# Module 3 Lesson 4: Evaluating Algebraic Expressions

Lori

Created on July 12, 2024

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## Transcript

### Evaluating Algebraic Expressions

#### Module 3

Start

Lesson 4

Parts of Expressions

Exponent Review

Goals

- Substitute specific values for variables.
- Evaluate algebraic expressions by using substitution and order of operation.
- Evaluate algebraic expressions, including those that arise from real-world problems.

Objectives:

Answer

Problem, identify the operations and what should be completed first.

### Order of Operations Explanation

##### 2.6 • 4² - (25/5)

Finally, the last operation is subtraction.41.6 - 5 = 36.6

##### 36.6

##### 41.6 - 5

Now we multiply since M comes before S.2.6 times 16 = 41.6

##### 2.6 • 16 - 5

Next, we identify the value of the exponent.So 4 to the second power is 4 • 4 = 16

We first simplify what is in the parenthesis. So 25 divided by 5 is 5

##### 2.6 • 4² - 5

##### 2.6 • 4² - (25/5)

##### Posters

#### Order of Operations

##### 7x + 10 = 52 7(6) + 10 = 52 42 + 10 = 52 52 = 52

##### Check your answer.

Finally, add the terms together to get 52.

Using the order of operations, we multiplied 7•6 to get 42

We know x is equal to 6, so the value replaced the unknown.

Locate the variable and substitute (replace) it with a value.

### Evaluate the expression 7x + 10, if x = 6

##### 7x + 10

##### 52

##### 42 + 10

##### 7(6) + 10

#### Substitution (with 1 variable)

Step 1

Step 2

Step 4

Step 5

Step 3

##### Check your answer.

##### 4y + 5x = 32 4(3) + 5(2)² = 32 4(3) + 5(4) = 32 12 + 20 = 32 32=32

### Evaluate the expression 4y + 5x², if y = 3 and x = 2

##### 4y + 5x² 4(3) + 5(2)² 12 + 5(4) 12 + 20 32

#### Substitution (with 2 variables)

##### 5h - 2r, if h =4 and r =25(2) - 2(4)

##### 3m + 7, if m = 43(4) + 7

#### Practice

18.5 + m - 3t, if m = 1.5 and t = 5

18.5 + 1.5 - 3(5) 18.5 + 1.5 - 15 20 - 15 5

#### Practice

Simply means to replace something with something else.

What is substitution?

Simplify by working through specific operations.

Order of Operations?

#### Summary

https://www.cuemath.com/algebra/expression-definition/

- Begin to simplify the expression.
- Refer to the Order of Operations to help (PEMDAS).
- No parenthesis, so simplify exponents first.

##### 4y + 5x² 4(3) + 5(2)² 4(3) + 5(4)

### Step 3

https://csc3abc.weebly.com/2nd-term1.html

https://study.com/academy/lesson/exponent-definition-lesson-for-kids.html

- Continue to simplify the expression.
- Refer to the Order of Operations to help (PEMDAS).
- Next is to multiply or divide, in this case, we are multiplying.

##### 4y + 5x² 4(3) + 5(2)² 4(3) + 5(4) 12 + 20

### Step 4

##### 4y + 5x² 4(3) + 5(2)²

##### Substitute, or replace, any variable with its value.Pay close attention to the different variables and operations.

### Step 2

52 = 52The SAME value is on each side of the equal sign.

### left side = right side

- Continue to simplify the expression.
- Refer to the Order of Operations to help (PEMDAS).
- Finally, adding the two terms is the last step to simplifying this expression.

##### 4y + 5x² 4(3) + 5(2)² 4(3) + 5(4) 12 + 20 32

### Step 5

- terms
- operations
- variables

##### This is the original problem.Pay close attention to the components of the expression.

### Step 1

https://mymathresources.com/gemdas-order-of-operations-bulletin-board-poster/

- Subtraction
- Division
- Leaves you with the value of the variable.

##### 52 - 10 ÷ 7 = 642 ÷ 7 = 66 = 6

##### You can always work in reverse (SADMEP) to check your answer.

#### Order of Operations

32 = 32The SAME value is on each side of the equal sign.