Variables & Algebraic Expressions A symbol, usually a letter, that represents one or more numbers. Algebraic Expression A mathematical phrase that includes one or more variables. Numerical Expression A mathematical phrase involving numbers and operation symbols, but no variables. Equation A mathematical sentence that has an equal sign. If a plumber earns $60 per hour, in order to calculate how much money he made for a particular job, you would multiply the number of hours he worked by $60. hours worked pay (in dollars) 1 60 2 120 3 180 4 240 5 300 6 360 You could model this relationship with an algebraic expression using h as a variable to represent the number of hours worked.

Verbal Phrases Involving Addition The algebraic expression a + b can be used to represent several different verbal phrases. a plus b a added to b a is increased by b the sum of a and b b is added to a b more than a The word exceeds means “is more than”. So, the number that exceeds 5 by 2 can be written as “2 more than 5” or 5 + 2.

Verbal Phrases Involving Subtraction The algebraic expression a - b can be used to represent several different verbal phrases. a minus b a decreased by b b less than a b subtracted from a a diminished by b a reduced by b the difference between a and b

Verbal Phrases Involving Multiplication The algebraic expressions a X b, a . b, (a)(b), and ab can be used to represent several different verbal phrases. a times b the product of a and b b multiplied by a The preferred form to indicate multiplication in algebra is ab. In algebraic expressions, parenthesis may be used but are not needed. The multiplication symbol X is avoided in algebra because it can be confused with the variable x.

Verbal Phrases Involving Division The algebraic expressions and can be used to represent several different verbal phrases. a divided by b the quotient of a and b and means one-forth of a as well as a divided by 4. Commas are very important in some verbal phrases.. The product of x and y, decreased by 2. The product of x and y decreased by 2.

Translating Words to Algebra 3 more than a number 5 less than a number a number decreased by 7 the product of 6 and a number These are examples of Algebraic Expressions. twice a number decreased by 4 25, diminished by 4 times a number the sum of a number and 2, divided by 9

Got It? 1) What is an algebraic expression for 18 more than a number n? 2) What is an algebraic expression for each word phrase? a) 6 times a number n b) The quotient of 18 and a number n 3) What is an algebraic expression for each word phrase? a) 8 less than the product of a number x and 4 b) Twice the sum of a number x and 8 c) The quotient of 5 and the sum of 12 and a number x 4) What word phrase can you use to represent the algebraic expression? d) a) b) c) The sum of a number x and 8.1 The sum of 10 times a number x and 9 The quotient of a number n and 3 Five times a number x less 1

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Modeling Relationships with Equations A mathematical sentence that uses an equal sign. Open Sentence An equation that contains one or more variables. Brianna paid 17 dollars for batteries and film for her camera. If the batteries cost x dollars, express the cost of the film in terms of x. That was easy Relate: Film equals $17 minus the cost of the batteries. Define: x = cost of batteries f = cost of film Write:

More Modeling Relationships with Equations CD’s Cost (in dollars) 1 15 2 30 3 45 4 60 Define the variable and write an equation to model the relationship in the table. Number of Workers Radios Built 1 11 2 22 3 33 4 44 Define: Define: n = number of CD’s c = cost of CD’s w = number of workers r = number of radios Asi de Facil Write: Write:

Even More Modeling Relationships with Equations Define the variable and write an equation to model the relationship in the table. Sales Earnings (in dollars) 3 21 6 42 9 63 12 84 Number of Hours Total Pay 5 $37.50 10 $75.00 15 $112.50 20 $150.00 First divide to determine the earnings for one sale. First divide to determine the pay for one hour. Define: Define: n = number of sales e = earnings Asi de Facil n = number of hours p = total pay Write: Write:

Writing a Rule to Describe a Pattern A state park charges an entrance fee of $ 20, plus $18 for each night of camping. a) If n is the number of nights that you spend camping, write an expression that gives the total cost, c, of camping for n nights. b) What is the total cost of camping for 3 nights? total cost of camping price per night # of nights entrance fee (constant) That was easy

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Now I’ll try doing 3 times 2 first. Order of Operations Let’s look at an example of a computation with more than one operation. I’ll try doing 11 – 3 first. Now I’ll try doing 3 times 2 first. That was easy Please Excuse My Dear Aunt Sally Please Excuse My Dear Aunt Sally Parentheses Exponents Multiplication Division Addition Subtraction

Examples Simplify the following. For all fractions, express the exact value and the rational approximation rounded to the nearest hundredth.

Examples Simplify the following. For all fractions, express the exact value and the rational approximation rounded to the nearest hundredth.

Examples Simplify the following. For all fractions, express the exact value and the rational approximation rounded to the nearest hundredth.

Evaluating Algebraic Expressions To evaluate an algebraic expression, replace the variables with the given values, and then follow the proper order of operations. Don’t forget about my dear Aunt Sally. Evaluate when Rewrite the expression with empty parenthesis where the variables are Replace the variables with the given values Follow the proper order of operations

More Evaluating Algebraic Expressions Evaluate Evaluate when when when

Using a Calculator to Evaluate Algebraic Expressions The given values can be stored in the calculator. when Press (-) 4 STO [ ALPHA A ENTER Evaluate 10 STO [ ALPHA N ENTER when 3 STO [ ALPHA D ENTER 2A/5+(N-1)D ENTER 10 STO [ ALPHA A ENTER 2A/5+(N-1)D (-) 6 STO [ ALPHA N ENTER ENTER (-) 5 STO [ ALPHA D ENTER

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