Answer :
Sure! To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], we need to find a number that divides both the numerator (24) and the denominator (30) without leaving a remainder. This number is known as the greatest common divisor (GCD).
1. Find the GCD of 24 and 30:
- The divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
- The divisors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
- The common divisors of 24 and 30 are: 1, 2, 3, 6.
- The greatest common divisor is 6.
2. Simplify the fraction by dividing by the GCD:
- Divide the numerator by the GCD: [tex]\(\frac{24}{6} = 4\)[/tex].
- Divide the denominator by the GCD: [tex]\(\frac{30}{6} = 5\)[/tex].
3. Write the simplified fraction:
- So, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
Therefore, the simplified form of [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex], which corresponds to option C.
1. Find the GCD of 24 and 30:
- The divisors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24.
- The divisors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
- The common divisors of 24 and 30 are: 1, 2, 3, 6.
- The greatest common divisor is 6.
2. Simplify the fraction by dividing by the GCD:
- Divide the numerator by the GCD: [tex]\(\frac{24}{6} = 4\)[/tex].
- Divide the denominator by the GCD: [tex]\(\frac{30}{6} = 5\)[/tex].
3. Write the simplified fraction:
- So, [tex]\(\frac{24}{30}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].
Therefore, the simplified form of [tex]\(\frac{24}{30}\)[/tex] is [tex]\(\frac{4}{5}\)[/tex], which corresponds to option C.
