Question

Are the ratios 1:2 and 7:14 equivalent?

Answer 1

does 1/2 = 7/14 ?

Answer 2

hby87

Answer 3

[AI-generated answer — Explain Bot]

To determine whether the ratios 1:2 and 7:14 are equivalent, we need to compare them to see if they represent the same relationship between quantities. A ratio is equivalent to another ratio if the two ratios are proportional, meaning they have the same value when simplified.

To simplify a ratio, we find the greatest common divisor (GCD) of its terms and then divide both terms by the GCD. Let's simplify the ratios 1:2 and 7:14.

For the ratio 1:2, the GCD of 1 and 2 is 1. Divide both terms by 1: 1 ÷ 1 = 1, and 2 ÷ 1 = 2. Therefore, the simplified form of 1:2 is 1:2.

For the ratio 7:14, the GCD of 7 and 14 is 7. Divide both terms by 7: 7 ÷ 7 = 1, and 14 ÷ 7 = 2. Therefore, the simplified form of 7:14 is 1:2.

Since both ratios simplify to 1:2, they are indeed equivalent.