Unit 0 Lessons 1-3 Evaluating expressions using order of operations By R. Portteus and By Miss Klien modified by LHope.

Slides:



Advertisements
Similar presentations
Variables and Expressions
Advertisements

7.1Variable Notation.
Distributive Property
Section I: Distributive Property Section II: Order of Operations.
Bell Work Simplify the expression: 1. 2(x +4) 2. 4x + 3y – x + 2y 3. 3(x – 6) x Answers: 2x+ 8 3x + 5y 11x – 14.
Basic Algebra Grade: 9 th Gustavo Miranda LRC 320.
Solving Linear Equations
Algebraic Expressions and Formulas
1-7 The Distributive Property
Homework Answers (1-2 Worksheet)
Evaluating Expressions R. Portteus. Order of Operations Review How do you follow the order of operations?
In this lesson, you will be shown how to combine like terms along with using the distributive property.
The Distributive Property
Evaluating and Rewriting Expressions Evaluate an expression. 2.Determine all values that cause an expression to be undefined. 3.Rewrite an expression.
Sets and Expressions Number Sets
Algebra 1 Final Exam Review – 5 days (2nd Semester)
 Vocabulary: ◦ Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. ◦ Variable expression.
Math 002 College Algebra Final Exam Review.
Algebraic Expressions & Polynomials
The Distributive Property allows you to multiply each number inside a set of parenthesis by a factor outside the parenthesis and find the sum or difference.
Factoring means finding the things you multiply together to get a given answer.
Order of Operations: Parenthesis Exponents (including roots) Multiplication & Division Addition & Subtraction Always Work Left to Right.
Lesson 1 Using properties of real numbers. A set is a collection of objects  If all the members of one set are also members of a second set, then the.
Chapter 1 Review College Algebra Remember the phrase “Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2.
Solving Equations. The equations are equivalent If they have the same solution(s)
Exponents and Order of Operations. Exponents The exponent (little number) indicates how many times the base (big number) appears as a factor.
MM150 Unit 3 Seminar Agenda Seminar Topics Order of Operations Linear Equations in One Variable Formulas Applications of Linear Equations.
Copyright © Ed2Net Learning, Inc.1 Properties of Numbers Grade 7 Pre-Algebra.
Regents Review #1 Expressions & Equations (x – 4)(2x + 5) 3x 3 – 4x 2 + 2x – 1 (4a – 9) – (7a 2 + 5a + 9) 4x 2 + 8x + 1 = 0 (x – 5) 2 = 25 10x 3 5x 5 x.
Math Vocabulary. Algebra The area of mathematics where letters (like x or y) or other symbols are used to represent unknown numbers. Example: in x - 5.
The Distributive Property You will be able to use the distributive property You will be able to simplify expressions with like terms.
Algebra 1 Shelby Ferreira. Vocabulary Variable Coefficient Exponent Like terms Expression Equation.
Evaluating Expressions and Combining Like Terms
Choctaw High School Algebra I EOI Review 1 Simplifying Expressions To simplify an algebraic expressions, you need to combine the like terms. Like terms.
Algebra 1 Shelby Ferreira. Group Activity Half a number plus 5 is 11.What is the number? Explain your reasoning and create an equation that represents.
1.Homework Folders are marked and can be picked up 1.Late for 50% hand in to Mr. Dalton 2.Map test dates are on the wiki homepage 3.Lesson: Distributive.
Polynomial – a monomial or sum of monomials Can now have + or – but still no division by a variable. MonomialBinomialTrinomial 13x 13x – 4 6x 2 – 5x +
The Five Basic Skills of Algebra : Simplifying Evaluating Solving Factoring Graphing Do whatever you are allowed to do, according to the rules of algebra.
Combining Like Terms and the Distributive Property Objectives: Students will be able to explain the difference between algebraic equations and expressions.
MTH 091 Sections 3.1 and 9.2 Simplifying Algebraic Expressions.
Question of the Day Solve for b: 2b + 7 = 15. Expressions and Equations Collecting Like Terms and Distributive Property.
Combine Like Terms and Distributive Property. IN THIS LESSON, YOU WILL BE SHOWN HOW TO COMBINE LIKE TERMS ALONG WITH USING THE DISTRIBUTIVE PROPERTY.
Combine Like Terms and Distributive Property Mrs. Lovelace January 2016 Edited from… mrstallingsmath.edublogs.org.
3.1 – Simplifying Algebraic Expressions
The Distributive Property
Evaluating Expressions and Combining Like Terms
Evaluating Expressions and Combining Like Terms
Section I: Distributive Property Section II: Order of Operations
Rational Expressions with Like Denominators
Combine Like Terms and Distributive Property
The Distributive Property
Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.
Algebraic Expressions
Do Now Write down any math properties you know and give an example. (ex. Commutative) Write down any similarities or differences between expressions and.
The Distributive Property
Combine Like Terms and Distributive Property
Variables in Algebra Chapter 1 Section 1.
Evaluating Expressions and Combining Like Terms
Variables and Expressions
 Warm-up: n HW: Pg. 10 (40) Pg. 12 (75, 79, 84, 85, 8996, 110)
Variables and Expressions
Variables and Expressions
Algebraic Expressions
Variables and Expressions
Title of Notes: Combining Like Terms & Distributive Property
Bell Ringer (NWEA) 1. Katie completed the following problem and got it incorrect. Can you tell Katie what you did wrong?  
Variables and Expressions
Evaluating Expressions and Combining Like Terms
1.3 Algebraic Expressions
Combine Like Terms Notes Page 23
Presentation transcript:

Unit 0 Lessons 1-3 Evaluating expressions using order of operations By R. Portteus and By Miss Klien modified by LHope

Evaluating Expressions and Combining Like Terms

Evaluating Expressions Vocabulary: – Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number. – Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign) – Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result.

How do you describe a variable expression? Variable Expression MeaningOperation 5x, 5·x, (5)(x) (same as x·5) 5 times xMultiplication 5 divided by x Division 5 + x (same as x + 5) 5 plus xAddition 5 – x5 minus xsubtraction

Substitute 4 for n. Simplify Simplify (means to solve the problem or perform as many of the indicated operations as possible.) Solution: Substitute 4 for n. Simplify Solution: Evaluate a Variable Expression Example 1: Evaluate each expression when n = 4. a. n + 3 n + 3 = = 7 b.n – 3 n – 3 = 4 – 3 = 1

Substitute 8 for x. Simplify Solution: Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8. Substitute 8 for x. Simplify Recall that division problems are also fractions – this problem could be written as: Evaluate an Algebraic Expression Example 2: Evaluate each expression if x = 8. a.5x 5x = 5(8) = 40 b.x ÷ 4 x ÷ 4 = 8 ÷ 4 = 2

Substitute 4 for x; 6 for y. simplify Solution: Evaluating More Expressions Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. a.5xy 5xy = 5(4)(6) = 120 b. = 4 Solution: Substitute 24 for z; 6 for y. Simplify.

A A A A A A Now You Try… Evaluate each expression given that a = 6, b = 12, and c = ac 2.a ÷ c 3.a + b + c 4.ba 5.b – c 6.c ÷ b

Substitute the value for a = 6 and c = 3 into the problem and multiply Click to return to “You try it” slide You Try #1 Evaluate each expression given that a = 6, b = 12, and c = ac 4ac = 4(6)(3) = (24)(3) = 72

Substitute the value for a = 6 and c = 3 into the problem and divide Click to return to “You try it” slide You Try #2 Evaluate each expression given that a = 6, b = 12, and c = 3. 2.a ÷ c a ÷ c = 6 ÷ 3 = 2

Substitute the value for a = 6, b=12, and c = 3 into the problem, then add. Click to return to “You try it” slide You Try #3 Evaluate each expression given that a = 6, b = 12, and c = 3. 3.a + b + c a + b + c = = = 21

Substitute the value for b=12 and a = 6 into the problem, then multiply. Click to return to “You try it” slide You Try #4 Evaluate each expression given that a = 6, b = 12, and c = 3. 4.ba ba = (12)(6) = 72

Substitute the value for b=12 and a = 3 into the problem, then subtract. Click to return to “You try it” slide You Try #5 Evaluate each expression given that a = 6, b = 12, and c = 3. 5.b - c b – c = 12 – 3 = 9

Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Substitute the value for c=3 and b = 12 into the problem, then Divide Note: It is better to rewrite this division problem as a fraction. This fraction can now be reduced to its simplest form. Divide both numerator and denominator by the GCF = (3) to reduce this fraction. It is OK to have a fraction as an answer. Click to return to “You try it” slide You Try #6 Evaluate each expression given that a = 6, b = 12, and c = 3. 6.c ÷ b

Expressions compared to Equations Expressions 8y, 16a/b, 4r + s, 7 Equations 3x + 4 = 6 3r = 9

Combining Like Terms Now that we have seen some algebraic expressions, we need to know how to simplify them. Vocabulary – Like terms: In an expression, like terms are the terms that have the same variables, raised to the same powers (same exponents). i.e. 4x and -3x or 2y 2 and –y 2 – Coefficient: A constant that multiplies a variable. i.e. the 3 in 3a or the -1 in –b

Like Terms In a term that is the product of a number and a variable, the number is the coefficient of the variable. -1 is the coefficient of x 3 is the coefficient of

Combining Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

Like Terms Like terms are terms in an expression that have the same variable raised to the same power. In the expression above, 5x and –3x are like terms, but 5x and –x 2 are not like terms. The constant terms –4 and2 are also like terms.

Let’s try one… Simplify the expression. 4x + 5x x + 7 4x, 5x, and -2x -2 and 7 4x+5x-2x = 9x-2x = 7x -2+7 = 5 7x + 5

Another example… 10x – 4y + 3x 2 + 2x – 2y 3x 2 10x, + 2x -4y – 2y 3x x – 6y Remember you cannot combine terms with the same variable but different exponents.

Now you try… Simplify the following: 5x + 3y - 6x + 4y + 3z 3b - 3a - 5c + 4b 4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4 5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

You Try #1 Simplify the following: 1.5x + 3y - 6x + 4y + 3z 5x - 6x 3y + 4y 3z -x + 7y + 3z

You Try #2 Simplify the following: 2.3b - 3a - 5c + 4b 3b + 4b -3a -5c -3a + 7b – 5c

You Try #3 Simplify the following: 3.4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4 4ab - ab -2a 2 b + 2a 2 b ab 2 3ab + ab 2 + 9

You Try #4 Simplify the following: 4.5xy – 2yx + 7y + 3x – 4xy + 2x 5xy - 2yx - 4xy 7y 3x + 2x -xy + 7y + 5x

Conclusion A variable or algebraic expression is an expression that consists of one or more ________ and _________ along with one or more ________ _________. (Note: No _______ sign) To evaluate an expression write the _________, substitute a _______ for each variable, and _________ the result. numbers variables arithmetic operationsequal expression number simplify

Conclusion Continued… In an expression, __________ are the terms that have the same ______ __, raised to the same ____ (same exponents). A coefficient is a number that ________ a variable. like terms variables power multiplies

Try 2x + 6 – x + 6y -5y x y 3(3x + 7) 9x (c – 3) + 2c 4c – c 6c -12 What is still confusing?

The Distributive Property You will be able to use the distributive property and simplify expressions with like terms

The Distributive Property The product of a and ( b+c): a(b+c) = ab + ac ex: 5(x + 2) = 5x + 10 (b + c)a = ba + ca ex: (x + 4)8 = 8x + 32 The product of a and (b-c): a(b-c) = ab – ac ex: 4(x –7)= 4x –28 (b-c)a = ba – ca ex: (x-5)9 = 9x - 45 Sharing what is Outside the parentheses with EVERYTHING INSIDE the parentheses.

What You Already Know… You have been using this property in a simplified form since third grade. Now we give it the algebraic term, and we extend it a bit. OR

A Visual Example of the Distributive property Find the area of this rectangle. We could say that this is 4(x + 2) x +2 Or.. x2 4

x So we can say that 4(x+2) = 4x+8

Example using the distributive property

Another Example

Like terms, continued… The distributive property allows you to combine like terms that have variables by adding coefficients. An expression is simplified if it has no grouping symbols and if all the like terms have been combined.

Try