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What is the simplified form of the fraction below?

[tex]\[\frac{24}{30}\][/tex]

A. [tex]\[\frac{5}{6}\][/tex]

B. [tex]\[\frac{2}{3}\][/tex]

C. [tex]\[\frac{4}{5}\][/tex]

D. [tex]\[\frac{3}{4}\][/tex]

Answer :

To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], you should look for the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.

1. Identify the Factors:
- Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

2. Find the Greatest Common Divisor (GCD):
- Common factors of 24 and 30 are: 1, 2, 3, 6
- The greatest of these common factors is 6.

3. Divide Both Numerator and Denominator by the GCD:
- [tex]\(\frac{24}{30} = \frac{24 \div 6}{30 \div 6} = \frac{4}{5}\)[/tex]

So, the simplified form of the fraction [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].

Thus, the answer is option C: [tex]\(\frac{4}{5}\)[/tex].

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