Use the table to answer the question.

Question

Simplify to prove each ratio is equivalent.
2/10= , 6/30=, 10/50=, 12/60

Answer 1

To prove that the ratios \( \frac{2}{10} \), \( \frac{6}{30} \), \( \frac{10}{50} \), and \( \frac{12}{60} \) are equivalent, we can simplify each fraction.

1. Simplifying \( \frac{2}{10} \): \[ \frac{2}{10} = \frac{2 \div 2}{10 \div 2} = \frac{1}{5} \]

2. Simplifying \( \frac{6}{30} \): \[ \frac{6}{30} = \frac{6 \div 6}{30 \div 6} = \frac{1}{5} \]

3. Simplifying \( \frac{10}{50} \): \[ \frac{10}{50} = \frac{10 \div 10}{50 \div 10} = \frac{1}{5} \]

4. Simplifying \( \frac{12}{60} \): \[ \frac{12}{60} = \frac{12 \div 12}{60 \div 12} = \frac{1}{5} \]

After simplifying each fraction, we find that all of them reduce to \( \frac{1}{5} \).

Thus, the ratios \( \frac{2}{10} \), \( \frac{6}{30} \), \( \frac{10}{50} \), and \( \frac{12}{60} \) are equivalent.