Ratio and Proportion Worksheets - Math Monks - Free Printable

Of course! Let's solve each problem step by step. The goal is to determine whether each pair of ratios forms a proportion.

> 💡 What is a proportion?
> Two ratios form a proportion if they are equal. That means the fractions represent the same value. We can check this by:
> - Simplifying both fractions to lowest terms, or
> - Cross-multiplying: if `a/b = c/d`, then `a × d = b × c`.

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Problem 1: $\frac{5}{15}$ and $\frac{3}{9}$

- Simplify $\frac{5}{15}$: divide numerator and denominator by 5 → $\frac{1}{3}$
- Simplify $\frac{3}{9}$: divide numerator and denominator by 3 → $\frac{1}{3}$
- ✔ Both equal $\frac{1}{3}$ → Yes, they form a proportion

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Problem 2: $\frac{2}{3}$ and $\frac{18}{27}$

- $\frac{2}{3}$ is already simplified.
- Simplify $\frac{18}{27}$: divide numerator and denominator by 9 → $\frac{2}{3}$
- ✔ Both equal $\frac{2}{3}$ → Yes, they form a proportion

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Problem 3: $\frac{68}{7}$ and $\frac{19}{3}$

- $\frac{68}{7}$ is about 9.71
- $\frac{19}{3}$ is about 6.33
- They are clearly not equal.
- Cross-multiply: $68 × 3 = 204$, $7 × 19 = 133$ → 204 ≠ 133
- ✘ Not equal → No, they do NOT form a proportion

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Problem 4: $\frac{6}{12}$ and $\frac{2}{4}$

- Simplify $\frac{6}{12}$ → $\frac{1}{2}$
- Simplify $\frac{2}{4}$ → $\frac{1}{2}$
- ✔ Both equal $\frac{1}{2}$ → Yes, they form a proportion

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Problem 5: $\frac{12}{8}$ and $\frac{4}{5}$

- Simplify $\frac{12}{8}$ → $\frac{3}{2}$ (divide by 4)
- $\frac{4}{5}$ is already simplified.
- $\frac{3}{2} = 1.5$, $\frac{4}{5} = 0.8$ → not equal
- Cross-multiply: $12 × 5 = 60$, $8 × 4 = 32$ → 60 ≠ 32
- ✘ Not equal → No, they do NOT form a proportion

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Problem 6: $\frac{3}{27}$ and $\frac{1}{9}$

- Simplify $\frac{3}{27}$ → divide by 3 → $\frac{1}{9}$
- $\frac{1}{9}$ is already simplified.
- ✔ Both equal $\frac{1}{9}$ → Yes, they form a proportion

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Problem 7: $\frac{18}{4}$ and $\frac{9}{2}$

- Simplify $\frac{18}{4}$ → divide by 2 → $\frac{9}{2}$
- $\frac{9}{2}$ is already simplified.
- ✔ Both equal $\frac{9}{2}$ → Yes, they form a proportion

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Problem 8: $\frac{4}{5}$ and $\frac{20}{25}$

- $\frac{4}{5}$ is already simplified.
- Simplify $\frac{20}{25}$ → divide by 5 → $\frac{4}{5}$
- ✔ Both equal $\frac{4}{5}$ → Yes, they form a proportion

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## ✔ Final Answers:

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

Let me know if you’d like to see the cross-multiplication steps for any of them!