Question

Are the given two ratios equivalent?

1. 12 large sweaters for every 18 small sweaters.
2. 8 large sweaters for every 12 small sweaters.

a. Yes
b. No

Answer 1

By simplifying both ratios to their lowest terms, we find that the ratios 12:18 and 8:12 both reduce to 2:3, which means they are equivalent. Therefore, the answer is yes, the two ratios are equivalent.

Step-by-step explanation:

To determine if the given two ratios are equivalent, we need to compare them by simplifying them to their lowest terms or finding a common multiplier that allows us to compare them directly. The two ratios given are:

• 12 large sweaters for every 18 small sweaters
• 8 large sweaters for every 12 small sweaters

We can simplify both ratios by dividing both the numerator and the denominator of each ratio by their greatest common divisor (GCD). For the first ratio, the GCD of 12 and 18 is 6, so we can simplify it as follows: 12/18 = 2/3. For the second ratio, the GCD of 8 and 12 is 4, so we can simplify that ratio as follows: 8/12 = 2/3. Since both simplified ratios equal to 2/3, the answer is:

a. Yes, the given two ratios are equivalent.