PA_M3_S2_T4_Prime Factoring Fractions Transcript
One of the things that we always want to do with fractions is to write
them in their most reduced or lowest form. In order to do that the
easiest thing to do is to write the numerator and the denominator as a
set of prime factors. So we're going to start with that, and rewrite
these two fractions so that the numerator is all prime factors and so is
the denominator.
The prime factors of 12 are 2*2*3 because 12 is 4*3 and 4 can factor to
2*2, so those are all prime numbers, 2*2*3. In the denominator I have
3*5, 3 and 5 are prime and the product of 3 and 5 is 15.
By being able to write these things in factored form like this, I'm able
to recognize when I have a common factors in both the top and bottom.
Let's factor this next one, 70/144. I want to follow the same technique.
My prime factors of 70 are 2*5*7, and the prime factors of 144 are
2*2*2*2*3*3, and once again, by using this prime factorization technique,
I can identify when I have two factors that are common to both the top
and bottom.
This is how we're going to approach reducing our fractions to lowest
terms, but for now we want to just practice with writing each of my
numerators and denominators in their fully factored form using prime
factorization.