Example: 3x + 4y + 2x + 6y
- I am going to add my x's first. 3x + 2x = 5x
- I'll add my y's next. 4y + 6y = 10y
So, my expression is equivalent to 5x + 10y.
ASSOCIATIVE PROPERTY
(14x + 6) + 12x
is equivalent to
(14x + 12x) + 6
because I can move my
parentheses around.
COMMUTATIVE PROPERTY
12y + 7x + 6y
is equivalent to
12y + 6y + 7x
because I can move my numbers
around when I am adding.
DISTRIBUTIVE PROPERTY
4(2x + 3y)
is equivalent to
8x + 12y.
IDENTITY PROPERTY
4x + 0
4x - 0
4x times 1
4x divided by 1
are ALL equivalent because they don't change.
OK, let's see if we've got it!
p. 497, letter e
3x + 9y + 2x
I am going to use the Commutative Property because I can move my numbers around in addition.
3x + 2x + 9y
is equivalent to
5x + 9y
Now let's do "f" together.
7(3x + y)
Let's use the __________ property.
7 times 3x is?
7 times y is?
My equivalent expression is ________.
Please try letter "g" on your own!
Please try p. 498, # 1-6 on your own.
Once you finish, fill in your Venn diagram for
"Rate Yourself" and then get ready to move
into Stations.
6.EE.3: I can identify equivalent expressions using all
4 Properties of Math.
Equivalent Expressions
Remember, you can always use your
mathematical properties to find equivalent equations!
EQUIVALENT EXPRESSIONS
ARE TWO SETS OF EXPRESSIONS
THAT EQUAL THE SAME THING.
Example: 24x is equivalent to 6(4x)
because 6 times 4x is 24x.
Example: 5(3x + 4y) is equivalent to 15x +20ybecause 5 times 3x is 15x and 5 times
4y is 20y.
Our Vocabulary
- term
- like term
- coefficient
- constant
In your IMN (Student Side), copy and label the following parts of this expression
CONSTANT
TERM
COEFFICIENT
LIKE TERMS
What if I have more than one variable?
LIKE TERMS CAN BE ADDED TOGETHER
TO HELP SIMPLIFY AN EXPRESSION.
In this case,
add the like terms together.
Example: 3x + 4x + 7x = 14x
When simplifying like terms,
DO NOT add the variables.