Combining like terms

Unit 5:

Reasoning

About

Expressions

Lesson 1: Combining Like Terms

Learning Standards

NC.7.EE.1 Apply properties of operations as strategies to:

• Add, subtract, and expand linear expressions with rational

coefficients.

• Factor linear expression with an integer GCF.

Learning Targets

●I can define term, variable, coefficient, constant, and operator in the context of mathematical
expressions.

●I can create an equivalent expression by combining like terms.

What is an Expression?

5b + 2f + s + 2i + 20

The example below can be referred to as a
mathematical expression.

Expression: a mathematical phrase that
contains numbers, variables and/or
operators. Expressions DO NOT contain equal
signs

• Coefficient: numbers directly in front of variables

• Variable: letters that represent unknown AND changing amounts

• Constant: a number that stands alone without a variable

• Operators: operation signs that tell you what to do between the terms (add, subtract, multiply, divide, etc.

• Term: each value that is connected to an operator

  
  

  
  

​

Parts of an expression

• ​Terms are separated by operators

• MAKE SURE TO TAKE THE OPERATOR IN FRONT OF THE NUMBER WHEN YOU ARE SEPARATING YOUR TERMS

​

How do we separate/count terms?

Multiple Choice

Identify the number of terms: 3x + 9 + 4p - 2

• 3

• 4

• none

• 2

Multiple Select

Choose all the coefficients in the expression: n + 4x + 9 + 2p

• 9

• 1

• 2

• 4

Multiple Select

Choose all the constants in the expression: 7p + 9n + 4x

• 7

• 9

• 4

• none

Multiple Choice

Identify the constant:

7c + 8 y + 32

• 7

• c

• y

• 32

• 8

Multiple Choice

Identify the coefficient of the second term:

-9b + 4x - 9

• -9

• 9

• 4

• b

• x

Ridiculous Fast Food Order

How could he have made this order more simple?

Multiple Choice

List the terms in this expression.
7x-6+8

• 7x & 8
• 7
• 7, 6, 8
• 7x, 6 & 8

2 bacon cheeseburgers, 1 small fry, 3 chocolate milkshakes, 2 small fries, a chicken sandwich, 3 bacon cheeseburgers, 2 small sprites, $0.65, 1 small fry, $1.15.

Order with change

How can we simplify this order?

What Does Combine Like Terms Mean?

We can simplify expressions the same way we can simplify a fast food order. To combine like terms is to put together terms that are all constants, or terms that all have the same
variable.

Note: The variable terms must have the same exponent if exponents are used.

2b + f + s + i + 2b + f + b + i + 10 =

5b + 2f + s + 2i + 10

Combining Like Terms

2n + t + d + q + n + 2t + f + f + n + 2q + t + d =

Step 1: Separate the terms
Step 2: List the terms that are alike
Step 3: Combine the terms by adding them

What can we

combine?

What

cannot be
combined?

Combining like terms rules

Simplifying Expressions: Examples

Expression

Simplified Version

Explanation

12 - 3

9

“I ate 9 Oreos today”

is shorter and easier

than “I ate 12 - 3

Oreos today.”

2x + 4x

6x

“6x” is shorter and

easier than “2x + 4x.”

8k + 10 - 3k

5k + 10

“5k + 10” is shorter

and easier than “8k +

10k - 3k.”

Draw

Separate the terms and use the same color/shape to indicate which terms are alike

11x - 21 + 11 - 6x

Draw

Separate the terms and use the same color/shape to indicate which terms are alike

11x - 21 + 11 - 6x

Practice Simplifying Expressions

Question 1. Simplify the following expression:

3x - 5 + 6x + 10

Practice Simplifying Expressions

Question 2. Simplify the following expression:

8 - 6m + 6n - 7 + 10m

Practice Simplifying Expressions

Question 3. Simplify the following expression:

3t + 6z - 4t + 9z + z

Practice Simplifying Expressions

Question 4. Simplify the following expression:

3f + g + 13 - 4f - g

Multiple Choice

Simplify the expression by combining like-terms:

$$-3y+1+9y-4$$  

• $$3y$$  

• $$6y-3$$  

• $$12y+3$$  

Multiple Choice

Identify the like terms.

7 + 4p - 5 + p + 2y

• 4p, -5, 2y

• 4p, p, 2y

• 7, 5 AND 4p, p

• 7, -5 AND 4p, p

Multiple Choice

Combining like terms:

$$b-3n+12-6b+2n$$

• $$5b+n\ +12$$

• $$5b+n-12$$

• $$-5b-n+12$$

• $$-17bn$$

Multiple Choice

Simplify the expression.

14 - 3z + 8 + z

• -2z + 22

• 2z + 22

• 4z + 22

• -4z + 22

Multiple Choice

Describe the meaning of perimeter for the given figure.

• Inside the rectangle
• The distance along the 2 marked edges
• The distance around all 4 sides
• L x W

Multiple Choice

Write an algebraic expression to represent the perimeter of the rectangle.

• 2w - 3x + 9 + 6w - 2x - 10
• 2w - 3x + 9 + 6w - 2x - 10 + 2w - 3x + 9 + 6w - 2x - 10
• 2w - 3x + 9
•  6w - 2x - 10

Multiple Choice

If the perimeter of the rectangle is represented by the expression:
2w - 3x + 9 + 6w - 2x - 10 + 2w - 3x + 9 + 6w - 2x - 10
Write the simplified expression to represent the perimeter by combining like terms.

• 2w - 3x + 9 + 6w - 2x - 10 + 2w - 3x + 9 + 6w - 2x - 10
• 8w - 5x - 1
• 16w - 10x - 2
• 2

Practice Simplifying Expressions Challenge

Question 5. Simplify the following expression:

5x + 3(x + 1) + 2x - 9