Select all ratios equivalent to 5:15.
Understand the Problem
The question is asking to identify which of the given ratios are equivalent to the ratio 5:15. This involves finding ratios that simplify to the same value as 5:15, which is 1:3.
Answer
The equivalent ratio is \(6:18\).
Answer for screen readers
The only ratio equivalent to (5:15) is (6:18).
Steps to Solve
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Understand the original ratio
The original ratio is (5:15). We need to simplify this ratio to its simplest form.
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Simplify the original ratio
Divide both numbers in the ratio (5:15) by their greatest common divisor (GCD), which is 5:
[ \frac{5}{5} : \frac{15}{5} = 1 : 3 ]
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Examine the given ratios
We need to check if the other ratios simplify to (1:3):
- For (6:18), simplify it by dividing both terms by 6:
[ \frac{6}{6} : \frac{18}{6} = 1 : 3 ]
- For (18:21), simplify it by dividing both terms by 3:
[ \frac{18}{3} : \frac{21}{3} = 6 : 7 \quad (\text{not } 1:3) ]
- For (2:3), it is already in simplest form (2:3) (not equivalent).
- For (3:5), it is also in simplest form (3:5) (not equivalent).
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Identify equivalent ratios
The only ratio that simplifies to (1:3) is (6:18).
The only ratio equivalent to (5:15) is (6:18).
More Information
The ratio (5:15) simplifies to (1:3). Therefore, any ratio that reduces to (1:3) is considered equivalent. The GCD is essential for simplifying ratios.
Tips
- Forgetting to simplify a ratio to its simplest form before comparing.
- Not recognizing that some ratios may appear similar but do not simplify to the same value.
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