Select all ratios equivalent to 5:15.
Understand the Problem
The question is asking to identify which of the provided ratios are equivalent to the ratio 5:15. To solve this, we need to simplify the given ratios and compare them with the simplified form of 5:15.
Answer
The ratios equivalent to $5:15$ are $2:6$ and $3:9$.
Answer for screen readers
The ratios equivalent to $5:15$ are $2:6$ and $3:9$.
Steps to Solve
- Simplify the original ratio
First, simplify the ratio $5:15$. To simplify, divide both parts by their greatest common divisor (GCD), which is $5$.
$$ \frac{5}{5} : \frac{15}{5} = 1:3 $$
- Simplify the first ratio (2:6)
Next, simplify the ratio $2:6$. The GCD of $2$ and $6$ is $2$.
$$ \frac{2}{2} : \frac{6}{2} = 1:3 $$
- Simplify the second ratio (1:5)
Now, look at the ratio $1:5$. Since there is no common factor, it stays the same.
$$ 1:5 $$
- Simplify the third ratio (3:9)
Finally, simplify the ratio $3:9$. The GCD of $3$ and $9$ is $3$.
$$ \frac{3}{3} : \frac{9}{3} = 1:3 $$
- Compare all simplified ratios
Now compare all the simplified ratios to the simplified form of $5:15$ (which is $1:3$).
- $2:6$ simplifies to $1:3$ (equivalent)
- $1:5$ does not simplify to $1:3$ (not equivalent)
- $3:9$ simplifies to $1:3$ (equivalent)
The ratios equivalent to $5:15$ are $2:6$ and $3:9$.
More Information
The ratio $5:15$ simplifies to $1:3$, which means that for every 1 part of the first quantity, there are 3 parts of the second quantity. Ratios can often be simplified by finding their greatest common divisor.
Tips
- Forgetting to simplify the ratios can lead to incorrect comparisons.
- Miscalculating the GCD can result in incorrect simplification.
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