Answer :
To simplify the fraction [tex]\(\frac{27}{30}\)[/tex], follow these steps:
1. Identify the Greatest Common Divisor (GCD):
- First, find the greatest common divisor of the numerator (27) and the denominator (30). The GCD is the largest number that can divide both numbers without leaving a remainder.
2. Calculate the GCD of 27 and 30:
- List the factors of each number:
- Factors of 27: 1, 3, 9, 27
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- The common factors are 1 and 3. The greatest common factor is 3.
3. Divide Both Numerator and Denominator by the GCD:
- Divide the numerator and the denominator by the GCD (which is 3).
- [tex]\(\frac{27 \div 3}{30 \div 3} = \frac{9}{10}\)[/tex]
4. Write the Simplified Fraction:
- The fraction [tex]\(\frac{27}{30}\)[/tex] simplifies to [tex]\(\frac{9}{10}\)[/tex].
Therefore, the simplest form of the fraction [tex]\(\frac{27}{30}\)[/tex] is [tex]\(\frac{9}{10}\)[/tex].
1. Identify the Greatest Common Divisor (GCD):
- First, find the greatest common divisor of the numerator (27) and the denominator (30). The GCD is the largest number that can divide both numbers without leaving a remainder.
2. Calculate the GCD of 27 and 30:
- List the factors of each number:
- Factors of 27: 1, 3, 9, 27
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- The common factors are 1 and 3. The greatest common factor is 3.
3. Divide Both Numerator and Denominator by the GCD:
- Divide the numerator and the denominator by the GCD (which is 3).
- [tex]\(\frac{27 \div 3}{30 \div 3} = \frac{9}{10}\)[/tex]
4. Write the Simplified Fraction:
- The fraction [tex]\(\frac{27}{30}\)[/tex] simplifies to [tex]\(\frac{9}{10}\)[/tex].
Therefore, the simplest form of the fraction [tex]\(\frac{27}{30}\)[/tex] is [tex]\(\frac{9}{10}\)[/tex].
