Question
Are these ratios equivalent? How do you know?
8/24 and 10/30
8/24 and 10/30
Answers
GPT-4o mini
To determine if the ratios \( \frac{8}{24} \) and \( \frac{10}{30} \) are equivalent, we can simplify both fractions.
Starting with \( \frac{8}{24} \):
1. Find the greatest common divisor (GCD) of 8 and 24, which is 8.
2. Divide both the numerator and the denominator by their GCD:
\[
\frac{8 \div 8}{24 \div 8} = \frac{1}{3}
\]
Now, simplify \( \frac{10}{30} \):
1. The GCD of 10 and 30 is 10.
2. Divide both the numerator and the denominator by their GCD:
\[
\frac{10 \div 10}{30 \div 10} = \frac{1}{3}
\]
Since both \( \frac{8}{24} \) and \( \frac{10}{30} \) simplify to \( \frac{1}{3} \), the two ratios are equivalent.
Therefore, \( \frac{8}{24} \) and \( \frac{10}{30} \) are indeed equivalent ratios.
Starting with \( \frac{8}{24} \):
1. Find the greatest common divisor (GCD) of 8 and 24, which is 8.
2. Divide both the numerator and the denominator by their GCD:
\[
\frac{8 \div 8}{24 \div 8} = \frac{1}{3}
\]
Now, simplify \( \frac{10}{30} \):
1. The GCD of 10 and 30 is 10.
2. Divide both the numerator and the denominator by their GCD:
\[
\frac{10 \div 10}{30 \div 10} = \frac{1}{3}
\]
Since both \( \frac{8}{24} \) and \( \frac{10}{30} \) simplify to \( \frac{1}{3} \), the two ratios are equivalent.
Therefore, \( \frac{8}{24} \) and \( \frac{10}{30} \) are indeed equivalent ratios.