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Answer :
To express the fraction [tex]\( \frac{24}{30} \)[/tex] in its lowest terms, follow these steps:
1. Identify the Greatest Common Divisor (GCD):
- First, determine the greatest common divisor of the numerator (24) and the denominator (30). The GCD is the largest number that can divide both numerator and denominator without leaving a remainder.
2. Calculate the GCD:
- 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 largest common factor is 6.
3. Divide the Numerator and Denominator by the GCD:
- Divide both the numerator and the denominator by the GCD (6):
[tex]\[
\text{Numerator: } \frac{24}{6} = 4
\][/tex]
[tex]\[
\text{Denominator: } \frac{30}{6} = 5
\][/tex]
4. Write the Simplified Fraction:
- After dividing, the fraction in lowest terms is [tex]\( \frac{4}{5} \)[/tex].
Thus, the fraction [tex]\( \frac{24}{30} \)[/tex] simplified to its lowest terms is [tex]\( \frac{4}{5} \)[/tex].
1. Identify the Greatest Common Divisor (GCD):
- First, determine the greatest common divisor of the numerator (24) and the denominator (30). The GCD is the largest number that can divide both numerator and denominator without leaving a remainder.
2. Calculate the GCD:
- 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 largest common factor is 6.
3. Divide the Numerator and Denominator by the GCD:
- Divide both the numerator and the denominator by the GCD (6):
[tex]\[
\text{Numerator: } \frac{24}{6} = 4
\][/tex]
[tex]\[
\text{Denominator: } \frac{30}{6} = 5
\][/tex]
4. Write the Simplified Fraction:
- After dividing, the fraction in lowest terms is [tex]\( \frac{4}{5} \)[/tex].
Thus, the fraction [tex]\( \frac{24}{30} \)[/tex] simplified to its lowest terms is [tex]\( \frac{4}{5} \)[/tex].
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