Simplify Improper Fractions worksheet with multiple-choice questions.

Let's solve each of these problems step by step. The goal is to simplify improper fractions and express them in their simplest form, which usually means converting them into a mixed number (whole number + proper fraction) if needed, and reducing the fraction part to lowest terms.

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1) Simplify: $ \frac{75}{20} $

- First, divide 75 by 20:
- $ 75 ÷ 20 = 3 $ with a remainder of $ 15 $
- So, $ \frac{75}{20} = 3 \frac{15}{20} $
- Now simplify $ \frac{15}{20} $: both divisible by 5 → $ \frac{3}{4} $
- So, $ \frac{75}{20} = 3 \frac{3}{4} $

But looking at the options:
> (i) $ \frac{35}{2} $
> (ii) $ \frac{25}{4} $
> (iii) $ \frac{15}{4} $
> (iv) $ \frac{25}{15} $

Wait — none of the options are mixed numbers. Let’s check if any of the improper fractions match $ \frac{75}{20} $ in simplified form.

Simplify $ \frac{75}{20} $:
- Divide numerator and denominator by GCF(75,20) = 5
- $ \frac{75 ÷ 5}{20 ÷ 5} = \frac{15}{4} $

✔ So the simplest form is $ \frac{15}{4} $

Answer: (iii) $ \frac{15}{4} $

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2) Simplify: $ \frac{48}{36} $

- GCF of 48 and 36 is 12
- $ \frac{48 ÷ 12}{36 ÷ 12} = \frac{4}{3} $
- $ \frac{4}{3} = 1 \frac{1}{3} $

Now look at options:
> (i) $ \frac{24}{18} $ → not simplified
> (ii) $ 1 \frac{1}{3} $ ✔
> (iii) $ \frac{24}{5} $ → too big
> (iv) $ 2 \frac{1}{3} $ → too big

So correct answer is:

Answer: (ii) $ 1 \frac{1}{3} $

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3) Simplify: $ \frac{54}{20} $

- GCF of 54 and 20 is 2
- $ \frac{54 ÷ 2}{20 ÷ 2} = \frac{27}{10} $
- $ \frac{27}{10} = 2 \frac{7}{10} $

Check options:
> (i) $ \frac{27}{15} $ → not simplified
> (ii) $ \frac{5}{4} $ → too small
> (iii) $ 1 \frac{7}{10} $ → wrong
> (iv) $ 2 \frac{7}{10} $ ✔

Answer: (iv) $ 2 \frac{7}{10} $

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4) Simplify: $ \frac{60}{38} $

- GCF of 60 and 38 is 2
- $ \frac{60 ÷ 2}{38 ÷ 2} = \frac{30}{19} $
- $ \frac{30}{19} = 1 \frac{11}{19} $

Now check options:
> (i) $ 1 \frac{10}{19} $ → close but wrong
> (ii) $ \frac{30}{19} $ ✔
> (iii) $ \frac{20}{19} $ → too small
> (iv) $ \frac{5}{19} $ → way too small

So $ \frac{30}{19} $ is the simplified improper fraction.

Answer: (ii) $ \frac{30}{19} $

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5) Simplify: $ \frac{45}{25} $

- GCF of 45 and 25 is 5
- $ \frac{45 ÷ 5}{25 ÷ 5} = \frac{9}{5} $
- $ \frac{9}{5} = 1 \frac{4}{5} $

Options:
> (i) $ 1 \frac{4}{5} $ ✔
> (ii) $ \frac{25}{3} $ → no
> (iii) $ \frac{9}{4} $ → no
> (iv) $ 1 \frac{3}{5} $ → no

Answer: (i) $ 1 \frac{4}{5} $

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6) Simplify: $ \frac{90}{48} $

- GCF of 90 and 48 is 6
- $ \frac{90 ÷ 6}{48 ÷ 6} = \frac{15}{8} $
- $ \frac{15}{8} = 1 \frac{7}{8} $

Now check options:
> (i) $ \frac{45}{24} $ → not simplified
> (ii) $ 1 \frac{5}{8} $ → close but wrong
> (iii) $ \frac{30}{24} $ → not simplified
> (iv) $ \frac{15}{8} $ ✔

So $ \frac{15}{8} $ is the simplified improper fraction.

Answer: (iv) $ \frac{15}{8} $

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✔ Final Answers:

1) (iii) $ \frac{15}{4} $
2) (ii) $ 1 \frac{1}{3} $
3) (iv) $ 2 \frac{7}{10} $
4) (ii) $ \frac{30}{19} $
5) (i) $ 1 \frac{4}{5} $
6) (iv) $ \frac{15}{8} $

Let me know if you'd like this explained visually or with diagrams!