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Section I: Distributive Property Section II: Order of Operations. Objective. Section I: The Distributive Property. Use the distributive property to simplify expressions. The process of distributing the number on the outside of the parentheses to each term on the inside . - PowerPoint PPT Presentation
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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 + caa(b - c) = ab - ac and (b - c) a = ba - ca
Example #15(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 + 3z2. (a + b) c = ac + bc3. 5(2 + 3x) = 10 + 3x4. 6(3k - 4) = 18k - 24
Which statement demonstrates the distributive property incorrectly?
1. 3(x + y + z) = 3x + 3y + 3z2. (a + b) c = ac + bc3. 5(2 + 3x) = 10 + 3x4. 6(3k - 4) = 18k - 24
Answer Now
A term is a1) number, or2) variable, or3) a product (quotient of numbers
and variables).Example
5m
2x2
The coefficient isthe numerical part of the term.
Examples1) 4a 4
2) y2 1
3) 5x2
7
57
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 termsand are like terms
12a2) 6.1y - 3.2y
2.9y3) 4x2y + x2y
5x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2
10m2n + 6mn2
Simplify1) 5a + 7a
21a + 6b6) 4d + 6a2 - d + 12a2
18a2 + 3d3y4
y4
7)
3y4
1y4
4y4
1y
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 OPERATIONS1. Parentheses - ( ) or [ ] 2. Exponents or Powers3. 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. -3,2362. 43. 1074. 16,996
Which of the following represents 112 + 18 - 33 5 in simplified form?
1. -3,2362. 43. 1074. 16,996
Simplify16 - 2(10 - 3)
1. 22. -73. 124. 98
Simplify16 - 2(10 - 3)
1. 22. -73. 124. 98
Simplify24 – 6 4 ÷ 2
1. 722. 363. 124. 0
Simplify24 – 6 4 ÷ 2
1. 722. 363. 124. 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 ofif n = -8, m = 4, and t = 2 ?
tmn2
1. 102. -103. -64. 6
What is the value ofif n = -8, m = 4, and t = 2 ?
tmn2
1. 102. -103. -64. 6
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