Ratio and Proportion Worksheets - Math Monks - Free Printable

Let's solve each problem step by step to determine whether the x and y values are proportional.

🔍 What does it mean for x and y to be proportional?

Two variables $ x $ and $ y $ are proportional if their ratio $ \frac{y}{x} $ is constant for all pairs. That is:

$$
\frac{y_1}{x_1} = \frac{y_2}{x_2} = \frac{y_3}{x_3} = \dots = k \quad \text{(a constant)}
$$

We'll check this ratio for each pair in every table.

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✔ Problem 1:

| x | 4 | 19 | 22 | 18 |
|---|----|----|----|----|
| y | 32 | 76 | 88 | 72 |

Compute $ \frac{y}{x} $:
- $ \frac{32}{4} = 8 $
- $ \frac{76}{19} = 4 $
- $ \frac{88}{22} = 4 $
- $ \frac{72}{18} = 4 $

→ Ratios: 8, 4, 4, 4 → Not constant

✘ Not proportional

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✔ Problem 2:

| x | 3 | 6 | 9 | 12 |
|---|----|----|----|----|
| y | 12 | 24 | 36 | 48 |

$ \frac{y}{x} $:
- $ \frac{12}{3} = 4 $
- $ \frac{24}{6} = 4 $
- $ \frac{36}{9} = 4 $
- $ \frac{48}{12} = 4 $

→ All ratios = 4 → ✔ Proportional

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✔ Problem 3:

| x | -6 | -4 | -5 | -8 |
|-----|----|----|----|----|
| y | -48| -32| 40 | 64 |

$ \frac{y}{x} $:
- $ \frac{-48}{-6} = 8 $
- $ \frac{-32}{-4} = 8 $
- $ \frac{40}{-5} = -8 $
- $ \frac{64}{-8} = -8 $

→ Ratios: 8, 8, -8, -8 → Not constant

✘ Not proportional

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✔ Problem 4:

| x | -54 | 18 | -27 | 45 |
|-----|-----|----|-----|----|
| y | 6 | -2 | 3 | -5 |

$ \frac{y}{x} $:
- $ \frac{6}{-54} = -\frac{1}{9} $
- $ \frac{-2}{18} = -\frac{1}{9} $
- $ \frac{3}{-27} = -\frac{1}{9} $
- $ \frac{-5}{45} = -\frac{1}{9} $

→ All ratios = $ -\frac{1}{9} $ → ✔ Proportional

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✔ Problem 5:

| x | 18 | 15 | 14 | 12 |
|---|----|----|----|----|
| y | 90 | 75 | 70 | 60 |

$ \frac{y}{x} $:
- $ \frac{90}{18} = 5 $
- $ \frac{75}{15} = 5 $
- $ \frac{70}{14} = 5 $
- $ \frac{60}{12} = 5 $

→ All = 5 → ✔ Proportional

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✔ Problem 6:

| x | 9 | 3 | 2 | 6 |
|---|---|---|---|---|
| y | 0 | 6 | 10| 3 |

$ \frac{y}{x} $:
- $ \frac{0}{9} = 0 $
- $ \frac{6}{3} = 2 $
- $ \frac{10}{2} = 5 $
- $ \frac{3}{6} = 0.5 $

→ Ratios: 0, 2, 5, 0.5 → ✘ Not proportional

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✔ Problem 7:

| x | 4 | 2 | 3 | 9 |
|---|---|---|---|---|
| y | 20| 10| 15| 45|

$ \frac{y}{x} $:
- $ \frac{20}{4} = 5 $
- $ \frac{10}{2} = 5 $
- $ \frac{15}{3} = 5 $
- $ \frac{45}{9} = 5 $

→ All = 5 → ✔ Proportional

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✔ Problem 8:

| x | 10 | 16 | 20 | 26 |
|---|----|----|----|----|
| y | 5 | 8 | 10 | 13 |

$ \frac{y}{x} $:
- $ \frac{5}{10} = 0.5 $
- $ \frac{8}{16} = 0.5 $
- $ \frac{10}{20} = 0.5 $
- $ \frac{13}{26} = 0.5 $

→ All = 0.5 → ✔ Proportional

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✔ Problem 9:

| x | 5 | 10 | 15 | 20 |
|---|---|----|----|----|
| y | 2 | 4 | 6 | 8 |

$ \frac{y}{x} $:
- $ \frac{2}{5} = 0.4 $
- $ \frac{4}{10} = 0.4 $
- $ \frac{6}{15} = 0.4 $
- $ \frac{8}{20} = 0.4 $

→ All = 0.4 → ✔ Proportional

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✔ Problem 10:

| x | -4 | -2 | 6 | 2 |
|----|----|----|---|---|
| y | -14| -7 | 21| 7 |

$ \frac{y}{x} $:
- $ \frac{-14}{-4} = 3.5 $
- $ \frac{-7}{-2} = 3.5 $
- $ \frac{21}{6} = 3.5 $
- $ \frac{7}{2} = 3.5 $

→ All = 3.5 → ✔ Proportional

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✔ Final Answers:

1) ✘ Not proportional
2) ✔ Proportional
3) ✘ Not proportional
4) ✔ Proportional
5) ✔ Proportional
6) ✘ Not proportional
7) ✔ Proportional
8) ✔ Proportional
9) ✔ Proportional
10) ✔ Proportional

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📝 Summary Table:

| Problem | Proportional? |
|--------|----------------|
| 1 | No |
| 2 | Yes |
| 3 | No |
| 4 | Yes |
| 5 | Yes |
| 6 | No |
| 7 | Yes |
| 8 | Yes |
| 9 | Yes |
| 10 | Yes |

✔ Total Proportional: 7 out of 10

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