Questions: Which of the following ratios are equivalent? Select all correct options

Which of the following ratios are equivalent? Select all correct options
Transcript text: Which of the following ratios are equivalent? Select all correct options
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Solution

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Solution Steps

Solution Approach

To determine which ratios are equivalent, we need to simplify each ratio to its lowest terms and then compare them. Ratios that simplify to the same values are equivalent.

Step 1: Identify the Ratios

We are given the following ratios to analyze for equivalence: \[ (2, 4), (3, 6), (4, 8), (5, 10), (1, 3) \]

Step 2: Simplify Each Ratio

We simplify each ratio to its lowest terms:

  • \( \frac{2}{4} = \frac{1}{2} \)
  • \( \frac{3}{6} = \frac{1}{2} \)
  • \( \frac{4}{8} = \frac{1}{2} \)
  • \( \frac{5}{10} = \frac{1}{2} \)
  • \( \frac{1}{3} \) remains as \( \frac{1}{3} \)
Step 3: Compare Simplified Ratios

The simplified ratios are: \[ \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{2}, \frac{1}{3} \] The ratios \( (2, 4), (3, 6), (4, 8), (5, 10) \) all simplify to \( \frac{1}{2} \), indicating they are equivalent. The ratio \( (1, 3) \) simplifies to \( \frac{1}{3} \) and is not equivalent to the others.

Step 4: List Equivalent Ratios

The equivalent ratios identified are:

  • \( (2, 4) \) and \( (3, 6) \)
  • \( (2, 4) \) and \( (4, 8) \)
  • \( (2, 4) \) and \( (5, 10) \)
  • \( (3, 6) \) and \( (4, 8) \)
  • \( (3, 6) \) and \( (5, 10) \)
  • \( (4, 8) \) and \( (5, 10) \)

Final Answer

The equivalent ratios are: \[ \boxed{((2, 4), (3, 6)), ((2, 4), (4, 8)), ((2, 4), (5, 10)), ((3, 6), (4, 8)), ((3, 6), (5, 10)), ((4, 8), (5, 10))} \]

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