Objective The student will be able to: use the order of operations to evaluate expressions. Designed by Skip Tyler, Varina High School

Evaluate 7 + 4 • 3. Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

Remember the phrase “Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

Once again, evaluate 7 + 4  3 and use the order of operations. = 7 + 12 (Multiply.) = 19 (Add.)

Example #1 14 ÷ 7 • 2 - 3 = 2 • 2 - 3 (Divide l/r.) = 4 - 3 (Multiply.) = 1 (Subtract.)

Example #2 3(3 + 7) 2 ÷ 5 = 3(10) 2 ÷ 5 (parentheses) = 3(100) ÷ 5 (exponents) = 300 ÷ 5 (multiplication) = 60 (division)

Example #3 20 - 3 • 6 + 102 + (6 + 1) • 4 = 20 - 3 • 6 + 102 + (7) • 4 (parentheses) = 20 - 3 • 6 + 100 + (7) • 4 (exponents) = 20 - 18 + 100 + (7) • 4 (Multiply l/r.) = 20 - 18 + 100 + 28 (Multiply l/r.) = 2 + 100 + 28 (Subtract l/r.) = 102 + 28 (Add l/r.) = 130 (Add.)

Which of the following represents 112 + 18 - 33 · 5 in simplified form? -3,236 4 107 16,996 Answer Now

Simplify 16 - 2(10 - 3) 2 -7 12 98 Answer Now

Simplify 24 – 6 · 4 ÷ 2 72 36 12 Answer Now

Evaluating a Variable Expression To evaluate a variable expression: substitute the given numbers for each variable. use order of operations to solve.

Example # 4 n + (13 - n)  5 for n = 8 = 8 + (13 - 8)  5 (Substitute.) = 8 + 5  5 (parentheses) = 8 + 1 (Divide l/r.) = 9 (Add l/r.)

Example # 5 8y - 3x2 + 2n for x = 5, y = 2, n =3 = 8  2 - 3  52 + 2  3 (Substitute.) = 8  2 - 3  25 + 2  3 (exponents) = 16 - 3  25 + 2  3 (Multiply l/r.) = 16 - 75 + 2  3 (Multiply l/r.) = 16 - 75 + 6 (Multiply l/r.) = -59 + 6 (Subtract l/r.) = -53 (Add l/r.)

What is the value of -10 – 4x if x = -13? -62 -42 42 52 Answer Now

What is the value of 5k3 if k = -4? -8000 -320 -60 320 Answer Now

What is the value of if n = -8, m = 4, and t = 2 ? 10 -10 -6 6 Answer Now

Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×

Commutative Properties Changing the order of the numbers in addition or multiplication will not change the result. Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

Associative Properties Changing the grouping of the numbers in addition or multiplication will not change the result. Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

Distributive Property Multiplication distributes over addition.

Additive Identity Property There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

Multiplicative Identity Property There exists a unique number 1 such that the number 1 preserves identities under multiplication. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

Additive Inverse Property For each real number a there exists a unique real number –a such that their sum is zero. a + (-a) = 0 In other words opposites add to zero.

Multiplicative Inverse Property For each real number a there exists a unique real number such that their product is 1.

Let’s play “Name that property!”

State the property or properties that justify the following. 3 + 2 = 2 + 3

State the property or properties that justify the following. 3 + 2 = 2 + 3 Commutative Property

State the property or properties that justify the following. 10(1/10) = 1

State the property or properties that justify the following. 10(1/10) = 1 Multiplicative Inverse Property

State the property or properties that justify the following. 3(x – 10) = 3x – 30

State the property or properties that justify the following. 3(x – 10) = 3x – 30 Distributive Property

State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5

State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9

State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

Which Property? 3 + 7 = 7 + 3

Commutative Property of Addition Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

Which Property? 8 + 0 = 8

Identity Property of Addition Which Property? 8 + 0 = 8 Identity Property of Addition

Which Property? 6 • 4 = 4 • 6

Commutative Property of Multiplication Which Property? 6 • 4 = 4 • 6 Commutative Property of Multiplication

Which Property? 17 + (-17) = 0

Inverse Property of Addition Which Property? 17 + (-17) = 0 Inverse Property of Addition

Which Property? 2(5) = 5(2)

Commutative Property of Multiplication Which Property? 2(5) = 5(2) Commutative Property of Multiplication

Which Property? (2 + 1) + 4 = 2 + (1 + 4)

Associative Property of Addition Which Property? (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition

Which Property? even + even = even

Which Property? 3(2 + 5) = 3•2 + 3•5

Distributive Property Which Property? 3(2 + 5) = 3•2 + 3•5 Distributive Property

Which Property? 6(7•8) = (6•7)8

Associative Property of Multiplication Which Property? 6(7•8) = (6•7)8 Associative Property of Multiplication

Which Property? 5 • 1 = 5

Identity Property of Multiplication Which Property? 5 • 1 = 5 Identity Property of Multiplication

Properties Using Negatives

Which Property? (6 – 3)4 = 6•4 – 3•4

Distributive Property Which Property? (6 – 3)4 = 6•4 – 3•4 Distributive Property

Which Property? 1(-9) = -9

Identity Property of Multiplication Which Property? 1(-9) = -9 Identity Property of Multiplication

Which Property? 3 + (-3) = 0

Inverse Property of Addition Which Property? 3 + (-3) = 0 Inverse Property of Addition

Which Property? 1 + [-9 + 3] = [1 + (-9)] + 3

Associative Property of Addition Which Property? 1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition

Which Property? -3(6) = 6(-3)

Commutative Property of Multiplication Which Property? -3(6) = 6(-3) Commutative Property of Multiplication

Which Property? -8 + 0 = -8

Identity Property of Addition Which Property? -8 + 0 = -8 Identity Property of Addition

Which Property? 3•7 – 3•4 = 3(7 – 4)

Distributive Property Which Property? 3•7 – 3•4 = 3(7 – 4) Distributive Property

Which Property? 6 + [(3 + (-2)] = (6 + 3) + (- 2)

Associative Property of Addition Which Property? 6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition

Which Property? 7 + (-5) = -5 + 7

Commutative Property of Addition Which Property? 7 + (-5) = -5 + 7 Commutative Property of Addition

Which Property? (5 + 4)9 = 45 + 36

Distributive Property Which Property? (5 + 4)9 = 45 + 36 Distributive Property

Which Property? -3(5 • 4) = (-3 • 5)4

Associative Property of Multiplication Which Property? -3(5 • 4) = (-3 • 5)4 Associative Property of Multiplication

Which Property? -8(4) = 4(-8)

Commutative Property of Multiplication Which Property? -8(4) = 4(-8) Commutative Property of Multiplication

Properties Using Fractions

Which Property? 51/7 + 0 = 51/7

Identity Property of Addition Which Property? 51/7 + 0 = 51/7 Identity Property of Addition

Which Property? 3/4 – 6/7 = – 6/7 + 3/4

Commutative Property of Addition Which Property? 3/4 – 6/7 = – 6/7 + 3/4 Commutative Property of Addition

Which Property? 12/5 • 1 = 12/5

Identity Property of Multiplication Which Property? 12/5 • 1 = 12/5 Identity Property of Multiplication

Which Property? -8 2/5 + 0 = -8 2/5

Identity Property of Addition Which Property? -8 2/5 + 0 = -8 2/5 Identity Property of Addition

Which Property? [(-2/3)(5)]9 = -2/3[(5)(9)]

Associative Property of Multiplication Which Property? [(-2/3)(5)]9 = -2/3[(5)(9)] Associative Property of Multiplication

Properties Using Variables

Which Property? 6(3 – 2n) = 18 – 12n

Distributive Property Which Property? 6(3 – 2n) = 18 – 12n Distributive Property

Which Property? 2x + 3 = 3 + 2x

Commutative Property of Addition Which Property? 2x + 3 = 3 + 2x Commutative Property of Addition

Which Property? ab = ba

Commutative Property of Multiplication Which Property? ab = ba Commutative Property of Multiplication

Which Property? a + 0 = a

Identity Property of Addition Which Property? a + 0 = a Identity Property of Addition

Which Property? a(bc) = (ab)c

Associative Property of Multiplication Which Property? a(bc) = (ab)c Associative Property of Multiplication

Which Property? a•1 = a

Identity Property of Multiplication Which Property? a•1 = a Identity Property of Multiplication

Which Property? a +b = b + a

Commutative Property of Addition Which Property? a +b = b + a Commutative Property of Addition

Which Property? a(b + c) = ab + ac

Distributive Property Which Property? a(b + c) = ab + ac Distributive Property

Which Property? a + (b + c) = (a +b) + c

Associative Property of Addition Which Property? a + (b + c) = (a +b) + c Associative Property of Addition

Which Property? a + (-a) = 0

Inverse Property of Addition Which Property? a + (-a) = 0 Inverse Property of Addition

Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×