Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Variables, Algebraic Expressions, and Simple Equations 1 Can you form your own definition of a variable based on the following? These are variables These are not A = # , C = #, X = #,r = #, n = # =# =# 3, 10, 75, 8, 12, 1, 0 2 Discuss and make a list of similarities and differences (compare and contrast) These are variables A = # , C = #, X = #,r = #, n = # =# =# How they’re the same: These are not 3, 10, 75, 8, 12, 1, 0 How they’re different: See if your definition that you came up with matches the definition of a variable: Variable is…. A letter or symbol that stands for an unknown number. Examples: a , C, x, N, , Copy this down in your notes 4 Algebraic Expressions • An expression consists of a combination of numbers, operation symbols, and grouping symbols such as parentheses ( ). An algebraic expression is an expression that contains one or more variables an operation and one or more numbers. • Expressions: 3+4 6–2 (6 + 3) -1 Algebraic Expressions 3 (c + 8) Notice that you don’t see any 2a equal signs 9–x 5 Reading and Writing Algebraic Expressions + plus sum more than increased by total in all added to - minus difference less than subtract decreased by Take away Subtracted from x times product multiplied each of divided quotient divided by Other ways to show Other ways to show division: multiplication : 5(6) 5·6 12/6 6 Glue this in your notes and go over examples of how to read/write algebraic expressions Using your notes, try to figure out what operation (+,-,x,/) to use for the following: 4 increased by a number 25 less than a number The phrase “a number” or “some number” means that a variable is needed. 7 Now, that we know the components of this expression, let’s try to write an algebraic expression for each word phrase 4 increased by a number 4+c *it does not matter what letter you use, just as long as you include a variable. 25 less than a number n – 25 *just because we see 25 first in the word phrase, doesn’t mean that 25 is written first in the expression. 8 Try to write these on your own: Add 3 to a number Some number multiplied by 16 9 Now, try to translate, or write the following algebraic expressions into a word phrase on your own. 1) n - 5 2) 9 + t 10 Now, try to translate, or write the following algebraic expressions into a word phrase on your own. Answers will vary… 1) n - 5 1) Take 5 away from a number 2) 9 + t 2) 9 added to a number 11 When we evaluate algebraic expressions, we are substituting a number in place of variable, then solving for an answer Evaluate each expression when a = 12 1) a + 3 2) 17 – a 12 When we evaluate algebraic expressions, we are substituting a number in place of variable, then solving for an answer Evaluate each expression when a = 12 1) a + 3 12 + 3 15 2) 17 – a 17 – 12 5 13 You try to evaluate the following when n = 4 1) 9n *(what operation does this mean when a number is right beside a variable? Look at your notes if you don’t know) 2) 40 / n 14 You try to evaluate the following when n = 4 1) 9n 9x4 36 2) 40 / n 40 / 4 10 15 An Equation is a complete sentence that is either true or false = shows that each side has the same value examples: x + 7 = 14 7 + 7 = 14 14 = 14 47 = 50 – 3 y – 6 = 13 16 Determine if the following are expressions or equations: 1) 7x 2) (6-3) – 1 = 2 3) 14 = 7(2) 4) X + 9 = 13 5) 12 – 5 17 Determine if the following are expressions or equations: 1) 7x 2) (6-3) – 1 = 2 3) 14 = 7(2) 4) X + 9 = 13 5) 12 – 5 • • • • • 1) expression 2) equation 3) equation 4) equation 5) expression How could you tell the difference between the two? 18 #1 - In your own words, tell me what a variable is? #2 - Write down at least 2 examples of variables: #1 - In your own words, tell me what a variable is? A variable is a letter or symbol that represents an unknown # #2 - Write down at least 2 examples of variables: C, x, n, Answers may vary Write an algebraic expression for each word phrase: #3) subtract 14 from a number #4) 15 is decreased by a number #5) add 8 to a number Write an algebraic expression for each word phrase: #3) take 14 from a number n – 14 #4) 15 is decreased by a number 15 – n #5) add 8 to a number n + 8 or 8 + n • Evaluate means to substiture a value, then solve the problem. Evaluate each expression when x=9 #6) 7 + x _________ #7) x – 3 _________ Evaluate each expression when x=9 #6) 7 + x _________ 7 + 9 = 16 #7) x – 3 _________ 9–3=6