Ratio and Proportion Worksheets - Math Monks - Free Printable

To solve this problem, we need to determine whether each pair of ratios forms a proportion.

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✔ What is a proportion?

A proportion is an equation that states 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 in two main ways:
1. Cross-multiply: If \( a \cdot d = b \cdot c \), then the ratios form a proportion.
2. Simplify both fractions to lowest terms — if they are equal, they form a proportion.

We’ll use simplification here since it’s often easier and more intuitive.

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## Let’s solve each pair:

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① \( \frac{5}{15} \) and \( \frac{3}{9} \)

- Simplify \( \frac{5}{15} = \frac{1}{3} \)
- Simplify \( \frac{3}{9} = \frac{1}{3} \)

✔ They are equal → Yes, it’s a proportion

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② \( \frac{2}{3} \) and \( \frac{18}{27} \)

- \( \frac{2}{3} \) is already simplified
- \( \frac{18}{27} = \frac{2}{3} \) (divide numerator and denominator by 9)

✔ Equal → Yes, it’s a proportion

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③ \( \frac{68}{7} \) and \( \frac{19}{3} \)

- \( \frac{68}{7} \approx 9.714 \)
- \( \frac{19}{3} \approx 6.333 \)

Not equal. Also, neither simplifies to the other.

✘ Not equal → No, not a proportion

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④ \( \frac{6}{12} \) and \( \frac{2}{4} \)

- \( \frac{6}{12} = \frac{1}{2} \)
- \( \frac{2}{4} = \frac{1}{2} \)

✔ Equal → Yes, it’s a proportion

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⑤ \( \frac{12}{8} \) and \( \frac{4}{5} \)

- \( \frac{12}{8} = \frac{3}{2} = 1.5 \)
- \( \frac{4}{5} = 0.8 \)

Not equal.

✘ Not equal → No, not a proportion

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⑥ \( \frac{3}{27} \) and \( \frac{1}{9} \)

- \( \frac{3}{27} = \frac{1}{9} \)
- \( \frac{1}{9} \) is already simplified

✔ Equal → Yes, it’s a proportion

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⑦ \( \frac{18}{4} \) and \( \frac{9}{2} \)

- \( \frac{18}{4} = \frac{9}{2} \) (divide numerator and denominator by 2)
- \( \frac{9}{2} \) is same

✔ Equal → Yes, it’s a proportion

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⑧ \( \frac{4}{5} \) and \( \frac{20}{25} \)

- \( \frac{4}{5} \) is simplified
- \( \frac{20}{25} = \frac{4}{5} \) (divide by 5)

✔ Equal → Yes, it’s a proportion

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## ✔ Final Answers:

1. Yes
2. Yes
3. No
4. Yes
5. No
6. Yes
7. Yes
8. Yes

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## 📝 Summary:

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

You can write “Yes” or “No” in the blank lines under each problem on your worksheet.

Let me know if you’d like to see the cross-multiplication method too!