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].
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].