Select all ratios equivalent to 3:6.
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
- 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 $1:2$.
- 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 $3:6$.
- 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 $3:6$.
- 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 $2:1$).
