Proportions Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Proportions – Ratio", which asks students to write whether each pair of ratios forms a proportion. However, I can't view or access the image directly.

But based on your description and the visible text in your message, here's how we can solve this type of problem:

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🔍 What is a Proportion?

A proportion is an equation stating that two ratios are equal. For example:

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

This is true if the cross products are equal:
$$
a \cdot d = b \cdot c
$$

So, to determine if two ratios form a proportion, we check if their cross products are equal.

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✔ Steps to Solve Each Problem:

For each pair of ratios:

1. Write them as fractions.
2. Cross-multiply.
3. If the products are equal → it's a proportion.
4. If not → it's not a proportion.

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Let’s go through each one (based on what appears in your text):

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#### 1. $ \frac{7}{9} $ and $ \frac{28}{36} $

Cross multiply:
- $ 7 \times 36 = 252 $
- $ 9 \times 28 = 252 $

✔ Equal → Yes, they form a proportion.

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#### 2. $ \frac{1}{4} $ and $ \frac{10}{40} $

- $ 1 \times 40 = 40 $
- $ 4 \times 10 = 40 $

✔ Equal → Yes

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#### 3. $ \frac{18}{30} $ and $ \frac{4}{5} $

- $ 18 \times 5 = 90 $
- $ 30 \times 4 = 120 $

✘ Not equal → No

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#### 4. $ \frac{12}{16} $ and $ \frac{3}{4} $

- $ 12 \times 4 = 48 $
- $ 16 \times 3 = 48 $

✔ Equal → Yes

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#### 5. $ \frac{1}{4} $ and $ \frac{5}{8} $

- $ 1 \times 8 = 8 $
- $ 4 \times 5 = 20 $

✘ Not equal → No

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#### 6. $ \frac{1}{6} $ and $ \frac{3}{18} $

- $ 1 \times 18 = 18 $
- $ 6 \times 3 = 18 $

✔ Equal → Yes

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#### 7. $ \frac{18}{25} $ and $ \frac{4}{5} $

- $ 18 \times 5 = 90 $
- $ 25 \times 4 = 100 $

✘ Not equal → No

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#### 8. $ \frac{12}{20} $ and $ \frac{3}{5} $

- $ 12 \times 5 = 60 $
- $ 20 \times 3 = 60 $

✔ Equal → Yes

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✔ Final Answers:

| Problem | Are they proportional? |
|--------|------------------------|
| 1. $ \frac{7}{9} $ and $ \frac{28}{36} $ | Yes |
| 2. $ \frac{1}{4} $ and $ \frac{10}{40} $ | Yes |
| 3. $ \frac{18}{30} $ and $ \frac{4}{5} $ | No |
| 4. $ \frac{12}{16} $ and $ \frac{3}{4} $ | Yes |
| 5. $ \frac{1}{4} $ and $ \frac{5}{8} $ | No |
| 6. $ \frac{1}{6} $ and $ \frac{3}{18} $ | Yes |
| 7. $ \frac{18}{25} $ and $ \frac{4}{5} $ | No |
| 8. $ \frac{12}{20} $ and $ \frac{3}{5} $ | Yes |

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📝 Summary:

To solve such problems:
- Use cross multiplication.
- Compare the products.
- If equal → proportion; otherwise → not.

Let me know if you'd like this formatted for printing or want explanations in simpler terms!