Simplify each ratio completely in Columns A and B.

Let's solve each ratio in Column A and Column B by simplifying them completely. We'll reduce each ratio to its simplest form by dividing both numbers by their greatest common divisor (GCD).

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✔ Column A

1) 3 : 15
GCD of 3 and 15 is 3
→ $ \frac{3}{3} : \frac{15}{3} = 1 : 5 $

2) 16 to 12
GCD of 16 and 12 is 4
→ $ \frac{16}{4} : \frac{12}{4} = 4 : 3 $

3) 10 : 30
GCD of 10 and 30 is 10
→ $ \frac{10}{10} : \frac{30}{10} = 1 : 3 $

4) 4 to 18
GCD of 4 and 18 is 2
→ $ \frac{4}{2} : \frac{18}{2} = 2 : 9 $

5) 12 to 32
GCD of 12 and 32 is 4
→ $ \frac{12}{4} : \frac{32}{4} = 3 : 8 $

6) 72 / 27
This is a fraction, but we treat it as a ratio: $ 72 : 27 $
GCD of 72 and 27 is 9
→ $ \frac{72}{9} : \frac{27}{9} = 8 : 3 $

7) 45 / 15
$ 45 : 15 $
GCD is 15
→ $ \frac{45}{15} : \frac{15}{15} = 3 : 1 $

8) 36 : 24
GCD of 36 and 24 is 12
→ $ \frac{36}{12} : \frac{24}{12} = 3 : 2 $

9) 16 to 64
GCD of 16 and 64 is 16
→ $ \frac{16}{16} : \frac{64}{16} = 1 : 4 $

10) 17 / 34
$ 17 : 34 $
GCD is 17
→ $ \frac{17}{17} : \frac{34}{17} = 1 : 2 $

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✔ Column B

1) 4 to 20
GCD of 4 and 20 is 4
→ $ \frac{4}{4} : \frac{20}{4} = 1 : 5 $

2) 8 : 6
GCD of 8 and 6 is 2
→ $ \frac{8}{2} : \frac{6}{2} = 4 : 3 $

3) 8 : 24
GCD of 8 and 24 is 8
→ $ \frac{8}{8} : \frac{24}{8} = 1 : 3 $

4) 3 : 6
GCD of 3 and 6 is 3
→ $ \frac{3}{3} : \frac{6}{3} = 1 : 2 $

5) 15 to 40
GCD of 15 and 40 is 5
→ $ \frac{15}{5} : \frac{40}{5} = 3 : 8 $

6) 32 / 12
$ 32 : 12 $
GCD of 32 and 12 is 4
→ $ \frac{32}{4} : \frac{12}{4} = 8 : 3 $

7) 60 : 20
GCD of 60 and 20 is 20
→ $ \frac{60}{20} : \frac{20}{20} = 3 : 1 $

8) 4 : 6
GCD of 4 and 6 is 2
→ $ \frac{4}{2} : \frac{6}{2} = 2 : 3 $

9) 25 to 100
GCD of 25 and 100 is 25
→ $ \frac{25}{25} : \frac{100}{25} = 1 : 4 $

10) 18 / 28
$ 18 : 28 $
GCD of 18 and 28 is 2
→ $ \frac{18}{2} : \frac{28}{2} = 9 : 14 $

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✔ Final Simplified Ratios

#### Column A
1) 1 : 5
2) 4 : 3
3) 1 : 3
4) 2 : 9
5) 3 : 8
6) 8 : 3
7) 3 : 1
8) 3 : 2
9) 1 : 4
10) 1 : 2

#### Column B
1) 1 : 5
2) 4 : 3
3) 1 : 3
4) 1 : 2
5) 3 : 8
6) 8 : 3
7) 3 : 1
8) 2 : 3
9) 1 : 4
10) 9 : 14

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🔄 Observation:

Some ratios are identical between the two columns:
- 1) 1:5
- 2) 4:3
- 3) 1:3
- 5) 3:8
- 6) 8:3
- 7) 3:1
- 9) 1:4

But others differ (e.g., Column A has 2:9 and 3:2, while Column B has 1:2 and 2:3).

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✔ Answer Summary:
All ratios have been simplified completely using GCDs. The final answers are listed above.