 < 4 → proper

- An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Example: $ \frac{5}{4} $ → 5 > 4 → improper

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## A) Circle the proper fractions

We need to identify which fractions have numerator < denominator.

List:
- $ \frac{7}{10} $ → 7 < 10 → ✔ Proper
- $ \frac{2}{9} $ → 2 < 9 → ✔ Proper
- $ \frac{12}{11} $ → 12 > 11 → ✘ Not proper
- $ \frac{5}{2} $ → 5 > 2 → ✘ Not proper
- $ \frac{9}{4} $ → 9 > 4 → ✘ Not proper
- $ \frac{3}{14} $ → 3 < 14 → ✔ Proper
- $ \frac{1}{2} $ → 1 < 2 → ✔ Proper

✔ Proper fractions to circle:
$ \frac{7}{10}, \frac{2}{9}, \frac{3}{14}, \frac{1}{2} $

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## B) Circle the improper fractions

Now find fractions where numerator ≥ denominator.

List:
- $ \frac{5}{4} $ → 5 > 4 → ✔ Improper
- $ \frac{13}{12} $ → 13 > 12 → ✔ Improper
- $ \frac{2}{3} $ → 2 < 3 → ✘ Not improper
- $ \frac{15}{8} $ → 15 > 8 → ✔ Improper
- $ \frac{5}{6} $ → 5 < 6 → ✘ Not improper
- $ \frac{8}{7} $ → 8 > 7 → ✔ Improper
- $ \frac{11}{5} $ → 11 > 5 → ✔ Improper

✔ Improper fractions to circle:
$ \frac{5}{4}, \frac{13}{12}, \frac{15}{8}, \frac{8}{7}, \frac{11}{5} $

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## C) Read each statement and check "Yes" or "No"

1) $ \frac{3}{4} $ is a proper fraction.

- 3 < 4 → Yes, it's proper → ✔ Yes

2) $ \frac{9}{8} $ is not an improper fraction.

- 9 > 8 → it is an improper fraction → So saying "it is not an improper fraction" is false → ✘ No

3) $ \frac{10}{7} $ is an improper fraction.

- 10 > 7 → yes, it is improper → ✔ Yes

4) $ \frac{14}{13} $ is a proper fraction.

- 14 > 13 → it’s improper, so this statement is false → ✘ No

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✔ Final Answers:

#### A) Proper fractions:
Circle:
$ \boxed{\frac{7}{10}}, \boxed{\frac{2}{9}}, \boxed{\frac{3}{14}}, \boxed{\frac{1}{2}} $

#### B) Improper fractions:
Circle:
$ \boxed{\frac{5}{4}}, \boxed{\frac{13}{12}}, \boxed{\frac{15}{8}}, \boxed{\frac{8}{7}}, \boxed{\frac{11}{5}} $

#### C) True/False:
1) $ \frac{3}{4} $ is a proper fraction. → Yes
2) $ \frac{9}{8} $ is not an improper fraction. → No
3) $ \frac{10}{7} $ is an improper fraction. → Yes
4) $ \frac{14}{13} $ is a proper fraction. → No

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