int math 2 section 2-2 1011

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Section 2-2 Order of Operations

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Order of Operations

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Page 1: Int Math 2 Section 2-2 1011

Section 2-2Order of Operations

Page 2: Int Math 2 Section 2-2 1011

Essential Question

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

✤ Where you’ll see this:

✤ Part-time jobs, fitness, entertainment, population

Page 3: Int Math 2 Section 2-2 1011

Vocabulary

1. Numerical Expression:

2. Value:

3. Simplify:

4. Exponent:

5. Variable Expression:

6. Evaluate:

Page 4: Int Math 2 Section 2-2 1011

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:

Page 5: Int Math 2 Section 2-2 1011

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:

Page 6: Int Math 2 Section 2-2 1011

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:

Page 7: Int Math 2 Section 2-2 1011

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:

Page 8: Int Math 2 Section 2-2 1011

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:

Page 9: Int Math 2 Section 2-2 1011

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

Page 10: Int Math 2 Section 2-2 1011

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

Page 11: Int Math 2 Section 2-2 1011

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

P: Parentheses

Page 12: Int Math 2 Section 2-2 1011

What is the Order of Operations?

“Please Excuse My Dear Aunt Sally”

P: Parentheses

E: Exponents

Page 13: Int Math 2 Section 2-2 1011

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

Page 14: Int Math 2 Section 2-2 1011

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

Page 15: Int Math 2 Section 2-2 1011

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

Page 16: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

Page 17: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

Page 18: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24

Page 19: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24 = 16 − (5i2)

Page 20: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24 = 16 − (5i2)

= 16 − 10

Page 21: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

a. 12 + (3i4) b. 16 − (5i 2 )

= 12 + 12

= 24 = 16 − (5i2)

= 16 − 10 = 6

Page 22: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) d. -(10-8)2 − 23

Page 23: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) =-5i16 + 3

d. -(10-8)2 − 23

Page 24: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

d. -(10-8)2 − 23

Page 25: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Page 26: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

=-(2)2 − 23 c. -5i42 − (−3)

=-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Page 27: Int Math 2 Section 2-2 1011

Example 1

Simplify each numerical expression.

=-(2)2 − 23

= −4 − 8

c. -5i42 − (−3) =-5i16 + 3 = −80 + 3

= −77

d. -(10-8)2 − 23

Page 28: Int Math 2 Section 2-2 1011

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

Page 29: Int Math 2 Section 2-2 1011

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

Page 30: Int Math 2 Section 2-2 1011

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

Page 31: Int Math 2 Section 2-2 1011

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

Page 32: Int Math 2 Section 2-2 1011

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

Page 33: Int Math 2 Section 2-2 1011

Example 2

Evaluate each variable expression for k =

23

a. 1

2k2

b. 1

3k − k2

=

12i

23

⎛⎝⎜

⎞⎠⎟

2

=

12i49

=

418

=29

Page 34: Int Math 2 Section 2-2 1011

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

Page 35: Int Math 2 Section 2-2 1011

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

Page 36: Int Math 2 Section 2-2 1011

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

Page 37: Int Math 2 Section 2-2 1011

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.

Page 38: Int Math 2 Section 2-2 1011

Problem Set

Page 39: Int Math 2 Section 2-2 1011

Problem Set

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

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