Question

Are these ratios equivalent? 65 cookies for every 30 brownies 13 cookies for every 6 brownies

Answer 1

To determine if the ratios \( \frac{65 \text{ cookies}}{30 \text{ brownies}} \) and \( \frac{13 \text{ cookies}}{6 \text{ brownies}} \) are equivalent, we can simplify both ratios.

1. **Simplifying the first ratio** \( \frac{65}{30} \):
- Find the greatest common divisor (GCD) of 65 and 30. The GCD is 5.
- Divide both the numerator and denominator by 5:
\[
\frac{65 \div 5}{30 \div 5} = \frac{13}{6}
\]

2. **The second ratio** is already \( \frac{13}{6} \).

Since both ratios simplify to \( \frac{13}{6} \), they are equivalent. Thus, **yes**, the ratios \( 65 \text{ cookies for every } 30 \text{ brownies} \) and \( 13 \text{ cookies for every } 6 \text{ brownies} \) are equivalent.