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What is the simplified form of the fraction below?

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

A. [tex]\frac{2}{3}[/tex]
B. [tex]\frac{3}{4}[/tex]
C. [tex]\frac{4}{5}[/tex]
D. [tex]\frac{5}{6}[/tex]

Answer :

To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator (24) and the denominator (30). The GCD is the largest number that divides both numbers evenly.

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

2. Identify the common factors:
- The common factors are 1, 2, 3, and 6.

3. Select the greatest common factor:
- The greatest common divisor is 6.

4. Divide both the numerator and the denominator by the GCD:
- Simplified numerator: [tex]\( \frac{24}{6} = 4 \)[/tex]
- Simplified denominator: [tex]\( \frac{30}{6} = 5 \)[/tex]

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

So, the correct choice is D. [tex]\(\frac{4}{5}\)[/tex].

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