Variables, Algebraic Expressions, and Simple Equations

Can you form your own definition of a variable based on the following? These are variables These are not 3, 10, 75, 8, 12, 1, 0 A = # , C = #, X = #,r = #, n = # = #

Discuss and make a list of similarities and differences (compare and contrast) These are variables These are not How they’re the same: A = # , C = #, X = #,r = #, n = # = # 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

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: Algebraic Expressions 3 + 4 3 (c + 8) 6 – 2 2 a (6 + 3) -1 9 – x Notice that you don’t see any equal signs

+ - x ¸ plus sum more than increased by total in all added to minus Reading and Writing Algebraic Expressions + - x ¸ plus sum more than increased by total in all added to minus difference less than subtract decreased by Take away Subtracted from times product multiplied each of divided quotient divided by Other ways to show division: 12/6 Other ways to show multiplication : 5(6) 5 · 6 Glue this in your notes and go over examples of how to read/write algebraic expressions

4 increased by a number 25 less than a number 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.

4 increased by a number 4 + c 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.

Try to write these on your own: Add 3 to a number Some number multiplied by 16

Now, try to translate, or write the following algebraic expressions into a word phrase on your own.

Now, try to translate, or write the following algebraic expressions into a word phrase on your own. Answers will vary… Take 5 away from a number 9 added to a number n - 5 9 + t

Evaluate each expression when 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 a + 3 17 – a

Evaluate each expression when 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 a + 3 12 + 3 15 2) 17 – a 17 – 12 5

You try to evaluate the following when n = 4 *(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

You try to evaluate the following when n = 4 9 x 4 36 40 / n 40 / 4 10

An Equation is a complete sentence that is either true or false = shows that each side has the same value examples: x + 7 = 14 47 = 50 – 3 7 + 7 = 14 y – 6 = 13 14 = 14

Determine if the following are expressions or equations: (6-3) – 1 = 2 14 = 7(2) X + 9 = 13 12 – 5

Determine if the following are expressions or equations: (6-3) – 1 = 2 14 = 7(2) X + 9 = 13 12 – 5 1) expression 2) equation 3) equation 4) equation 5) expression How could you tell the difference between the two?

#1 - In your own words, tell me what a variable is? #2 - Write down at least 2 examples of variables:

#2 - Write down at least 2 examples of variables: C, x, n, #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

Evaluate each expression when x = 9 7 + 9 = 16 #7) x – 3 _________ 9 – 3 = 6