Question

1. which ratio is equivalent to 10:15?

a. 3:2
b. 5:3
c. 2:3
d. 15:10

Explanation:

Step1: Simplify 10:15

To simplify a ratio, divide both terms by their greatest common divisor (GCD). The GCD of 10 and 15 is 5. So, divide 10 and 15 by 5: $\frac{10}{5}:\frac{15}{5}=2:3$? Wait, no, wait. Wait, 10 ÷ 5 = 2, 15 ÷ 5 = 3? Wait, no, the ratio is 10:15. Wait, maybe I made a mistake. Wait, let's check the options. Wait, the question is which ratio is equivalent to 10:15. Let's simplify 10:15. The GCD of 10 and 15 is 5. So divide both by 5: 10 ÷ 5 = 2, 15 ÷ 5 = 3? Wait, no, 10:15 simplifies to 2:3? Wait, but let's check the options. Option C is 2:3? Wait, no, wait the options are A. 3:2, B.5:3, C.2:3, D.15:10. Wait, 10:15 can be simplified by dividing both by 5: 10/5 = 2, 15/5 = 3, so 2:3. So the equivalent ratio is 2:3, which is option C? Wait, no, wait maybe I messed up. Wait, 10:15, if we divide both by 5, we get 2:3. So option C is 2:3. Wait, but let's check other options. Option D is 15:10, which is the reciprocal. Option A is 3:2, reciprocal. Option B is 5:3, which is not. So the correct answer is C. 2:3. Wait, but let's recheck. 10:15 = (10÷5):(15÷5) = 2:3. Yes. So the equivalent ratio is 2:3, which is option C.

Step2: Verify each option

• Option A: 3:2. Is 10:15 equal to 3:2? Cross-multiply: 10×2 = 20, 15×3 = 45. 20≠45, so not equivalent.
• Option B: 5:3. Cross-multiply: 10×3 = 30, 15×5 = 75. 30≠75, not equivalent.
• Option C: 2:3. Cross-multiply: 10×3 = 30, 15×2 = 30. 30=30, so equivalent.
• Option D: 15:10. Cross-multiply: 10×10 = 100, 15×15 = 225. 100≠225, not equivalent.

Answer:

C. 2:3