Order of operations

Order of Operations & Evaluate Algebraic Expressions

Learning Outcome 2: I can use the order of operations to evaluate algebraic expressions.

Order of Operations

Exponents and Order of Operations

Order of Operations

Why are parenthesis important?

Poll

What is your current level of mastery of "Learning Outcome 2: I can use the order of operations to evaluate algebraic expressions."?

• 4 Advanced

• 3 Independent

• 2 Developing

• 1 Emerging

Poll

Which one is correct?

• 5+4x7=63

• 5+4x7=33

REVIEW EXPONENTS

Remember that exponents are repeated multiplication.

What do you think will happen if I add parenthesis?

(5+4)x7

5+4x7

5+(4x7)

GEMDAS - What does each letter mean?

• G - Grouping. This is the parenthesis part of the problem.

• E - Exponents. Pretty self explanatory.

• MD - Multiply & Divide. You solve these from LEFT to RIGHT in the problem.

• AS - Add and Subtract. Again, solve these from LEFT to RIGHT in the problem.

Let's try to translate a verbal expression to a numerical expression:

The sum of 2 and 5 multiplied by 6

REVIEW EXPONENTS

VOCABULARY

Base: the number being multiplied.

Exponent: the number of times you multiply the base by itself.

Power: the base and the exponent together.

The sum of 2 and 5 multiplied by 6

The word sum, differrence, product, and quotient imply parenthesis

(2 + 5) x 6

Multiple Choice

1. What is the order of operations?

• Step 1: Parenthesis (grouping symbols)

  Step 2: Exponents

  Step 3: Multiplication and Division from left to right as they appear

  Step 4: Addition and Subtraction from left to right as they appear

• Step 1: Parenthesis

  Step 2: Exponents

  Step 3: Multiplication

  Step 4: Division

  Step 5: Addition

  Step 6: Subtraction

• Parenthesis, Exponents, Addition, Subtraction, Multiplication, and Division all from left to right as they appear.

• The order of operations depends on the problem.

Fill in the Blank

56 divided by the difference between 15 and 8.

$$\$$

/

(

-

)

REVIEW OF EXPONENTS

Expanded form

Write the power as repeated multiplication

Here is the expanded form of 5³

Standard form

The value of the power after doing the repeated multiplication.

5³ = 125

Fill in the Blank

The sum of 3 and 4 multiplied by the sum of 2 and 9

(

+

)

(

+

)

Multiple Choice

Pick the correct order for Order of Operations

• Parentheses, Multiplication, Division, Addition, Exponents, Subtraction

• Exponents, Multiplication, Division, Addition, Parentheses, Subtraction

• Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Fill in the Blank

Practice evaluating expressions:

$$17+\left(21+3^2\right)\div\left(5\times2\right)$$  

Fill in the Blank

$$5^2\div\left(48-43\right)\times\left(2+3\right)$$  

Order of Operations

• Step 1: Parenthesis (grouping symbols)

• Step 2: Exponents
  

• Step 3: Multiplication and Division from left to right as they appear

• Step 4: Addition and Subtraction from left to right as they appear

Fill in the Blank

$$\left(4^2-8+2\times10\right)\div\left(3^2-5\right)$$  

Fill in the Blank

Identify the base of 6³

Fill in the Blank

$$\left(8\times\left(64\div4^2+2\right)\right)+6^2\div4$$  

Grouping

Anytime we have parenthesis in a problem, must solve the part of the problem that in those parenthesis. We still follow the rules of GEMDAS when solving the inside problem.

Example: 2 x (3 + 4 x 2)

We have to start with the part of the problem inside the grouping part. But we must still follow GEMDAS and solve the multiplying part of the group, then add. Once we finish the grouping, then we multiply the outside number.

Fill in the Blank

Identify the exponent of 10⁵

Note: The ^ symbol will be used to represent that the number that follows is an exponent.

Example: 4^2 means 4 to the power of 2 OR 4 with an exponent of 2

Fill in the Blank

Write 2⁴ in expanded form.

Multiple Choice

Which operation is performed FIRST?

(13 - 1) + 4

• addition outside of grouping symbols

• subtraction inside of grouping symbols

• multiplication by grouping symbols

Fill in the Blank

Write 2⁴ in standard form.

Take Notes and Show Your Work

Have your math notebook or paper and something to write with at hand. As you attempt and review the following problems be sure to copy the original problems and show each step needed to solve the problem. If you answer a question incorrectly you should then copy the correct steps from the following slide to refer back to as a guide.

Multiple Choice

What form is 7x7?

• Exponential form

• Expanded form

• Standard form

Multiple Choice

(24 - 16) ÷ 8 =

• 8

• 1

• 2

• 7

Multiple Choice

What form is 4⁸

• Exponential form

• Expanded form

• Standard form

Multiple Choice

2. What is the first step?

$$40÷\left(8-6\right)^2$$  

• raise 2 to the power of 2

• subtract 8 and 6
  

• divide 40 and 4

• divide 40 and 2

• raise 8 to the power of 2

Multiple Choice

Write 9² in standard form

• 81

• 18

• 9x9

• 9+9

Exponents

REVIEW OF ORDER OF OPERATIONS

Multiple Choice

3. What is the second step?

$$40÷\left(8-6\right)^2$$  

• raise 2 to the power of 2

• subtract 8 and 6
  

• divide 40 and 4

• divide 40 and 2

• raise 8 to the power of 2

EXAMPLE:

9 X 5 + 6 - 2

Step 1: = 45 + 6 - 2

Step 2: = 51 - 2

Step 3: = 49

Multiple Choice

3⁴ Which number is the base?

• 3

• 4

EXAMPLE

4² - (5 +2) x 2

Step 1: = 4² - 7 x 2

Step 2: = 16 - 7 x 2

Step 3: = 16 - 14

Step 4: = 2

Multiple Choice

4. What is the third step?

$$40÷\left(8-6\right)^2$$  

• raise 2 to the power of 2

• subtract 8 and 6
  

• divide 40 and 4

• divide 40 and 2

• raise 8 to the power of 2

Multiple Choice

What would this expression look like after the first step?

4 + 5 x 8

• 9 x 8

• 4 + 40

Multiple Choice

Write with an exponent:
$$3\cdot3\cdot3\cdot3\cdot3$$  

• $$3^5$$  

• $$5^3$$  

Multiple Choice

Which operation would you do first in this problem?

$$10\div5\ \times4\ +\ 8$$  

• Multiplication

• Division

• Addition

$40\; ÷\; (8\; –\; 6)^2$

• undefined  Step 1: Parenthesis (Subtract 8 and 6)

•  undefined      Step 2: Exponent (Raise 2 to the power of 2)

•  undefined             Step 3: Division (Divide 40 and 4)

Multiple Choice

Which operation would you do LAST in this problem?

$$7^2\ -5\ +8$$  

• Exponent

• Subtraction

• Addition

Multiple Choice

Which is equivalent to 5 x 5 x 5 x 5

• 5³
• 5⁴
• 4⁵
• 5⁵

Fill in the Blank

What is the value of this expression?

6² + 5 x 2

Multiple Choice

5. Simplify.

$$40-2\cdot4^2$$  

• 8

• -24

• 24
  

• 608

Fill in the Blank

What is the value of this expression?

$$8\ +\ 3\ \times5$$  

Multiple Choice

2⁴=?

• 4

• 6

• 8

• 16

Fill in the Blank

What is the value of this expression?

(5 - 1 x 2) + 3 x 2

40 – 2 • 4^2

• undefined  Step 1: Exponent (Raise 4 to the power of 2)

•  undefined     Step 2: Multiplication (Multiply 2 and 16)

•  undefined                 Step 3: Subtraction (Subtract 40 and 32)

Multiple Choice

The M and D in PEMDAS stand for Multiplication and Division.

Which operation do you do first?

• Multiplication

• Division

• Whichever comes first in the expression as you read it from left to right

Multiple Choice

6. Simplify.

$$20÷2⋅5−5+2$$  

• 47

• -1

• 13

• 43

Multiple Choice

The A and S in PEMDAS stand for Addition and Subtraction.

Which operation do you do first?

• Addition

• Subtraction

• Whichever comes first in the expression as you read it from left to right

20 ÷ 2 ⋅ 5 − 5 + 2

• undefined  Step 1: Division (Divide 20 and 2)

•  undefined      Step 2: Multiplication (Multiply 10 and 5)

•  undefined            Step 3: Subtraction (Subtract 50 and 5)

• undefined                    Step 4: Addition (Add 45 and 2)

Multiple Choice

Solve the following:

(2 + 7 - 1) ÷ 2²

• 16

• 2

• 4

• 8

Multiple Choice

7. Simplify.

$$8^2-3\left(4-2\right)+25$$  

• 83

• 33

• 35

• -15

Multiple Choice

(7 + 41) ÷ 2 – 15 =

• 19

• 9

• 25

• 3

8^2 – 3(4 – 2) + 25

• undefined       Step 1: Parenthesis (Subtract 4 and 2)

•  undefined      Step 2: Exponent (Raise 8 to the power of 2)

•  undefined            Step 3: Multiplication (Multiply 3 and 2)

• undefined                     Step 4: Subtraction (Subtract 64 and 6)

• undefined                               Step 5: Addition (Add 58 and 25)

Multiple Choice

8. Evaluate for a = 3 and b = 4.

$$21-\left(b-a\right)^3$$  

• 20

• 22

• 18

• 44

Evaluate for a = 3 and b = 4. 

$21\; –\; (b\; –\; a)^3$

•  undefined      Step 1: Substitution (Substitute 3 for a and 4 for b)

•  undefined             Step 2: Parenthesis (Subtract 4 and 3)

• undefined                   Step 3: Exponent (Raise 1 to the power of 3)
  

• undefined                          Step 4: Subtraction (Subtract 21 and 1)
  

Multiple Choice

9. Evaluate for r = 2 and s = 5.

3sr^2 ÷ 6 – 3

• 7

• 17601.16

• 20

• 47

Evaluate for r = 2 and s = 5. 

$3sr^2\; ÷\; 6\; –\; 3$

•  undefined     Step 1: Substitution                                                                                               (Substitute 2 for r and 5 for s)

•  undefined       Step 2: Exponent (Raise 2 to the power of 2)

• undefined            Step 3: Multiplication (Multiply 3 by 5)
  

• undefined                  Step 4: Multiplication (Multiply 15 and 4)
  

• undefined                          Step 5: Division (Divide 60 and 6)

• undefined                                    Step 6: Subtraction (Subtract 10 and 3)

Multiple Choice

10.  Simplify.

$$\frac{9+3•6}{9÷3+6}$$  

• 3

• 8

• 72

• 27

Simplify. $(9+3•6)/(9÷3+6)$

•  undefined          Step 1: Top Multiplication (Multiply 3 and 6)

•  undefined          Step 2: Top Addition (Add 9 and 18)

• undefined                  Step 3: Bottom Division (Divide 9 and 3)
  

• undefined                       Step 4: Bottom Addition (Add 3 and 6)
  

• undefined                          Step 5: Divide Top by Bottom (Divide 27 and 9)

Poll

What is your current level of mastery of "Learning Outcome 2: I can use the order of operations to evaluate algebraic expressions."?

• 4 Advanced

• 3 Independent

• 2 Developing

• 1 Emerging