Document Sample

Evaluating Expressions and Combining Like Terms R. Portteus 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 Meaning Operation Expression 5x, 5·x, (5)(x) 5 times x Multiplication (same as x·5) 5 5 divided by Division ,5 x x x 5 + x (same as x + 5 plus x Addition 5) 5–x 5 minus x subtraction Evaluate a Variable Expression • Example 1: Evaluate each expression when n = 4. Simplify (means to solve the problem or perform as many of the indicated operations as possible.) a. n + 3 Solution: n + 3 = 4 + 3 Substitute 4 for n. Simplify =7 b. n – 3 Solution: n – 3 = 4 – 3 Substitute 4 for n. Simplify =1 Evaluate an Algebraic Expression • Example 2: Evaluate each expression if x = 8. a. 5x Substitute 8 for x. Simplify Solution: 5x = 5(8) Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are = 40 5 · 8 and 5 x 8. b. x ÷ 4 Substitute 8 for x. Simplify Solution: x÷4=8÷4 x 8 = 2 Recall that division problems are also fractions – this problem could be 4 4 2; written as: because x x4 4 Evaluating More Expressions • Example 3: Evaluate each expression if x = 4, y = 6, and z = 24. a. 5xy Substitute 4 for x; 6 for y. simplify Solution: 5xy = 5(4)(6) = 120 b. z Substitute 24 for z; 6 for y. Simplify. y z 24 Solution: y 6 =4 Now You Try… Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 4ac A 2. a÷c A 3. a+b+c A 4. ba A 5. b–c A 6. c÷b A You Try #1 Evaluate each expression given that a = 6, b = 12, and c = 3. 1. 4ac Substitute the value for a = 6 and c = 3 into the problem and multiply 4ac = 4(6)(3) = (24)(3) = 72 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 Substitute the value for a = 6 and c = 3 into the problem and divide a÷c=6÷3 =2 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 Substitute the value for a = 6, b=12, and c = 3 into the problem, then add. a + b + c = 6 + 12 + 3 = 18 + 3 = 21 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 Substitute the value for b=12 and a = 6 into the problem, then multiply. ba = (12)(6) = 72 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 Substitute the value for b=12 and a = 3 into the problem, then subtract. b – c = 12 – 3 =9 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 Substitute the value for c=3 and b = 12 into the problem, then Divide c 3 Note: It is better to rewrite this division Divide both numerator and c b problem as a fraction. denominator by b 12 This fraction can now be reduced to its 3 3 1 the GCF = (3) to simplest form. reduce this fraction. 12 3 4 as an answer. It is OK to have a fraction Click to return to “You try it” slide 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 2y2 and –y2 – Coefficient: A constant that multiplies a variable. • i.e. the 3 in 3a or the -1 in –b 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. Let’s try one… • Step One: Write the expression. 4x + 5x -2 - 2x + 7 • Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. 4x, 5x, and -2x -2 and 7 • Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x • Simplify the constant (number) terms. -2+7 = 5 • You have a simplified expression by writing all of the results from simplifying. 7x + 5 Another example… • 10x – 4y + 3x2 + 2x – 2y 3x2 Remember you cannot 10x, 2x combine terms with the same variable but -4y – 2y different exponents. • 3x2 + 12x – 6y Now you try… Simplify the following: • 5x + 3y - 6x + 4y + 3z A • 3b - 3a - 5c + 4b A • 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4 A • 5xy – 2yx + 7y + 3x – 4xy + 2x 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 – 2a2b + 5 – ab + ab2 + 2a2b + 4 4ab, -ab -2a2b, 2a2b 5, 4 ab2 3ab + ab2 + 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 numbers variables or more ________ _________. (Note: No arithmetic operations _______ sign) equal • To evaluate an expression write the _________, substitute a _______ for expression number each variable, and _________ the result. simplify Conclusion Continued… • In an expression, __________ are like terms the terms that have the same ________, raised to the same variables ________ (same exponents). power • A coefficient is a number that ________ a variable. multiplies

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 0 |

posted: | 3/15/2013 |

language: | Unknown |

pages: | 24 |

OTHER DOCS BY dffhrtcv3

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.