Question

1. are these ratios equivalent?

9 girls to 12 boys
3 girls to 4 boys
yes
no

1. are these ratios equivalent?

4 red bottles to 16 blue bottles
5 red bottles to 15 blue bottles
yes

Explanation:

Question 1

Step1: Simplify the first ratio

The ratio of girls to boys is \( 9:12 \). We can simplify this ratio by dividing both numbers by their greatest common divisor, which is 3. So, \( \frac{9}{3}:\frac{12}{3} = 3:4 \).

Step2: Compare with the second ratio

The second ratio is \( 3:4 \). Since the simplified form of the first ratio is the same as the second ratio, they are equivalent.

Step1: Simplify the first ratio

The ratio of red bottles to blue bottles is \( 4:16 \). Divide both numbers by their greatest common divisor, which is 4. So, \( \frac{4}{4}:\frac{16}{4} = 1:4 \).

Step2: Simplify the second ratio

The ratio of red bottles to blue bottles is \( 5:15 \). Divide both numbers by their greatest common divisor, which is 5. So, \( \frac{5}{5}:\frac{15}{5} = 1:3 \).

Step3: Compare the two simplified ratios

The first simplified ratio is \( 1:4 \) and the second is \( 1:3 \). Since \( 1:4
eq 1:3 \), the ratios are not equivalent.

Answer:

Yes

Question 2