Something New I Learned in 5th Grade!

As you know I have been substitute teaching this school year. I am enjoying it because I learn new things each day! Usually I am learning new ways to better organize my files, or manage behavior, etc. But this week I learned something new in 5th grade math!We all know how to reduce fractions...you find a number that will go into both the numerator and denominator evenly and divide.

Traditional Example:
12
16

normally you would look at this and say 2 or 4 can go into both ofthese numbers evenly. 4 can go into 12 three times and can gointo 16 four times equaling =
3
4
The traditional method works well and may be easiest when dealing with low number you are familiar with. The Prime factorization method is better for larger number you are unsure of.

Prime Factorization: This method has you find the prime factors for both the numerator and denominator. This is done by asking yourself what two factors can I multiply to get the numerator? If the numbers are prime (a prime number has only two factors...itself and 1) you write them down. If they are not you continue asking yourself the factors until you get the prime numbers. Repeat this for the denominator. Then, you cross out any matching prime numbers from the numerator and denominator (there must be one from each side). Multiply the remaining factors and you are done! It is much easier than it sounds! I am really excited about this method!

Example:
12
51
I think in my head that 2x6 are factors of 12. 2 is a prime number so I write itdown (see ex. 1)

(ex.1)
12 2
51

Then I turn my attention to the 6. It is not a prime number so I find two factors for it.... 2x3 both of these are prime so I write them down (see ex.2)

(ex.2)
12 2 x 2 x 3
51

Next I do the same process for the denominator. Based on divisibility rules I know that
51 is divisible by 3. So...3x17 are my factors. Both areprime, so I write them down (see ex.3)

(ex.3)
12 2 x 2 x 3
51 3 x 17

Now I look at my numerator and denominator row. If there are anymatching numbers they are eliminated (see ex. 4)

(ex. 4)
12 2 x 2 x 3
51 3 x 17

(pretend the colored numbers are crossed out) Finally you multiply the remaining numerators together and the denominators together (see ex5)

(ex.5)
12 2 x 2 = 4
51 17 = 17

so our reduced fraction is
4
17

There you have it! I hope you enjoyed this as much as I did!