Answer :
To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], you need to find the greatest common divisor (GCD) of the numerator and the denominator. Here's a step-by-step explanation:
1. Identify the numerator and the denominator of the fraction. Here, the numerator is 24, and the denominator is 30.
2. Find the GCD of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.
- Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
- The common factors are: 1, 2, 3, 6
- The greatest common factor is 6.
3. Divide both the numerator and the denominator by their GCD (which is 6 in this case):
[tex]\[
\frac{24}{6} = 4
\][/tex]
[tex]\[
\frac{30}{6} = 5
\][/tex]
4. The simplified form of the fraction [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
So, the correct answer is:
C. [tex]\(\frac{4}{5}\)[/tex]
1. Identify the numerator and the denominator of the fraction. Here, the numerator is 24, and the denominator is 30.
2. Find the GCD of the numerator and the denominator. The GCD is the largest number that divides both numbers without leaving a remainder.
- Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
- The common factors are: 1, 2, 3, 6
- The greatest common factor is 6.
3. Divide both the numerator and the denominator by their GCD (which is 6 in this case):
[tex]\[
\frac{24}{6} = 4
\][/tex]
[tex]\[
\frac{30}{6} = 5
\][/tex]
4. The simplified form of the fraction [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex].
So, the correct answer is:
C. [tex]\(\frac{4}{5}\)[/tex]
