How do you simplify fractions by using factor trees?

Answer 1

The idea is to eliminate common factors. Let me show you an example (start with a fraction, then show all the factors for numerator and denominator, then eliminate common factors - in the example, 2 and 5):

20 / 30 = (2 x 2 x 5) / (2 x 3 x 5) = 2 / 3

It is often faster not to do the complete factorization, but to find common factors. IN the above example, it is obvious that both are divisible by 10, so you can immeidately divide both by 10. If numerator and denominator are both even, divide both by 2; if both end with 5 or 0, divide both by 5. So, just see whether there are small factors in common (at least 2, 3, 5, and 7), and simplify, before doing the complete factorization.

There are a few other situations where you can avoid complete factorization - for example, you can't simplify a fraction:

• If there is a difference of 1 between numerator and denominator.
• If the numerator is 1.
• If one of the two (numerator vs. denominator) is a Prime number, and the other isn't divisi9ble by that prime number.