The problem asks to simplify the fractions $\frac{27}{63}$ and $\frac{36}{42}$.

1. Problem Description

The problem asks to simplify the fractions $\frac{27}{63}$ and $\frac{36}{42}$.

2. Solution Steps

First, we simplify $\frac{27}{63}$.

Find the greatest common divisor (GCD) of 27 and

6

3. The factors of 27 are 1, 3, 9, and

2

7. The factors of 63 are 1, 3, 7, 9, 21, and

6

3. The greatest common divisor of 27 and 63 is

9. Divide both the numerator and the denominator by

9. $\frac{27}{63} = \frac{27 \div 9}{63 \div 9} = \frac{3}{7}$

Next, we simplify $\frac{36}{42}$.

Find the greatest common divisor (GCD) of 36 and

4

2. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and

3

6. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and

4

2. The greatest common divisor of 36 and 42 is

6. Divide both the numerator and the denominator by

6. $\frac{36}{42} = \frac{36 \div 6}{42 \div 6} = \frac{6}{7}$

3. Final Answer

$\frac{27}{63} = \frac{3}{7}$

$\frac{36}{42} = \frac{6}{7}$