section i: distributive property section ii: order of operations

Section I: Distributive Property

Section II: Order of Operations

Objective

Use the distributive property to simplify expressions.

Section I: The Distributive Property

The process of distributing the number on the outside of the parentheses to each term on the inside.

a(b + c) = ab + ac and (b + c) a = ba + ca

a(b - c) = ab - ac and (b - c) a = ba - ca

Example #1

5(x + 7)

5 x + 5 75x + 35

Example #2

3(m - 4)3 m - 3 4

3m - 12

Example #3

-2(y + 3)-2 y + (-2) 3

-2y + (-6)-2y - 6

Which statement demonstrates the distributive property incorrectly?

1. 3(x + y + z) = 3x + 3y + 3z

2. (a + b) c = ac + bc

3. 5(2 + 3x) = 10 + 3x

4. 6(3k - 4) = 18k - 24

Which statement demonstrates the distributive property incorrectly?

1. 3(x + y + z) = 3x + 3y + 3z

2. (a + b) c = ac + bc

3. 5(2 + 3x) = 10 + 3x

4. 6(3k - 4) = 18k - 24

Answer Now

A term is a1) number, or

2) variable, or

3) a product (quotient of numbers and variables).

Example

5

m

2x2

The coefficient isthe numerical part of the term.

Examples1) 4a 4

2) y2 1

3) 5x2

7

5

7

Like Terms are terms with the same variable AND exponent.

To simplify expressions with like terms, simply combine the like terms.

Are these like terms?

1) 13k, 22k

Yes, the variables are the same.

2) 5ab, 4ba

Yes, the order of the variables doesn’t matter.

3) x3y, xy3

No, the exponents are on different variables.

8x 2 2x2 5a a

The above expression simplifies to:

10x2 6a

8x 2 2x2

5a and a are like terms

and are like terms

12a

2) 6.1y - 3.2y

2.9y

3) 4x2y + x2y

5x2y

4) 3m2n + 10mn2 + 7m2n - 4mn2

10m2n + 6mn2

Simplify1) 5a + 7a

21a + 6b

6) 4d + 6a2 - d + 12a2

18a2 + 3d3y

4

y

47)

3y

4

1y

4

4y

41y

y

5) 13a + 8a + 6b

Objective: Use the order of operations to evaluate expressions

Section II: Order of Operations

Simple question: 7 + 43=?

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.

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 x 3 and use the order of operations.

= 7 + 12 (Multiply.)

= 19 (Add.)

Example #1

14 ÷ 7 x 2 - 3

= 2 x 2 - 3 (Divide)

= 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 #320 - 3 x 6 + 102 + (6 + 1) x 4

= 20 - 3 x 6 + 102 + (7) x 4(parentheses)

= 20 - 3 x 6 + 100 + (7) x 4 (exponents)

= 20 - 18 + 100 + (7) x 4 (Multiply)

= 20 - 18 + 100 + 28 (Multiply)

= 2 + 100 + 28 (Subtract )

= 102 + 28 (Add)

= 130 (Add)

Which of the following represents 112 + 18 - 33 · 5 in simplified form?

1. -3,236

2. 4

3. 107

4. 16,996

Which of the following represents 112 + 18 - 33 5 in simplified form?

1. -3,236

2. 4

3. 107

4. 16,996

Simplify16 - 2(10 - 3)

1. 2

2. -7

3. 12

4. 98

Simplify16 - 2(10 - 3)

1. 2

2. -7

3. 12

4. 98

Simplify24 – 6 4 ÷ 2

1. 72

2. 36

3. 12

4. 0

Simplify24 – 6 4 ÷ 2

1. 72

2. 36

3. 12

4. 0

1. substitute the given numbers for each variable.

2. use order of operations to solve.

Evaluating a Variable ExpressionTo evaluate a variable expression:

Example # 4

n + (13 - n) 5 for n = 8

= 8 + (13 - 8) 5 (Substitute.)

= 8 + 5 5 (parentheses)

= 8 + 1 (Divide)

= 9 (Add)

Example # 58y - 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)

= 16 - 75 + 2 3 (Multiply)

= 16 - 75 + 6 (Multiply)= -59 + 6 (Subtract)= -53 (Add)

What is the value of

if n = -8, m = 4, and t = 2 ?

t

mn2

1. 10

2. -10

3. -6

4. 6

What is the value of

if n = -8, m = 4, and t = 2 ?

t

mn2

1. 10

2. -10

3. -6

4. 6