Equivalent Ratio Worksheets - Math Monks - Free Printable

Let's solve each part of the Equivalent Ratios Worksheet step by step.

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Part 1: Write two equivalent ratios of the given ratio

To find equivalent ratios, we multiply or divide both the numerator and denominator by the same non-zero number.

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#### 1) $ \frac{3}{4} = \frac{\square}{\square} = \frac{\square}{\square} $

Multiply numerator and denominator by 2:
- $ \frac{3 \times 2}{4 \times 2} = \frac{6}{8} $

Multiply by 3:
- $ \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $

✔ Answer: $ \frac{3}{4} = \frac{6}{8} = \frac{9}{12} $

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#### 2) $ \frac{2}{11} = \frac{\square}{\square} = \frac{\square}{\square} $

Multiply by 2:
- $ \frac{2 \times 2}{11 \times 2} = \frac{4}{22} $

Multiply by 3:
- $ \frac{2 \times 3}{11 \times 3} = \frac{6}{33} $

✔ Answer: $ \frac{2}{11} = \frac{4}{22} = \frac{6}{33} $

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#### 3) $ \frac{5}{6} = \frac{\square}{\square} = \frac{\square}{\square} $

Multiply by 2:
- $ \frac{10}{12} $

Multiply by 3:
- $ \frac{15}{18} $

✔ Answer: $ \frac{5}{6} = \frac{10}{12} = \frac{15}{18} $

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#### 4) $ \frac{15}{35} = \frac{\square}{\square} = \frac{\square}{\square} $

First, simplify $ \frac{15}{35} $:
- Divide numerator and denominator by 5: $ \frac{3}{7} $

Now write two equivalent ratios to $ \frac{3}{7} $:

Multiply by 2: $ \frac{6}{14} $

Multiply by 3: $ \frac{9}{21} $

✔ Answer: $ \frac{15}{35} = \frac{6}{14} = \frac{9}{21} $

*(Note: You could also write $ \frac{30}{70} $, etc., but simplified form is helpful.)*

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Part 2: Determine whether the ratios are equivalent

Two ratios are equivalent if their cross products are equal.

> For $ \frac{a}{b} $ and $ \frac{c}{d} $, they are equivalent if $ a \cdot d = b \cdot c $

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#### 5) $ \frac{2}{7} $ and $ \frac{10}{35} $

Cross-multiply:
- $ 2 \times 35 = 70 $
- $ 7 \times 10 = 70 $

Since $ 70 = 70 $, the ratios are equivalent.

✔ Answer: Yes

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#### 6) $ \frac{11}{2} $ and $ \frac{22}{3} $

Cross-multiply:
- $ 11 \times 3 = 33 $
- $ 2 \times 22 = 44 $

$ 33 \ne 44 $ → Not equivalent

✔ Answer: No

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#### 7) $ \frac{8}{3} $ and $ \frac{64}{24} $

Cross-multiply:
- $ 8 \times 24 = 192 $
- $ 3 \times 64 = 192 $

$ 192 = 192 $ → Equivalent

✔ Answer: Yes

(Also note: $ \frac{64}{24} $ simplifies to $ \frac{8}{3} $)

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#### 8) $ \frac{2}{5} $ and $ \frac{7}{5} $

Cross-multiply:
- $ 2 \times 5 = 10 $
- $ 5 \times 7 = 35 $

$ 10 \ne 35 $ → Not equivalent

✔ Answer: No

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Part 3: Use equivalent ratios to find the unknown value

We use cross multiplication to solve for the unknown.

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#### 9) $ \frac{2}{7} = \frac{x}{14} $

Cross-multiply:
- $ 2 \times 14 = 7x $
- $ 28 = 7x $
- $ x = \frac{28}{7} = 4 $

✔ $ x = 4 $

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#### 10) $ \frac{11}{10} = \frac{33}{p} $

Cross-multiply:
- $ 11 \times p = 10 \times 33 $
- $ 11p = 330 $
- $ p = \frac{330}{11} = 30 $

✔ $ p = 30 $

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#### 11) $ \frac{9}{y} = \frac{3}{27} $

Simplify right side:
- $ \frac{3}{27} = \frac{1}{9} $

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

Cross-multiply:
- $ 9 \times 9 = 1 \times y $
- $ 81 = y $

✔ $ y = 81 $

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✔ Final Answers:

#### Part 1: Equivalent Ratios
1) $ \frac{3}{4} = \frac{6}{8} = \frac{9}{12} $
2) $ \frac{2}{11} = \frac{4}{22} = \frac{6}{33} $
3) $ \frac{5}{6} = \frac{10}{12} = \frac{15}{18} $
4) $ \frac{15}{35} = \frac{6}{14} = \frac{9}{21} $

#### Part 2: Are ratios equivalent?
5) Yes
6) No
7) Yes
8) No

#### Part 3: Solve for unknown
9) $ x = 4 $
10) $ p = 30 $
11) $ y = 81 $

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