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Chapter 1: Foundations for Algebra 1.1 Variables and Expressions Objective: to write algebraic expressions August 17, 2015 by K.M. Showers High School I can… distinguish between algebraic and numerical expressions. identify the parts of an expression. Translate verbal expressions into math expressions and vice versa.(A.SSE.A.1a) Uses the structure of an expression to identify ways to rewrite it.(A.SSE.A.2) Vocabulary… Green Book: Algebra I Common Core-Pearson Quantity… Anything that can be measured or counted. Some remain constant. Others change, or vary…they are called variable quantities. Algebra… Uses symbols to represent quantities that are unknown or that vary. We use symbols and operations to represent mathematical phrases and real-world relationships. Question: What is the area of a rectangle? Length times Width If the length is 3 meters and the width is 2 meters, what is the area? A=LxW A = 3 x 2 = 6 meters2 A, L and W are the variables. It is any symbol, usually a letter, that represents the unknown value(s) of a variable quantity. An algebraic expression contains: 1) one or more numbers or variables, and 2) one or more arithmetic operations. Examples: x-3 3 • 2n 4 1 m In expressions, there are many different ways to write multiplication. 1) 2) 3) 4) 5) ab a•b a(b) or (a)b (a)(b) axb We are not going to use the multiplication symbol any more. Why? Division, on the other hand, is written as: x 1) 3 2) x ÷ 3 Throughout this year, you will hear many words that mean addition, subtraction, multiplication, and division. Complete the table with as many as you know. Addition Subtraction Multiplication Division Here are some phrases you may have listed. The terms with * are ones that are often used. Addition sum* increase plus add more than total Subtraction difference* decrease minus subtract less than Multiplication Division product* times multiplied quotient* divided ratio Write an algebraic expression for… 1) m increased by 5. m+5 2) 7 times the product of x and t. 7xt or 7(x)(t) or 7 • x • t 3) 11 less than 4 times a number. 4n - 11 4) two more than 6 times a number. 6n + 2 5) the quotient of a number and 12. x 12 Which of the following expressions represents 7 times a number decreased by 13? 1. 7x + 13 2. 7x - 13 3. 13 - 7x 4. 13 + 7x Answer Now Which one of the following expressions represents 28 less than three times a number? 1. 28 - 3x 2. 3x - 28 3. 28 + 3x 4. 3x + 28 Answer Now Write a verbal expression for: 1) 8 + a. The sum of 8 and a 2) m r . The ratio of m to r Do you have a different way of writing these? Which of the following verbal expressions represents 2x + 9? 1. 9 increased by twice a number 2. a number increased by nine 3. twice a number decreased by 9 4. 9 less than twice a number Answer Now Which of the following expressions represents the sum of 16 and five times a number? 1. 5x - 16 2. 16x + 5 3. 16 + 5x 4. 16 - 5x Answer Now When looking at the expression 103, 10 is called the base and 3 is called the exponent or power. 103 means 10 • 10 • 10 103 = 1000 How is it said? 21 Two to the first power 22 Two to the second power or two squared 23 Two to the third power or two cubed 2n7 Two times n to the seventh power Which of the following verbal expressions represents x2 + 2x? 1. the sum of a number squared and twice a number 2. the sum of a number and twice the number 3. twice a number less than the number squared 4. the sum of a number and twice the number squared Answer Now Which of the following expressions represents four less than the cube of a number? 1. 4 – x3 2. 4 – 3x 3. 3x – 4 4. x3 – 4 Answer Now Evaluate. 21 2 22 2•2=4 23 2•2•2=8 2n7 We can’t evaluate because we don’t know the value of n!! Is 35 the same as 53? Evaluate each and find out! 35 = 3 • 3 • 3 • 3 • 3 = 243 53 = 5 • 5 • 5 = 125 243 ≠ 125 They are not the same! Numerical Expression… Mathematical Phrase that involves numbers and operations, but no variables. • 3•3 • 9(5-2) • 4 + 68 Guided Practice: Lesson Check pp. 7, 1-8 1. Numerical, algebraic, numerical 2. 9t, x – 1/2, m + 7.1, 207/n 3. The product of 6 and a number c 4. the differences of a number x and 1 5. the quotient of a number t and 2 6. 4 less the product of a number t and 3 7. Numerical expressions are just numbers and operations. Algebraic expressions have variables, numbers and operations. 8. 49 + 0.75n Independent Practice… Pp. 7-9 Problems 9-34 all Answers only