Algebra Honors (Periods 5 & 6)

Dividing Monomials 5-2

There are 3 basic rules used to simplify fractions made up of monomials.
Property of Quotients
if a, b, c, d are real numbers with b≠0 and d ≠0

ac/bd = a/b ⋅c/d
Our example was 15/21 = (3⋅5)/(3⋅7) = 5/7
The rule for simplifying fractions follows ( when a = b)
(bc)/(bd) = c/d
This rule lets you divide both the numerator and the denominator by the same NON ZERO number.

35/42 = 5/6
-4xy/10x = -2y/5 which can also be written (-2/5)x as well as with out the (((HUGS)))

c⁷/c⁴ = c⁴c³/c4 = c³
another way we proved this was to write out all the c's
c⋅c⋅c⋅c⋅c⋅c⋅c⋅/c⋅c⋅c⋅c = and we realized we were left with
c⋅c⋅c = c³
In addition, we noticed that
c⁷/c⁴ = = c^7-4 = c³
THen we considered
c⁴/c⁷ =
c⋅c⋅c⋅c/c⋅c⋅c⋅c⋅c⋅c⋅c = 1/c⋅c⋅c = 1/c³ = c^-3

Since we all agreed that any number divided by itself was = 1
(our example was b⁵/b⁵ ), we proved the following
1 = b⁵/b⁵ = b^5-5 = b⁰

We finally arrived at the Rule of Exponents for Division

if m > n
a^m/aⁿ = a ^m-n

If n > m
a^m/aⁿ = 1/a ^n-m
and if m = n
a^m/aⁿ = 1

A quotient of monomials is simplified when
1)each base appears only once in the fraction,
2) there are NO POWERS of POWERS and
3)when the numerator and denominator are relatively prime, that is, they have no common factor other than 1.

35x³yz⁶/ 56x⁵yz
5z⁵/8x²

Finding the missing factor when you are given the following
48x³y²z⁴ = (3xy²z)⋅ (______)
we find that

48x³y²z⁴ = (3xy²z)⋅ (16x²z³)