7th Grade Math
Unit 6 Notes: Algebraic Reasoning
TERMS – all the parts of expressions or equations.
Ex: 2x+3=18 terms are 2x, 3, and 18
Kinds of terms: Variables - a symbol, usually a letter, used to
represent an unknown value.
Ex: x = “a number”
Coefficients – the numbers that are multiplied by the
variables.
Ex: 7x , the 7 is the coefficient
Constants – the numbers that are by themselves with no
variables.
Ex: 7x + 3 = 12, the 3 & 12 are constants
Ex2: 2x+3=18, variable
x, coefficient
2, constant
3 & 18
Identifying Like Terms – this is when you can group terms that
“look alike” together.
Ex1: 7x – 3x + 8 , the 7x & 3x are like terms
Ex2: 2x+7+3x+2-4y, the 2x & 3x are like terms, the 7 & 2 are
like terms, and the 4y has no other like terms
IDENTIFYING “LIKE TERMS” HELPS US SEE WHAT WE CAN COMBINE
TO SIMPLIFY AN EQUATION.
Combining Like Terms – this is when you simplify an expression or
equation by combining the like terms together by using order of
operations to simplify.
Ex: 7x-3x + 8
NOTICE: how the
operation signs (addition
4x + 8
& subtraction) also give
you the signs (positive
Ex2: 2x+7+3x+2-4y
or negative) of the
numbers right after
(2x + 3x) + (7 + 2) – 4y
them.
5x + 9 – 4y can also be written 5x – 4y + 9
USING MODELS TO UNDERSTAND SIMPLIFYING EXPRESSIONS &
EQUATIONS BY COMBINING LIKE TERMS
We can use symbols, shapes or pictures to help us understand how to combine like terms and
simplify and expression or equation.
EXAMPLE: Let’s look at the following equation…
12x –15y + 3 + 7y – 5x - 11
So lets pick a shape to represent each different term:
+x =
-x =
+1 =
+y =
-y =
-1 =
So this is what you would have if you modeled the above expression:
12x
-15y
3
7y
-5x
So you would combine the shapes that are the same. You can pair them
up (one positive and one negative) to create zero pairs and simplify.
12x – 5x
= 7x
-15y + 7y
= -8y
So the (answer) simplified expression is:
3 – 11
= -8
7x – 8y – 8