Select all ratios equivalent to 5:3.
Understand the Problem
The question is asking for the identification of ratios that are equivalent to the ratio 5:3. This requires finding whether the given options (4:1, 30:18, and 15:9) can be simplified or expressed in the same ratio as 5:3.
Answer
The ratios equivalent to $5:3$ are $30:18$ and $15:9$.
Answer for screen readers
The ratios equivalent to $5:3$ are:
- $30:18$
- $15:9$
Steps to Solve
-
Convert the given ratio to a fraction
Express the ratio $5:3$ as a fraction:
$$ \frac{5}{3} $$ -
Analyze each ratio option
For each ratio given (4:1, 30:18, and 15:9), convert them to fractions. -
Convert 4:1 to a fraction
Convert the ratio $4:1$ as:
$$ \frac{4}{1} $$
Now compare it with $\frac{5}{3}$:
$$ \frac{4}{1} \neq \frac{5}{3} $$ -
Convert 30:18 to a fraction
Convert the ratio $30:18$ as:
$$ \frac{30}{18} $$
Simplify this fraction:
$$ \frac{30}{18} = \frac{5 \times 6}{3 \times 6} = \frac{5}{3} $$
This ratio is equivalent to $5:3$. -
Convert 15:9 to a fraction
Convert the ratio $15:9$ as:
$$ \frac{15}{9} $$
Simplify this fraction:
$$ \frac{15}{9} = \frac{5 \times 3}{3 \times 3} = \frac{5}{3} $$
This ratio is also equivalent to $5:3$.
The ratios equivalent to $5:3$ are:
- $30:18$
- $15:9$
More Information
Ratios are equivalent if, when simplified, they remain the same. In this case, both $30:18$ and $15:9$ simplify to $5:3$, confirming their equivalence.
Tips
- Not simplifying properly: Failing to simplify the fractions may lead to incorrect conclusions about equivalence. Always simplify to their lowest terms before comparison.
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