Question

Select all ratios equivalent to 9:15.
6:10
12:20
27:45

Answer 1

To determine which ratios are equivalent to 9:15, we can simplify 9:15 first.

1. **Simplifying 9:15:**
- The greatest common divisor (GCD) of 9 and 15 is 3.
- Divide both terms by 3:
- 9 ÷ 3 = 3
- 15 ÷ 3 = 5
- Therefore, 9:15 simplifies to 3:5.

Now, let's simplify the other ratios:

2. **Simplifying 6:10:**
- The GCD of 6 and 10 is 2.
- Divide both terms by 2:
- 6 ÷ 2 = 3
- 10 ÷ 2 = 5
- So, 6:10 simplifies to 3:5.

3. **Simplifying 12:20:**
- The GCD of 12 and 20 is 4.
- Divide both terms by 4:
- 12 ÷ 4 = 3
- 20 ÷ 4 = 5
- So, 12:20 simplifies to 3:5.

4. **Simplifying 27:45:**
- The GCD of 27 and 45 is 9.
- Divide both terms by 9:
- 27 ÷ 9 = 3
- 45 ÷ 9 = 5
- So, 27:45 simplifies to 3:5.

**Conclusion:**
All the ratios given (6:10, 12:20, and 27:45) are equivalent to 9:15 since they all simplify to 3:5.