Writing Algebraic Expressions

The answer to an addition problem: __________ The answer to a subtraction problem: __________ The answer to a multiplication problem: __________ The answer to a division problem: __________ sum difference product quotient

Algebraic Representations Let a = 10 and b = 2 Sum: Difference: Product: Quotient: a + b 10 + 2 = 12 a - b 10 - 2 = 8 10 . 2 = 20 ab Nothing new yet, right? = 5 a b 10 2

Two Important Concepts #1: Products ab means a times b 3x means 3 times x Remember, 3 is the _________ and x is the _______ in the ____. 4gh means 4 times g times h coefficient variable term

Product Practice Let a = 4, b = 2, c = 5, and d = 3 ab = ____ 10acd = ____ b2d = ____ bc + ad = ____ 3c2 = ____ 100d = ____ 4bd = ____ abcd = ____ 7c = ____ 8 75 6 300 600 24 12 120 22 35

Two Important Concepts Remember, fractions mean division. #2: Quotients means a divided by b means x divided by 4 Remember, fractions mean division. a b x 4 6 3 = 2, because 6 ÷ 3 = 2

Quotient Practice Let w = 2, x = 5, y = 3, and z = 4 9 y 10w 4 = ____ 3 = ____ 5 z w 8y w 2 12 20 x xz 2 4 10 z2 2 180 wxy 8 6

5y + 6 A letter used to represent one or more numbers: The number which is multiplied by one or more variables or powers of variables in the term: A term that has a fixed value and does not contain variables: coefficient variable constant 5y + 6 The number in front of the letters. A number by itself. The Letter. Term Term Algebraic Expression

A ___________________ is an expression that contains only and numerical expression 1 numbers 2 3 4 5 6 7 8 9 10 operations. + - x ÷ 11 - 4 3 + 6 10 ÷ 5 9 3 8 x 2 7(9 + 3)

An __________________ is an expression that contains algebraic expression An __________________ is an expression that contains one or more . variables a b c r s t w x y z ab 3w 6m + n x y t - 5 2(4 - v)

x 2 + 5y + 3x + 6 x y x 2 5y 3x 6 Consider the expression: The variables are ___ and ___. x 2 5y There are four terms: ___, ___, ___ and ___. 3x 6

x 2 + 5y + 3x + 6 x 2 5y 3x 1 5 3 6 Consider the expression: There are three variable terms: ___, ___ and ___. x 2 5y 3x 1 They have coefficients of ___, ___ and ___. 5 3 6 There is one constant term: ___

expression algebraically: Represent each expression algebraically: n - 4 Four less than a number: ______ Two more than twice as many hours: ________ 2h + 2 d 3 Work Backwards One-third as many dollars: _____ Three times the sum of a number and five: _________ 3(x + 5)

Algebra now, Geometry later … The perimeter of a rectangle is the ‘distance around the outside’ The width + the length + the width perimeter = w + l + w + l p = 2w + 2l + the length