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What is the simplified form of the fraction below?

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

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

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) and then divide both by that number.

1. Find the GCD of 24 and 30:
- The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
- The common factors of 24 and 30 are: 1, 2, 3, 6
- The greatest common factor is 6.

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

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

Therefore, the correct answer is option B: [tex]\(\frac{4}{5}\)[/tex].

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