Select all ratios equivalent to 3:6.

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Understand the Problem

The question is asking to identify which of the provided ratios are equivalent to the ratio of 3:6. To solve this, we need to simplify the ratio 3:6 and check if the other ratios can be simplified to the same value.

Answer

The ratios equivalent to $3:6$ are $12:24$ and $7:14$.
Answer for screen readers

The ratios equivalent to $3:6$ are $12:24$ and $7:14$.

Steps to Solve

  1. Simplify the given ratio 3:6

To see which ratios are equivalent, we first simplify the ratio $3:6$.

The simplification is done by dividing both numbers by their greatest common divisor (GCD), which is 3:

$$ \frac{3}{3} : \frac{6}{3} = 1 : 2 $$

Thus, $3:6$ simplifies to $1:2$.

  1. Check the ratio 12:24

Now, we simplify the ratio $12:24$ by finding its GCD, which is 12:

$$ \frac{12}{12} : \frac{24}{12} = 1 : 2 $$

So, $12:24$ is equivalent to $3:6$.

  1. Check the ratio 8:4

Next, we simplify the ratio $8:4$ by finding its GCD, which is 4:

$$ \frac{8}{4} : \frac{4}{4} = 2 : 1 $$

Thus, $8:4$ is not equivalent to $3:6$.

  1. Check the ratio 7:14

Finally, we simplify the ratio $7:14$ by finding its GCD, which is 7:

$$ \frac{7}{7} : \frac{14}{7} = 1 : 2 $$

So, $7:14$ is also equivalent to $3:6$.

The ratios equivalent to $3:6$ are $12:24$ and $7:14$.

More Information

The ratio $3:6$ simplifies to $1:2$. Any ratio that can be simplified to $1:2$ is considered equivalent. Ratios are equivalent when their simplest forms are the same, which is determined by dividing both terms by their GCD.

Tips

  • Not simplifying ratios: Ensure all ratios are simplified to their lowest terms for accurate comparison.
  • Confusing order: Ratios are not interchangeable; the order of numbers matters (e.g., $1:2$ is not the same as $2:1$).
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