When simplifying a rational fraction, why do you need to factor the numerator and the denominator?
If there is a common factor in both the numerator and denominator, that factor will cancel, thus simplifying the fraction.
e.g.
15/18 = (3*5)/3*6)
=(3/3)*(5/6)
=(1)*5/6
=5/6
When simplifying a rational fraction, we factor the numerator and the denominator to see if there are any common factors. If there is a common factor between the numerator and denominator, we can cancel out that factor and simplify the fraction.
To factor a number, we break it down into its prime factors. For example, to factorize 18, we can break it down into 2 * 3 * 3. Similarly, to factorize 15, we can break it down into 3 * 5.
In the case of the fraction 15/18, we can factorize both the numerator and denominator. The numerator factors into 3 * 5 and the denominator factors into 3 * 3 * 2. We can see that there is a common factor of 3 between the numerator and denominator.
By canceling out the common factor of 3, we simplify the fraction to (3/3) * (5/6), which equals 1 * (5/6), and finally 5/6.
Factoring the numerator and denominator helps us identify any common factors that can be canceled out, leading to a simplified form of the fraction.