To simplify the fraction [tex]\( \frac{12}{15} \)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator and then divide both by this GCD.
Step-by-step process:
1. Identify the numerator and the denominator:
- Numerator: [tex]\(12\)[/tex]
- Denominator: [tex]\(15\)[/tex]
2. Find the GCD of 12 and 15:
- The divisors of 12 are: [tex]\(1, 2, 3, 4, 6, 12\)[/tex]
- The divisors of 15 are: [tex]\(1, 3, 5, 15\)[/tex]
- The common divisors are: [tex]\(1\)[/tex] and [tex]\(3\)[/tex]
- The greatest common divisor is [tex]\(3\)[/tex]
3. Divide both the numerator and the denominator by the GCD:
- Divide the numerator (12) by the GCD (3): [tex]\( \frac{12}{3} = 4 \)[/tex]
- Divide the denominator (15) by the GCD (3): [tex]\( \frac{15}{3} = 5 \)[/tex]
4. Write the simplified fraction:
- The simplified form of [tex]\( \frac{12}{15} \)[/tex] is [tex]\( \frac{4}{5} \)[/tex]
Therefore, the fraction [tex]\( \frac{12}{15} \)[/tex] simplifies to [tex]\( \frac{4}{5} \)[/tex].
