int math 2 section 2-2 1011

Section 2-2Order of Operations

Essential Question

✤ How do you evaluate numerical expressions using the order of operations?

✤ Where you’ll see this:

✤ Part-time jobs, fitness, entertainment, population

Vocabulary

1. Numerical Expression:

2. Value:

3. Simplify:

4. Exponent:

5. Variable Expression:

6. Evaluate:

Vocabulary

1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division)

2. Value:

3. Simplify:

4. Exponent:

5. Variable Expression:

6. Evaluate:

Vocabulary

1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division)

2. Value: Another name for the answer of the numerical expression

3. Simplify:

4. Exponent:

5. Variable Expression:

6. Evaluate:

Vocabulary

1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division)

2. Value: Another name for the answer of the numerical expression

3. Simplify: Finding the value of a numerical expression by applying the order of operations

4. Exponent:

5. Variable Expression:

6. Evaluate:

Vocabulary

1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division)

2. Value: Another name for the answer of the numerical expression

3. Simplify: Finding the value of a numerical expression by applying the order of operations

4. Exponent: Tells how many times we multiply a number by itself

5. Variable Expression:

6. Evaluate:

Vocabulary

1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division)

2. Value: Another name for the answer of the numerical expression

3. Simplify: Finding the value of a numerical expression by applying the order of operations

4. Exponent: Tells how many times we multiply a number by itself

5. Variable Expression: A collection of numbers and variables, combined using the four operations

6. Evaluate:

Vocabulary

1. Numerical Expression: Two or more numbers combined using the four operations (addition, subtraction, multiplication, and division)

2. Value: Another name for the answer of the numerical expression

3. Simplify: Finding the value of a numerical expression by applying the order of operations

4. Exponent: Tells how many times we multiply a number by itself

5. Variable Expression: A collection of numbers and variables, combined using the four operations

6. Evaluate: Substitute in for a variable, then simplify

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

P: Parentheses

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

P: Parentheses

E: Exponents

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

P: Parentheses

E: Exponents

M and D: Multiplication and Division as it appears from left to right

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

P: Parentheses

E: Exponents

M and D: Multiplication and Division as it appears from left to right

A and S: Addition and Subtraction as it appears from left to right

What is the Order of Operations?

“Golly, Excuse My Dear Aunt Sally”

G: Grouping symbols; parentheses, brackets, division bars, etc.

E: Exponents

M and D: Multiplication and Division as it appears from left to right

A and S: Addition and Subtraction as it appears from left to right

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24 = 16 − (5i2)

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24 = 16 − (5i2)

= 16 − 10

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24 = 16 − (5i2)

= 16 − 10 = 6

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) d. -(10-8)2 − 23

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) =-5i16 + 3

d. -(10-8)2 − 23

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

d. -(10-8)2 − 23

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Example 1

Simplify each numerical expression.

=-(2)2 − 23 c. -5i42 − (−3)

=-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Example 1

Simplify each numerical expression.

=-(2)2 − 23

= −4 − 8

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Example 1

Simplify each numerical expression.

=-(2)2 − 23

= −4 − 8 = −12

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

=29

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

=29

=

13i23−

23

⎛⎝⎜

⎞⎠⎟

2

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

=29

=

13i23−

23

⎛⎝⎜

⎞⎠⎟

2

=

29−

49

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

=29

=

13i23−

23

⎛⎝⎜

⎞⎠⎟

2

=

29−

49

= −

29

Extra Credit Challenge

Demonstrate that using only the number 2 and parentheses, exponents, the order of

operations, and the zero power, you can write expressions equal to each of the whole

numbers from 1 through 10.

Problem Set

Problem Set

p. 58 #1-10 all, 12, 13-30 odd

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