Simplifying Fractions (C) Worksheet | Fun and Engaging 4th Grade ... - Free Printable

Let's solve this step by step.

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Section A: Check the fractions that *can* be simplified.

We need to determine which fractions can be simplified (i.e., reduced to a simpler form by dividing both numerator and denominator by their greatest common divisor, GCD).

#### Fractions in Section A:
1. $ \frac{2}{8} $ → GCD(2,8) = 2 → Yes
2. $ \frac{1}{7} $ → GCD(1,7) = 1 → No
3. $ \frac{3}{6} $ → GCD(3,6) = 3 → Yes
4. $ \frac{3}{5} $ → GCD(3,5) = 1 → No
5. $ \frac{4}{10} $ → GCD(4,10) = 2 → Yes
6. $ \frac{6}{11} $ → GCD(6,11) = 1 → No
7. $ \frac{5}{15} $ → GCD(5,15) = 5 → Yes
8. $ \frac{2}{9} $ → GCD(2,9) = 1 → No
9. $ \frac{12}{24} $ → GCD(12,24) = 12 → Yes
10. $ \frac{10}{30} $ → GCD(10,30) = 10 → Yes
11. $ \frac{16}{21} $ → GCD(16,21) = 1 → No
12. $ \frac{7}{14} $ → GCD(7,14) = 7 → Yes

✔ Fractions that can be simplified (Section A):
- $ \frac{2}{8}, \frac{3}{6}, \frac{4}{10}, \frac{5}{15}, \frac{12}{24}, \frac{10}{30}, \frac{7}{14} $

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Section B: Check the fractions that *can* be simplified.

1. $ \frac{2}{22} $ → GCD(2,22) = 2 → Yes
2. $ \frac{15}{33} $ → GCD(15,33) = 3 → Yes
3. $ \frac{14}{35} $ → GCD(14,35) = 7 → Yes
4. $ \frac{9}{32} $ → GCD(9,32) = 1 → No
5. $ \frac{4}{100} $ → GCD(4,100) = 4 → Yes
6. $ \frac{12}{41} $ → GCD(12,41) = 1 → No
7. $ \frac{13}{52} $ → GCD(13,52) = 13 → Yes
8. $ \frac{18}{26} $ → GCD(18,26) = 2 → Yes
9. $ 2\frac{7}{12} $ → The fractional part $ \frac{7}{12} $: GCD(7,12)=1 → No, but the whole number doesn't affect simplification of fraction part → No
10. $ 9\frac{16}{20} $ → $ \frac{16}{20} $: GCD(16,20)=4 → Yes
11. $ \frac{19}{2} $ → GCD(19,2)=1 → No
12. $ \frac{28}{21} $ → GCD(28,21)=7 → Yes

✔ Fractions that can be simplified (Section B):
- $ \frac{2}{22}, \frac{15}{33}, \frac{14}{35}, \frac{4}{100}, \frac{13}{52}, \frac{18}{26}, 9\frac{16}{20}, \frac{28}{21} $

> Note: $ 2\frac{7}{12} $ cannot be simplified because $ \frac{7}{12} $ is already in simplest form.

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Section C: Simplify the following fractions.

We will simplify each fraction by dividing numerator and denominator by their GCD.

1) $ \frac{4}{8} $ → GCD = 4 → $ \frac{4÷4}{8÷4} = \frac{1}{2} $
2) $ \frac{5}{15} $ → GCD = 5 → $ \frac{5÷5}{15÷5} = \frac{1}{3} $
3) $ \frac{6}{18} $ → GCD = 6 → $ \frac{6÷6}{18÷6} = \frac{1}{3} $
4) $ \frac{12}{16} $ → GCD = 4 → $ \frac{12÷4}{16÷4} = \frac{3}{4} $
5) $ \frac{15}{18} $ → GCD = 3 → $ \frac{15÷3}{18÷3} = \frac{5}{6} $
6) $ \frac{4}{10} $ → GCD = 2 → $ \frac{4÷2}{10÷2} = \frac{2}{5} $
7) $ \frac{10}{25} $ → GCD = 5 → $ \frac{10÷5}{25÷5} = \frac{2}{5} $
8) $ \frac{8}{26} $ → GCD = 2 → $ \frac{8÷2}{26÷2} = \frac{4}{13} $
9) $ \frac{14}{22} $ → GCD = 2 → $ \frac{14÷2}{22÷2} = \frac{7}{11} $
10) $ \frac{6}{15} $ → GCD = 3 → $ \frac{6÷3}{15÷3} = \frac{2}{5} $
11) $ \frac{9}{30} $ → GCD = 3 → $ \frac{9÷3}{30÷3} = \frac{3}{10} $
12) $ \frac{14}{21} $ → GCD = 7 → $ \frac{14÷7}{21÷7} = \frac{2}{3} $

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✔ Final Answers:

#### Section A – Can be simplified:
$$
\boxed{\frac{2}{8},\ \frac{3}{6},\ \frac{4}{10},\ \frac{5}{15},\ \frac{12}{24},\ \frac{10}{30},\ \frac{7}{14}}
$$

#### Section B – Can be simplified:
$$
\boxed{\frac{2}{22},\ \frac{15}{33},\ \frac{14}{35},\ \frac{4}{100},\ \frac{13}{52},\ \frac{18}{26},\ 9\frac{16}{20},\ \frac{28}{21}}
$$

#### Section C – Simplified fractions:
1) $ \frac{1}{2} $
2) $ \frac{1}{3} $
3) $ \frac{1}{3} $
4) $ \frac{3}{4} $
5) $ \frac{5}{6} $
6) $ \frac{2}{5} $
7) $ \frac{2}{5} $
8) $ \frac{4}{13} $
9) $ \frac{7}{11} $
10) $ \frac{2}{5} $
11) $ \frac{3}{10} $
12) $ \frac{2}{3} $

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