Math worksheet for students to practice identifying proportions by comparing pairs of ratios.

Let's solve each problem step by step to determine whether each pair of ratios forms a proportion.

A proportion means that two ratios are equal. So, for two ratios $ \frac{a}{b} $ and $ \frac{c}{d} $, they form a proportion if:

$$
\frac{a}{b} = \frac{c}{d}
$$

We can check this by cross-multiplying:
- If $ a \times d = b \times c $, then the ratios form a proportion.
- Otherwise, they do not.

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1. $ \frac{5}{15} $ and $ \frac{3}{9} $

Simplify both:
- $ \frac{5}{15} = \frac{1}{3} $
- $ \frac{3}{9} = \frac{1}{3} $

Since both simplify to $ \frac{1}{3} $, they are equal.

✔ Yes, they form a proportion.

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2. $ \frac{2}{3} $ and $ \frac{18}{27} $

Simplify $ \frac{18}{27} $: divide numerator and denominator by 9 → $ \frac{2}{3} $

So, $ \frac{2}{3} = \frac{2}{3} $

✔ Yes, they form a proportion.

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3. $ \frac{68}{7} $ and $ \frac{19}{3} $

Cross-multiply:
- $ 68 \times 3 = 204 $
- $ 7 \times 19 = 133 $

$ 204 \neq 133 $

✘ No, they do not form a proportion.

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4. $ \frac{6}{12} $ and $ \frac{2}{4} $

Simplify:
- $ \frac{6}{12} = \frac{1}{2} $
- $ \frac{2}{4} = \frac{1}{2} $

Both equal $ \frac{1}{2} $

✔ Yes, they form a proportion.

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5. $ \frac{12}{8} $ and $ \frac{4}{5} $

Simplify $ \frac{12}{8} = \frac{3}{2} $

Compare $ \frac{3}{2} $ and $ \frac{4}{5} $

Cross-multiply:
- $ 3 \times 5 = 15 $
- $ 2 \times 4 = 8 $

$ 15 \neq 8 $

✘ No, they do not form a proportion.

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6. $ \frac{3}{27} $ and $ \frac{1}{9} $

Simplify $ \frac{3}{27} = \frac{1}{9} $

So $ \frac{1}{9} = \frac{1}{9} $

✔ Yes, they form a proportion.

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7. $ \frac{18}{4} $ and $ \frac{9}{2} $

Simplify $ \frac{18}{4} = \frac{9}{2} $

So $ \frac{9}{2} = \frac{9}{2} $

✔ Yes, they form a proportion.

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8. $ \frac{4}{5} $ and $ \frac{20}{25} $

Simplify $ \frac{20}{25} = \frac{4}{5} $

So $ \frac{4}{5} = \frac{4}{5} $

✔ Yes, they form a proportion.

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | Yes |
| 2 | Yes |
| 3 | No |
| 4 | Yes |
| 5 | No |
| 6 | Yes |
| 7 | Yes |
| 8 | Yes |

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✔ Summary:

The pairs that form a proportion are:
1, 2, 4, 6, 7, 8

The pairs that do not form a proportion:
3, 5

Let me know if you'd like this in a printable format!