Which ratio is equivalent to the ratio \( 2: 5 \) ?

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!