GOSEA 4 - Adding Like Terms

GOSEA 4

Adding Like Terms

This activity gives practice on identifying and adding/subtracting like terms which will be necessary in solving equations. Vocabulary is very important!!!

By continuing to the next slide and completing this lesson, you testify that you are the student who is enrolled in GOSA at BCHS with Mrs. Haley and that you are doing the lesson for yourself and no one else.

variable

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Multiple Select

Which symbols are not variables?

Check all that apply.

• a

• 7

• +

• $$\theta$$

constant

Multiple Choice

In the expression 14d + 6, what is the constant?

• 14

• d

• 6

Multiple Select

Which symbols are not constants?

Check all that apply.

• -3

• r

• 5.72

• $$\div$$

Multiple Choice

In the expression 27h, what is the constant?

• 27

• h

• 0 is the implied constant

operation symbols

Multiple Select

Which symbols are not operation symbols?

Check all that apply.

• ( )

• %

• x

• m

factor

a quantity being multiplied

Example: 2 and 3 are factors of 6 because 2 multiplied by 3 (and 3 multiplied by 2) equals 6

In the expression 7xy, 7 is a factor because it is being multiplied by xy;

xy is a factor because it is being multiplied by 7;

7x is factor because it is being multiplied by y;

y is a factor because it is being multiplied by 7x;

7y is a factor because it is being multiplied by x;

x is factor because it is being multiplied by 7y

Multiple Choice

Which symbol is not a factor in the expression 6sw + 4?

• 6

• s

• w

• 4

coefficient

another name for a factor

​

There are two types of coefficients: numerical and literal.

​

Typically, when we say "coefficient", we are referring to a numerical one.

numerical coefficient

a factor that is a numeral

​

Example: In the expression 8md, 8 is the numerical coefficient.

Multiple Choice

In the expression 17h, what is the numerical coefficient?

• 17

• h

• 17h

Multiple Choice

In the expression -5x, what is the numerical coefficient?

• -5

• x

• -5x

Multiple Choice

Which symbol is a numerical coefficient in the expression 12xy + 4

• 12

• x

• y

• 4

Multiple Choice

In the expression 8v - 19, what is the numerical coefficient?

• 8

• 19

• -19

Multiple Choice

What is the numerical coefficient of the expression p ?

• 0

• 1

• p does not have a numerical coefficient

Multiple Choice

What is the numerical coefficient of d + 18 ?

• d

• 0

• 1

• 18

literal coefficient

a factor that is a variable

​

Example: In the expression 8md, m and d are literal coefficients.

Multiple Choice

In the expression 7y, what is the literal coefficient?

• 7

• y

• 7y

Multiple Choice

Which symbol is NOT a literal coefficient in the expression -3a + bc?

• -3

• a

• b

• c

Multiple Choice

In the expression 4f + 13, what is the literal coefficient?

• 4

• f

• 13

expression

numbers, letters (variables), and operation symbols that are grouped together

​

Examples:  6 , x , 3h and d + 4 are all expressions

​

(Expressions joined together by an equals sign form equations.

2x + 3 = 8 is an equation containing the expressions 2x + 3 and 8.)

numerical expression

an expression that contains ONLY numerals and operation symbols

​

Examples:  7,  2 + 9,  12 - 8

Multiple Choice

Which expression is numerical?

• $$\frac{19}{4}$$  

• 15x

• km

• 3x + 2

algebraic expression

an expression that contains just numerals OR

an expression that contains numerals and operation symbols OR

an expression that contains just variables OR

an expression that contains variables and operations symbols OR

an expression that contains a combination of numerals and variables OR

an expression that contains a combination of numerals and variables with operation symbols

Examples: 9, 13 + 4, y, a + b, m + 6, 3p, 8b - 5

terms

made up of numerals and/or variables and separated by plus (+) or minus (-) signs

​

Example: In the expression 6x - 10, 6x is one term, 10 is the other term

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like terms

terms that have the same VARIABLES in the same form or equivalent forms

​

Examples of like terms: g and g; kk and k² ; 6t and -3t 

​

g and g² are NOT like terms (even though they have the same variables, the variables are not in the same form--have the same exponent)

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Multiple Choice

Does the expression g + 23 contain any like terms?

• yes

• no

Multiple Choice

Does the expression 4k + 5 - 2k contain any like terms?

• yes

• no

Multiple Choice

Are there any like terms in the expression   $$6y\ +\ 6y^2$$  ?

• yes

• no

Subtraction is just the addition

of a negative number

5 - 3 means the same thing as 5 + (-3) which equals 2

​

15 - 4 means 15 + (-4) which equals 11

​

7 - 16 means 7 + (-16) which equals -9

The same is true when

the terms contain variables

6x - 4x means the same thing as 6x + (-4x)

​

18r - 2r means 18r + (-2r)

​

16m - 25m means 16m + (-25m)

How do you add/subtract like terms?

Each term in an expression is considered to be positive or negative depending on the symbol immediately in front of it.

Multiple Choice

How many terms are in the expression 7x + 6 - 5x + 9 - 4

• 2

• 3

• 4

• 5

Multiple Select

7x + 6 - 5x + 9 - 4

Which terms are positive?

• 1st term

• 2nd term

• 3rd temr

• 4th term

• 5th term

Multiple Select

7x + 6 - 5x + 9 - 4

Which terms are negative?

• 1st term

• 2nd term

• 3rd term

• 4th term

• 5th term

7x + 6 - 5x + 9 - 4

The above expression has five terms.

7x is positive

6 is positive

5x is negative

9 is positive

4 is negative

​

The individual terms are 7x, 6, -5x, 9, and -4.

7x + 6 - 5x + 9 - 4

Which terms are "like"?

​

7x and -5x are like terms because they both contain an "x"

​

6, 9 and -4 are like terms because they are all constants

To add like terms in an expression, directions will often say...

​

"simplify by adding like terms" or

"add like terms" or just

"simplify".

simplify

a verb used in math directions that means to "do the operations indicated";

​

one does not "simplify" equations;

​

equations are "solved"

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WARNING!!!!

The following video demonstrates a habit that I do NOT condone.

Around the 4:50 mark of the video,

the tutor uses two equals sign on the same line.

No, no, no, no, no.

Trust me. I have my reasons!​

Subject | Subject

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To add or subtract like terms

in an expression...

• identify which terms are like

• add the numerical coefficients of the like terms together

• record the sum/difference of the variable terms using the same same variable as the original terms

Addition is commutative, so you can reorder the terms as long as you take the signs which each term.

It is not necessary to rewrite the order of the terms, but it is an option.

​7x + 6 - 5x + 9 - 4 can be rewritten as 7x - 5x + 6 + 9 - 4

​Then 7x and -5x are added together while 6, 9 and -4 are added together.

​The result is 2x + 11.

Multiple Choice

Simplify: 7 + 5

• 12

• 35

• 2

• none of the above

Multiple Choice

Simplify: 2x + 5x

• 7x²

• 7x

• 3x

• 10x

Multiple Choice

Simplify: 5k + k

• 5k

• 5k²

• 6k

• 6k²

Multiple Choice

Simplify: 8h + 7

• 15h

• 8h + 7

• 15h

• h

Multiple Choice

Simplify:

2x + 5 + 6x

• 13x

• 4x + 5

• 8x² + 5

• 8x + 5

Multiple Choice

Simplify:

8a - 7 + 4a + 10

• 12a - 3

• 12a + 3

• 12a² + 17

• 12a² - 3

Multiple Choice

Simplify:

-4 + 6t - 10t + 9 +2y

• 3ty

• -2ty + 5

• -4t + 2y + 5

• 4t + 2y + 5

Multiple Choice

Simplify:

5g - 3h + 5 - 2g + 10h - 15

• 0gh

• 10gh - 10

• 3g + 13h -10

• 3g + 7h - 10

Poll

Please choose the description that most accurately describes the level of help you received on this assignment. Please be honest so we will know how much more practice you may need on this topic.

• I did not have to receive any assistance from anyone on this assignment.

• I needed some assistance on this assignment.

Redo this assignment until you make a 100. That is the only way to get a 100 for Geometry.