When simplifying a rational fraction, why do you need to factor the numerator and the denominator? Include two examples!

if the top and bottom have a common factor, it can be eliminated to make the fraction simpler.

6/10 = 2*3 / 2*5 = 3/5

Did you know?

Did you know that when simplifying a rational fraction, you need to factor both the numerator and the denominator? Factoring allows us to simplify the fraction by identifying common factors and canceling them out. This simplification is crucial to finding the simplest form of the fraction. For example, let's consider the fraction 12/18. By factoring the numerator (12) and the denominator (18), we can see that both numbers have a common factor of 6. After canceling out this common factor, we get the simplified form of the fraction: 2/3. Similarly, let's look at the fraction 16/24. By factoring both the numerator (16) and denominator (24), we can identify the common factor of 8. Canceling out this common factor gives us the simplified form of the fraction: 2/3. So, remember to factor the numerator and the denominator while simplifying rational fractions to find the simplest form!