Math 7 (Period 4)

Combining Like Terms 2.2

Lots of VOCAB today

Try to understand what each means—rather than just memorizing

terms- a number andor a variable added/subtracted to another number and/or variable

factors: a number and/or variable multiplied by another number and/or variable

addition words: sum, total, plus, more than, greater than, addends, altogether,  both

subtraction words: difference, minus, less than, less, minuend, subtrahend

multiplication words: product, times, factors, each

division words:  quotient, dividend, divisor, shared  equally

expression: at least one term (with NO EQUAL SIGN)

equation: equal expressions (It MUST have an = sign)

numerical: all numbers (called constants)

variable: a letter or a symbol used to represent a number

algebraic or variable: has at least one variable

simplify a numerical expression—do order of Operations O³ you will get a simpler expression

evaluate given the value of the variable you ‘plug and chug’ in an algebraic expression and simplify using O³

Coefficient: the number attached to a variable. The number is written BEFORE the variable

Constant: a number with no variable attached.

Combining Like Terms

Need the follow:

1. Same exact variable or variables (or NO variable- meaning that they are constants)

2. Same exact exponent

You can combine by adding or subtraction LIKE TERMS

You cannot combine UNLIKE TERMS

Example:

3a + 4a = 7a

but

3a + 4b  just stays the same it is 3a + 4b

3a + 4a² also cannot be combined it remains 3a + 4a²

You should always combine like terms BEFORE you evaluate.

It is so much simpler to do

25a + 5a – 10a  when a = 25

First combine like terms

25a + 5a – 10a = 20a

Then plug in for a = 25

20(25) = 500

You can always simplify unlike terms with multiplication or division

That is

(5x)(6y) = 30xy

WHY?

Our BFF’s the Commutative and Associative Properties of Multiplication JUSTIFY why you can multiply

(5)(x)(6)(y) Break up the pairs using Associative Prop of Mult

(5)(6)(x)(y) Switch the order using Commutative Prop of Mult

The numbers are together and the variables are in alphabetical order

(5∙ 6)xy  group the tw onumbers together using the Associative Prop of Mult

30xy Simplify using the Order of Operation (O³)

Our properties also Justify combining like terms

b + 3 + 2b

becomes

1b + 3 + 2b  That’s the Identity Prop of Multiplication (IDx) because it lets you include the 1 to b+3+ 2b-à 1b + 3 + 2b

1b + 2b + 3 Commutative Prop of Addition(C+) lets you change the order of the  terms

(1b +2b) + 3 Associative Property of Addition (A+) lets you GROUP the two b terms

b( 1+ 3) + 3 Distributive Property  DP+( backwards) lets you take out the common b that was districbuted to two of the terms

b(3) + 3 Simplify using Order of Operations ( O³)

3b + 3    Commutative Prop of Mult ( Cx) lets you switch the ORDER of the b and 3 to proper form