Which ratio is equivalent to the ratio $$ 2: 5 $$ ?

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UpStudy AI · Accepted Answer

An equivalent ratio to $$ 2:5 $$ is any ratio that maintains the same relationship between the two numbers. This means you can multiply or divide both parts of the ratio by the same non-zero number to find an equivalent ratio.

**Examples of Equivalent Ratios to $$ 2:5 $$:**
- **Multiplication:**  
  - $$ 2 \times 2 : 5 \times 2 = 4:10 $$  
  - $$ 2 \times 3 : 5 \times 3 = 6:15 $$  
  - $$ 2 \times 4 : 5 \times 4 = 8:20 $$

- **Division (if both numbers are divisible by the same number):**  
  - If you have a larger ratio like $$ 10:25 $$, you can divide both by 5 to get $$ 2:5 $$.  
  - Similarly, $$ 14:35 $$ divided by 7 becomes $$ 2:5 $$.

**General Method to Find Equivalent Ratios:**
1. **Choose a multiplier (any non-zero number).**
2. **Multiply both terms of the original ratio by this number.**

For instance, choosing a multiplier of 3:
$$ 2 \times 3 : 5 \times 3 = 6:15 $$
So, $$ 6:15 $$ is equivalent to $$ 2:5 $$.

**Key Point:**  
All equivalent ratios maintain the same fraction or division relationship. For $$ 2:5 $$, the relationship is $$ \frac{2}{5} $$. Any ratio that simplifies to $$ \frac{2}{5} $$ when divided by their greatest common divisor (GCD) is equivalent to $$ 2:5 $$.

**Additional Examples:**
- $$ 10:25 $$ (since $$ \frac{10}{25} = \frac{2}{5} $$)
- $$ 16:40 $$ (since $$ \frac{16}{40} = \frac{2}{5} $$)
- $$ 18:45 $$ (since $$ \frac{18}{45} = \frac{2}{5} $$)

Feel free to choose any multiplier or find multiples/divisors to create equivalent ratios based on your specific needs!
Equivalent ratios to $$ 2:5 $$ include $$ 4:10 $$, $$ 6:15 $$, $$ 8:20 $$, and so on.

Which ratio is equivalent to the ratio ?

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