Question

pick all correct statements
select all ratios equivalent to 20:35
60:105
12:21
7:14

Answer 1

To determine which ratios are equivalent to 20:35, we can simplify 20:35 and check if any of the given ratios simplify to the same value.

1. **Simplifying 20:35:**
- Divide both the numerator and denominator by 5:
- \( 20 ÷ 5 = 4 \)
- \( 35 ÷ 5 = 7 \)
- So, \( 20:35 = 4:7 \).

Now, let's simplify each of the given ratios to see if any are equivalent to 4:7:

2. **60:105:**
- Divide both the numerator and denominator by 15:
- \( 60 ÷ 15 = 4 \)
- \( 105 ÷ 15 = 7 \)
- So, \( 60:105 = 4:7 \).

3. **12:21:**
- Divide both the numerator and denominator by 3:
- \( 12 ÷ 3 = 4 \)
- \( 21 ÷ 3 = 7 \)
- So, \( 12:21 = 4:7 \).

4. **7:14:**
- Divide both the numerator and denominator by 7:
- \( 7 ÷ 7 = 1 \)
- \( 14 ÷ 7 = 2 \)
- So, \( 7:14 = 1:2 \), which is not equivalent to \( 4:7 \).

### Conclusion:
The correct statements (ratios equivalent to 20:35) from your list are:

- 60:105
- 12:21