1 Simplifying Expressions Simplifying Expressions in Algebraic Expressions Applications in Atomic Sciences.

Slides:



Advertisements
Similar presentations
Evaluate expressions with grouping symbols
Advertisements

1-2 The Order of Operations Objective: Use the order of operations and grouping symbols.
Chapter 3 Math Vocabulary
Order Of Operations.
Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations.
Expressions Objective: EE.01 I can write and evaluate numerical expressions involving whole number exponents.
The Language of Algebra
4-1 6 th grade math Exponents. Objective To write and evaluate exponential expressions Why? To prepare you for higher learning in math and science. To.
Ch 1.3 – Order of Operations
Bell Ringer = – 5 = = ÷ -2 = =6. -7 – (-7) = After you have completed the bell ringer, take out your homework!
ORDER OF OPERATIONS x 2 Evaluate the following arithmetic expression: x 2 Each student interpreted the problem differently, resulting in.
Algebraic Expressions 1 Applications in atomic science.
Order of Operations.
Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.
Order of Operations - rules for arithmetic and algebra that describe what sequence to follow to evaluate an expression involving more than one operation.
Order of Operations 1-2. Objectives Evaluate numerical expressions by using the order of operations Evaluate algebraic expressions by using the order.
Divide. Evaluate power – 3 = – 3 EXAMPLE – 3 = 3 2 – – 3 = 6 – 3 Multiply. Evaluate expressions Multiply and divide from.
CONFIDENTIAL1 Warm-up: 1.) = 2.) = 3.)9 - 6 ÷ 3 = 4.)4 + 5 x 8 = 5.) = Today we will learn How to Evaluate Expressions.
1-2 Order of Operations and Evaluating Expressions.
ALGEBRA READINESS LESSON 2-6 Warm Up Lesson 2-6 Warm Up.
Intro to Exponents Learn to evaluate expressions with exponents.
Commutative and Associative Properties. Properties are rules in mathematics. You can use math properties to simplify algebraic expressions!
3. You MUST always tidy up after having company. 1. The Letters live on the left, The Numbers live on the right.
Holt CA Course 1 1-3Order of Operations AF1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator. Also.
1.2 Variables, Expressions, and Properties
Ch 1.2 Objective: To simplify expressions using the order of operations.
The Order of Operations Chapter Evaluate inside grouping symbols ( ), { }, [ ], | |, √ (square root), ─ (fraction bar) 2.Evaluate exponents 3.Multiply.
Commutative and Associative Properties
Course Look for a Pattern in Integer Exponents 4-2 Look for a Pattern in Integer Exponents Course 3 Warm Up Warm Up Lesson Presentation Lesson Presentation.
Equations Inequalities = > 3 5(8) - 4 Numerical
Day Problems Write an algebraic expression for each phrase.
Variables and Expressions Order of Operations Real Numbers and the Number Line Objective: To solve problems by using the order of operations.
Math Notebook, Pencil & Calculator.  Find the sum or difference. Write the polynomial decrease from left to right.  (5a^2 -3) +(8a^2 -1) =  (3x^2 -8)
Order of Operations Jan Sands Butterfly Science & Math 2008.
1-2 Order of Operations Objective: Use the order of operations to evaluate expressions.
The Order of Operations The Order of Operations Objective: Use the order of operations and grouping symbols.
2.8 Inverse of a Sum on Simplifying continued Goal: to simplify expressions involving parenthesis and to simplify with multiple grouping symbols.
Order of Operations ~ Use Order of Operations.
§ 1.8 Exponents and Order of Operations. Definition of Natural Number Exponent If b is a real number and n is a natural number, b is the base and n is.
ORDER OF OPERATIONS. 1.Perform any operations with grouping symbols. 2.Simplify powers. 3.Multiply and divide in order from left to right. 4.Add and subtract.
Algebraic Expressions with a Technical Example 1 Evaluating Algebraic Expressions Evaluating Expressions Using Technical Applications.
8 – Properties of Exponents No Calculator
Algebraic Expressions Applications in atomic science
So, to simplify an expression using order of operations, you should:
WARM-UP 8/29: Simplify: ) )
Learn to evaluate expressions with exponents.
Order Of Operations.
Simplifying Expressions in Algebraic Expressions
Lesson 2.1 How do you use properties of addition and multiplication?
Chapter 1 / Whole Numbers and Introduction to Algebra
G P EMDAS.
Rational Numbers & Equations
You replace it with its simplest name
Chapter 3: Lesson 3 Order of Operations
1-9 Order of operations and distributive property
Learn to evaluate expressions with exponents.
Chapter 4-2 Power and Exponents
Chapter 3-1 Distributive Property
Order of Operations.
1.1 Symbols and Expressions
Variables and Expressions 1-1
4-2 Warm Up Problem of the Day Lesson Presentation
Solve in Groups (Standard Write and Interpret numerical expressions )
ALGEBRA what you need to know..
Evaluating Algebraic Expressions
Evaluating Expressions
Ch 1-2 Order of Operations
Order of Operations.
Distributive Property
Presentation transcript:

1 Simplifying Expressions Simplifying Expressions in Algebraic Expressions Applications in Atomic Sciences

2 Simplifying Expressions Scientists, engineers and technicians need, develop, and use mathematics to explain, describe, and predict what nature, processes, and equipment do. Many times the math they use is the math that is taught in ALGEBRA 1!

3 Simplifying Expressions The Objective of this presentation is show how: to simplify algebraic expressions by using the rules for order operations to evaluate algebraic expressions.

4 Simplifying Expressions Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. Two Examples = = )( = )( )( = )( = = (a) (b) Rules =

5 Simplifying Expressions Perform operations within parenthesis first. Add (subtract) in order from left to right. Two Simple Examples (103)14-+10= = = =(103) (a) ? = = = Multiply (divide) in order from left to right. Perform operations within parentheses first. Add (subtract) in order from left to right. Rules

6 Simplifying Expressions = )( = )( )( = )( = Another way that technicians, scientists and engineers often simplify this type of algebraic expression. = )( )( 1 (9-4) (4 9) = )( = )( = Rules used? Perform operations within parentheses first. Multiply (divide) in order from left to right. (b) = Rule to use first? Perform operations within parenthesis Multiply (divide) in order from left to right.

7 Simplifying Expressions Two Generalization Examples = )( - d 1 b )( 1 (d – b) (b d) Simplifying Expressions Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. Rules (a) )( For the previous problem, b was equal to 4 and d was equal to 9

8 Simplifying Expressions = )( - n2n2 1 n1n )( (n 2 – n 1 ) 10 1 (n 1 n 2 ) This time the symbol n 1 replaces the letter b and the symbol n 2 replaces the letter d. (b) = )( - d 1 b )( (d – b) 10 1 (b d) Technical workers often use different symbol combinations for the letters b and d.

9 Simplifying Expressions Evaluation of a new expression )( - n2n2 1 n1n This time let n 1 equal 2 and n 2 equal 3 = ?0.014 )( = = )( )( (9 -4) 10 1 (4 9) 22 = ? NOTE: The calculations inside the parentheses were completed before multiplying by one tenth. )( =

Simplifying Expressions Perform operations within parenthesis first. Reciprocal Expressions 10 [ ] 1 = 10 [] = [] =0.10 Three easy examples of reciprocal expression manipulations a) b) [ ] 1 = 10 [ ] 1 = There is nothing to do inside this parentheses There is something to do inside this parentheses Multiply (divide) in order from left to right (2) +2 [ ] 1 = Rules Perform operations within parentheses first. Add (subtract) in order from left to right.

11 Simplifying Expressions These two expressions are same. )( - n2n2 1 n1n [] 1 = )( - n2n2 1 n1n [] c) )( [ ] 1 = = [ ] 1 )( [] A typical reciprocal (inverse) expression used in technology 10 [ ] 1 = This version is popular in technical applications because it takes up less space on a piece of paper and is easier to type on a computer. Rules Perform operations within parentheses first. Reciprocal Expressions

12 Simplifying Expressions What is the value of this expression when n 1 equals 2 and n 2 equals 3? )( - n2n2 1 n1n [] 1 = )( - n2n2 1 n1n [] Practice Problem Rules Perform operations within parentheses first. Reciprocal Expressions

13 Simplifying Expressions NOTE: 2 2 = 2 times 2 = = 3 times 3 = 9 = = Perform operations within all parentheses first! = )( [ ] )( 10 1 (9 -4) (4 9) [] = = )( [ ] )( [] [] 71.4 n 1 equals 2 and n 2 equals 3 The calculation of the inverse is the last thing done. )( - n2n2 1 n1n []

14 Simplifying Expressions = = Perform operations within parentheses first = )( [ ] )( 10 1 (9 -4) (4 9) [] = = )( [ ] )( [] [] 71.4 The calculation of the inverse is the last thing done () [] NOTE: = () is the inverse of the number ) 2)

15 Simplifying Expressions 3 quick review questions to see what we remember 1)What are, in the correct order of use, the rules for simplifying algebraic expressions? 2)What is another way to write the following algebraic expression? ) Perform operations within parentheses first. Multiply (divide) in order from left to right. Add (subtract) in order from left to right. )( - n2n2 1 n1n1 1 )( (n 2 – n 1 ) (n 1 n 2 ) = What is (b) (a) the inverse of ? () 1 () the reciprocal of the the number 71.4?

16 Simplifying Expressions What do you think? 1) (a) Is the inverse of a number always the same as the reciprocal of that number? Why/Why not? Are the two algebraic expressions show below equal? Why/why not? -2-2 )( - n2n2 1 n1n [] 2) (b) )( - n2n2 1 n1n [] 1 2

17 Simplifying Expressions