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Which of the following ratios are equivalent to [tex]$6:8$[/tex]?

A. [tex]\frac{15}{20}[/tex]

B. [tex]9:12[/tex]

C. 12 to 16

D. [tex]\frac{36}{40}[/tex]

E. 16 to 24

F. [tex]24:36[/tex]

Answer :

To find which of the given ratios are equivalent to [tex]\(6:8\)[/tex], we'll go through each option and simplify them to see if they match the simplified form of [tex]\(6:8\)[/tex].

First, let's simplify [tex]\(6:8\)[/tex]:
1. Find the greatest common divisor (GCD) of 6 and 8, which is 2.
2. Divide both numbers by the GCD:
- [tex]\(6 \div 2 = 3\)[/tex]
- [tex]\(8 \div 2 = 4\)[/tex]
3. So, the simplified form of [tex]\(6:8\)[/tex] is [tex]\(3:4\)[/tex].

Now, let's check each option one by one:

1. [tex]\(\frac{15}{20}\)[/tex]:
- Simplify [tex]\(\frac{15}{20}\)[/tex]:
- The GCD of 15 and 20 is 5.
- [tex]\(15 \div 5 = 3\)[/tex]
- [tex]\(20 \div 5 = 4\)[/tex]
- So, [tex]\(\frac{15}{20} = \frac{3}{4}\)[/tex], which is equivalent to [tex]\(3:4\)[/tex].

2. [tex]\(9:12\)[/tex]:
- Simplify [tex]\(9:12\)[/tex]:
- The GCD of 9 and 12 is 3.
- [tex]\(9 \div 3 = 3\)[/tex]
- [tex]\(12 \div 3 = 4\)[/tex]
- So, [tex]\(9:12 = 3:4\)[/tex], which is equivalent to [tex]\(3:4\)[/tex].

3. 12 to 16:
- Simplify 12 to 16:
- The GCD of 12 and 16 is 4.
- [tex]\(12 \div 4 = 3\)[/tex]
- [tex]\(16 \div 4 = 4\)[/tex]
- So, 12 to 16 simplifies to 3 to 4, which is equivalent to [tex]\(3:4\)[/tex].

4. [tex]\(\frac{36}{40}\)[/tex]:
- Simplify [tex]\(\frac{36}{40}\)[/tex]:
- The GCD of 36 and 40 is 4.
- [tex]\(36 \div 4 = 9\)[/tex]
- [tex]\(40 \div 4 = 10\)[/tex]
- So, [tex]\(\frac{36}{40} = \frac{9}{10}\)[/tex], which is not equivalent to [tex]\(3:4\)[/tex].

5. 16 to 24:
- Simplify 16 to 24:
- The GCD of 16 and 24 is 8.
- [tex]\(16 \div 8 = 2\)[/tex]
- [tex]\(24 \div 8 = 3\)[/tex]
- So, 16 to 24 simplifies to 2 to 3, which is not equivalent to [tex]\(3:4\)[/tex].

6. [tex]\(24:36\)[/tex]:
- Simplify [tex]\(24:36\)[/tex]:
- The GCD of 24 and 36 is 12.
- [tex]\(24 \div 12 = 2\)[/tex]
- [tex]\(36 \div 12 = 3\)[/tex]
- So, [tex]\(24:36 = 2:3\)[/tex], which is not equivalent to [tex]\(3:4\)[/tex].

Thus, the ratios equivalent to [tex]\(6:8\)[/tex] are [tex]\(\frac{15}{20}\)[/tex], [tex]\(9:12\)[/tex], and 12 to 16.

Thanks for taking the time to read Select all that apply Which of the following ratios are equivalent to tex 6 8 tex A tex frac 15 20 tex B tex 9. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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