ALGEBRA
Group 6
Good Afternoon All
We are from group 6, I am Ani Nuraini and my friend
Riska Sri Wahyuni
6.2 Simplifying Exspressions
Terms
A term that contains a number only is called a constant term. Compare the
terms 7 and 5x. Notice that the value of 7 never changes—it remains
constant. The value of 5x will change as the value of x changes. If x = 2, then
5x = 5(2) = 10, and if x = 3, then 5x = 5(3) = 15.
The numerical factor of a term that contains a variable is called the
coefficient of the variable. In the term 5x, the 5 is the coefficient of x.
Terms The Commutative Property
of Addition and Multiplication
The Commutative Property of Addition states that the order of terms being
added may be switched without changing the sum. 4 + 9 = 9 + 4 and x + 5 = 5 + x.
The Commutative Property of Multiplication states that the order of terms
being multiplied may be switched without changing the product.
2(8) = 8(2) and y 6 = 6y. The Commutative Property does not hold true for
subtraction or division. The order of the terms does affect the result.
7 - 3 = 4 but 3 - 7 = -4
6 ÷ 2 = 3 but 2 ÷ 6 = 1/3
The Associative Property
of Addition and Multiplication
The Commutative Property of Addition states that the order of terms
being added may be switched without changing the sum.
4+ 9 = 9 + 4 and x + 5 = 5 + x.
The Associative Property does not hold true for subtraction or division.
The grouping of the numbers does affect the result.
(9 - 7) - 5 = -3 but 9 - (7 - 4) = 6.
(12 ÷ 6) ÷ 2 = 1 but 12 ÷ (6 ÷ 2) = 4.
The Distributive Property
The Distributive Property of Multiplication over Addition states that
multiplying a sum by a number is the same as multiplying each addend by
that number and then adding the products. So, 4(3 + 5) = (4 3) + (4 5).
The Distributive Property Properties
of Zero and One
The Identity Property of Addition states that the sum of any number and
0 is that number. The additive identity is 0 because a + 0 = a and 0 + a = a.
The Identity Property of Multiplication states that the product of any
number and 1 is that number.
Equivalent Expressions
The Distributive Property can be used to write an equivalent
expression. Equivalent expressions are different ways of writing one
expression.
Distributing When the Factor is Negative
The Distributive Property is applied in the same way if the factor
to be distributed is negative.
The Distribute Property with Common Factors
Given the expression 6x + 9, you can use the Distributive
property to factor out the greatest common factor and write an
equivalent expression. Recognize that the greatest common
factor of the two terms is 3.
Like Terms
Like terms are terms that contain the exact same variables.
Constant terms are like terms because they do not contain
variables. Here are some examples of like terms.
Thank you
