pick all correct statements

Question

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