Select all ratios equivalent to 12:18.
Understand the Problem
The question is asking to identify which of the given ratios (8:12, 18:27, 36:54) are equivalent to the ratio 12:18. We will determine this by simplifying the ratios and comparing them.
Answer
$8:12$, $18:27$, $36:54$
Answer for screen readers
The ratios equivalent to $12:18$ are $8:12$, $18:27$, and $36:54$.
Steps to Solve
- Simplifying the given ratio 12:18
First, we simplify the ratio $12:18$ by dividing both numbers by their greatest common divisor (GCD), which is $6$.
$$ \frac{12 \div 6}{18 \div 6} = \frac{2}{3} $$
So, the simplified form of $12:18$ is $2:3$.
- Simplifying the ratio 8:12
Next, we simplify the ratio $8:12$. The GCD of $8$ and $12$ is $4$.
$$ \frac{8 \div 4}{12 \div 4} = \frac{2}{3} $$
This simplification shows that $8:12 = 2:3$.
- Simplifying the ratio 18:27
Now we simplify the ratio $18:27$. The GCD of $18$ and $27$ is $9$.
$$ \frac{18 \div 9}{27 \div 9} = \frac{2}{3} $$
Thus, $18:27 = 2:3$ as well.
- Simplifying the ratio 36:54
Finally, we simplify the ratio $36:54$. The GCD of $36$ and $54$ is $18$.
$$ \frac{36 \div 18}{54 \div 18} = \frac{2}{3} $$
This means $36:54 = 2:3$.
- Conclusion
All the simplified ratios ($8:12$, $18:27$, and $36:54$) equal $2:3$, which means they are all equivalent to $12:18$.
The ratios equivalent to $12:18$ are $8:12$, $18:27$, and $36:54$.
More Information
All the ratios were simplified to $2:3$, showing they share a common proportion. Understanding the GCD is essential for simplifying ratios.
Tips
- Confusing the initial ratio with the simplified ratio.
- Forgetting to check if both parts of each ratio can be simplified equally.
- Not finding the correct GCD to simplify the ratios.
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