Select all ratios equivalent to 3:1.
Understand the Problem
The question is asking to identify which of the given ratios are equivalent to the ratio 3:1. To solve this, we will check if each ratio can be simplified to match 3:1.
Answer
The ratio equivalent to $3:1$ is $21:7$.
Answer for screen readers
The ratios equivalent to $3:1$ are $21:7$.
Steps to Solve
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Identify the target ratio The target ratio is $3:1$. It can also be expressed as a fraction, which is $\frac{3}{1}$.
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Simplify each given ratio to determine equivalence
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For the ratio $5:10$: Simplifying the ratio: $$ \frac{5}{10} = \frac{1}{2} $$ This is not equivalent to $3:1$.
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For the ratio $10:3$: Simplifying the ratio: $$ \frac{10}{3} \text{ (which cannot be simplified further)} $$ This is not equivalent to $3:1$.
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For the ratio $21:7$: Simplifying the ratio: $$ \frac{21}{7} = 3 $$ This can be expressed as $3:1$, which is equivalent to the target ratio.
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Conclusion about the equivalences Based on the simplifications, the only ratio equivalent to $3:1$ is $21:7$.
The ratios equivalent to $3:1$ are $21:7$.
More Information
In the context of ratios, equivalent ratios maintain the same relationship between the two numbers. In this case, $21:7$ simplifies to $3:1$.
Tips
- Misunderstanding the simplification process; always ensure to divide both terms of the ratio by their greatest common divisor (GCD).
