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Order of Operations
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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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