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Order of Operations
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Bethune Junior High Math Name (First & Last)
8 S1C2PO5
Class/Hour
Order of Operations Date
8_S1C2PO5_Order_of_Operations.doc
M07-S1C2-05. Simplify numerical expressions using the order of operations and
appropriate mathematical properties.
M08-S1C2-05. Simplify numerical expressions using the order of operations that
include grouping symbols, square roots, cube roots, absolute values, and positive
exponents.
What is a mathematical expression? What is the difference between a square root and a cube root? What are grouping signs? Why does an answer change in a numerical expression when the grouping symbols are placed around different numbers?
Vocab Definition Example
Exponent
Square root
Cube root
Grouping Symbols
Simplify
Expression
Order of Operations Chart
(Sequence Thinking Map)
Important Note Concerning Order of Operations: The first step is to get whatever is inside the parenthesis/grouping symbol down to one value. If there is already one value inside each parenthesis/grouping, MOVE ON!
Example: 3(4+5) ÷ 10 vs. 2(3)(2)+ (4) ÷ 2
Activity: What’s the first step?
Directions: Simplify the expressions below using order of operations
1) 2(2 + 9) – 23
2) 5(3) - (36)
3) l5 – 4l + 42
4) .5(2 - 1)3
5) 7 – 4
6 - 3
6) 2(4)(2) – (8 ÷ 2)
7) 3(4) – 3(4)2
8) 4 + 3(5) – (9 – 3)
1) What is the simplest form of the expression?
(29 x 4 - 16) ÷ 10
A 17
B 10
C -7
D -34
2) Which is the simplest form of the expression?
7 x 5 + (8 - 3) - 8 ÷ 2
A 16
B 26
C 36
D 40
3) Which is the simplest form of the expression?
3 + 6 x 8 – (4 + 2)
A 66
B 51
C 49
D 45
4) What is the value of the expression below?
4(1+2)2-3
A 15
B 16
C 23
D 39
5) What is the simplest form of the expression?
(4 + 8)(12 - 9) ÷ (63 ÷ 7)
A 1
B 4
C 15
D 100
6) What is the simplest form of the expression?
(14 - 9) x (5 - 3) x 7
A 70
B 52
C -52
D -70
In the space below, develop 2 expressions to be solved with order of operations. Be sure to include at least one exponent and one grouping symbol. 1) 2) Properties that can help us simplify expressions: Distributive Property - multiplication distributes over addition and subtraction
Ex: a(b + c) = ab + ac or a(x – b) = ax - ab
Directions: Use the distributive property to simplify the expressions below.
1) 3(5 + x)
2) 4(2 + t)
3) 6(a - b)
4) x(y - z)
5) 3(2 + 4)
6) 5(p + 6)
Definition
In your own words:
Visual:
Numeric Examples:
7) 6(3 - 2)
8) 10(4 – x)
1) Which equation uses the Distributive Property to solve the problem below?
10(5 + 3) = ___
A (10 + 5) + (10 + 3) = 28
B (15) + (30) = 45
C (10 x 5) + (10 + 3) = 63
D (10 x 5) + (10 x 3) = 80
2) Which equation uses the Distributive Property to solve the problem below?
2 (5 - 3) = ___
A (5 - 2) - (3 - 2) = 2
B (2 x 5) - (2 x 3) = 4
C (2 x 5) - (2 + 3) = 5
D (2 x 5) + (2 x 3) = 16
Associative Property – groupings of all multiplication or all addition can be grouped in any order
Ex: a + (b + c) = (a + b) + c or a(bc) = (ab)c
1) Use the Associative Property of Multiplication to assist you in solving the problem below.
(3 x 4) x 5 = ____
A (3 + 4) + 5
B 3 x (4 - 5)
C 3 x (4 x 5)
D 3 - (4 x 5)
2) Which equation uses the Associative Property of Multiplication to solve the problem below?
5 x (2 x 40) =___
A (2 x 40) + (2 x 5) = 90
B (40 x 5) + (2 x 5) = 210
C (2 x 5) x 40 = 400
D (40 x 5) x (2 x 5) = 2,000
Definition:
In your own words:
Visual:
Numeric Examples:
Commutative Property- if an expression or equation is comprised of all addition or all multiplication, you can move things around Ex: a + b = b + a or ab = ba
1) Which represents the Commutative Property of Multiplication?
2 x 3 x 12 = _____
A 2 + 3 x 12
B 2 x 12 x 3
C 2 - 3 x 12
D 2 - 3 x 12
2) Which equation uses the Commutative Property of Addition?
7 + 15 + 3 = _____
A 3 - 15 - 7 = -19
B 15 - 3 - 7 = 5
C 7 + 3 + 15 = 25
D 15(3 + 7) = 150
Definition
In your own words:
Visual:
Numeric Examples:
DIRECTIONS: Four numbers are shown below. Answer the questions for the numbers by indicating a T for TRUE or an F for FALSE in the corresponding box.
MATCHING: Match the terms to the example by placing the corresponding letter next to each number.
1) The expression 30(2) 2 is equivalent to 30- 22
True/False
2) In order of operations addition comes before subtraction
True/False
3) Using the distributive property is especially helpful when working with variables
True/False
4) In order of operations you the first step is always simplifying exponents
True/False
5) The distributive property says you can move things around in an expression made up of all addition or multiplication
True/False (1 point)
1) Grouping symbol
A ) 4x + 5 = -4
2) The associative property B ) 3(6x2) = 6(3x2)
3) The commutative property C ) 2(3+4)= 2(3)+2(4)
4) The distributive property D ) 56t + 32
5) Expression E ) 3(4) = 4(3) F) ( ); | |; [ ]
