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Write the following comparison as a ratio in simplest form using a fraction, a colon (:), and the word "to":

198 cents to 234 cents

A. [tex]\(\frac{11}{13}\)[/tex], 11:13, 11 to 13
B. [tex]\(\frac{13}{11}\)[/tex], 13:11, 13 to 11
C. [tex]\(\frac{198}{234}\)[/tex], 198:234, 198 to 234
D. [tex]\(\frac{11}{234}\)[/tex], 11:234, 11 to 234
E. [tex]\(\frac{234}{198}\)[/tex], 234:198, 234 to 198

Answer :

To express the comparison of 198 cents to 234 cents as a ratio in simplest form, we can break it down into a few steps:

1. Identify the Two Values: We're comparing 198 cents to 234 cents.

2. Find the Greatest Common Divisor (GCD): The GCD is the largest number that divides both values without leaving a remainder. For 198 and 234, the GCD is 18.

3. Simplify the Ratio:
- Divide both values by their GCD to simplify.
- [tex]\( \frac{198}{18} = 11 \)[/tex]
- [tex]\( \frac{234}{18} = 13 \)[/tex]

4. Write the Ratio in Different Formats:
- As a fraction: [tex]\( \frac{11}{13} \)[/tex]
- Using a colon: [tex]\( 11:13 \)[/tex]
- Using the word "to": [tex]\( 11 \text{ to } 13 \)[/tex]

So, the simplest form of the ratio of 198 cents to 234 cents is [tex]\( \frac{11}{13} \)[/tex], [tex]\( 11:13 \)[/tex], or [tex]\( 11 \text{ to } 13 \)[/tex].

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