Answer :
To simplify the fraction [tex]\(\frac{24}{30}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator, which will help us reduce the fraction to its simplest form.
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 are: 1, 2, 3, 6.
- The greatest common divisor is 6.
2. Divide both numerator and denominator by the GCD:
- Divide the numerator (24) by the GCD (6): [tex]\( \frac{24}{6} = 4 \)[/tex].
- Divide the denominator (30) by the GCD (6): [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 are: 1, 2, 3, 6.
- The greatest common divisor is 6.
2. Divide both numerator and denominator by the GCD:
- Divide the numerator (24) by the GCD (6): [tex]\( \frac{24}{6} = 4 \)[/tex].
- Divide the denominator (30) by the GCD (6): [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.
