Determine if the given ratios are proportional by answering 'yes' or 'no'.

Let's solve each pair of ratios to determine if they are proportional. Two ratios are proportional if their simplified forms are equal, or if the cross products are equal.

We'll go through each pair one by one.

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1. 5 : 15 and 10 : 30

Simplify both:
- 5:15 → divide both by 5 → 1:3
- 10:30 → divide both by 10 → 1:3

✔ Both simplify to 1:3 → Yes, they are proportional.

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2. 16 : 4 and 25 : 5

Simplify both:
- 16:4 → divide by 4 → 4:1
- 25:5 → divide by 5 → 5:1

4:1 ≠ 5:1 → ✘ No, not proportional.

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3. 10 : 15 and 20 : 25

Simplify both:
- 10:15 → divide by 5 → 2:3
- 20:25 → divide by 5 → 4:5

2:3 ≠ 4:5 → ✘ No, not proportional.

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4. 20 : 60 and 30 : 90

Simplify both:
- 20:60 → divide by 20 → 1:3
- 30:90 → divide by 30 → 1:3

✔ Both simplify to 1:3 → Yes, proportional.

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5. 5 : 10 and 100 : 300

Simplify both:
- 5:10 → divide by 5 → 1:2
- 100:300 → divide by 100 → 1:3

1:2 ≠ 1:3 → ✘ No, not proportional.

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6. 12 : 10 and 24 : 20

Simplify both:
- 12:10 → divide by 2 → 6:5
- 24:20 → divide by 4 → 6:5

✔ Both simplify to 6:5 → Yes, proportional.

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✔ Final Answers:

1. Yes
2. No
3. No
4. Yes
5. No
6. Yes

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✔ Answer Key (in order):

Yes, No, No, Yes, No, Yes