Answer:
Explanation:
Step 1: Write the prime factors of the numerator and denominator.
The prime factors of 105 are 3, 5, and 7.
The prime factors of 126 are 2, 3, 3, and 7.
Step 2: Reorder and regroup the factors.
We can reorder the factors so that the common factors are next to each other.
105 = 3 x 5 x 7
126 = 2 x 3 x 3 x 7
Step 3: Make as many factors of 1 as possible.
We can make a factor of 1 by dividing both the numerator and denominator by the common factors.
In this case, the common factors are 3 and 7.
We divide both the numerator and denominator by 3 x 7 = 21.
105/126 = (3 x 5 x 7)/(2 x 3 x 3 x 7)
105/126 = (5)/(2 x 3)
105/126 = 5/6
Step 4: Simplify using the multiplicative identity.
The multiplicative identity states that any number multiplied by 1 is equal to itself.
We can use the multiplicative identity to write the fraction as an equivalent fraction with a denominator of 1.
5/6 = (5/6) x (1/1)
5/6 = 5/6