Select all ratios equivalent to 1:3.
Understand the Problem
The question is asking to identify whether the ratios 5:15, 4:12, and 6:18 are equivalent to the ratio 1:3. To do this, we need to simplify each ratio and compare them to see if they equal 1:3.
Answer
$5:15$, $4:12$, $6:18$ are all equivalent to $1:3$.
Answer for screen readers
The ratios equivalent to $1:3$ are:
- $5:15$
- $4:12$
- $6:18$
Steps to Solve
- Simplifying the Ratios
We need to simplify each of the given ratios to see if they are equivalent to $1:3$.
- Simplifying Ratio 5:15
For the ratio $5:15$, we divide both parts by their greatest common divisor (GCD), which is 5:
$$ \frac{5}{5} : \frac{15}{5} = 1:3 $$
- Simplifying Ratio 4:12
For the ratio $4:12$, we divide by the GCD, which is 4:
$$ \frac{4}{4} : \frac{12}{4} = 1:3 $$
- Simplifying Ratio 6:18
For the ratio $6:18$, we divide by the GCD, which is 6:
$$ \frac{6}{6} : \frac{18}{6} = 1:3 $$
- Comparison
Now, we compare the simplified ratios:
- $5:15$ simplifies to $1:3$
- $4:12$ simplifies to $1:3$
- $6:18$ simplifies to $1:3$
All three ratios are equivalent to $1:3$.
The ratios equivalent to $1:3$ are:
- $5:15$
- $4:12$
- $6:18$
More Information
All three ratios simplify to $1:3$, demonstrating that each of them maintains the same proportion despite different numerical values. This is a useful concept in various math applications, especially in ratios and proportions.
Tips
- Not simplifying correctly: Always ensure you divide by the GCD. Confirm each simplification step.
- Overlooking equivalent forms: Remember that different ratios can express the same relationship when simplified properly.
