Section 1-1 Algebra: Variables and Expressions

Why study algebra?

Variable: Symbols are used to represent unspecified numbers or values “vary”; it means that the value can vary, not fixed. a, b, z, e, f Variable Ex 1: Let t be the temperature of each day in a week. Is temperature a variable? Ex. 2: Is 5 a variable? Ex. 3: Let ϐ be the weight of a student in class. Is the weight a variable?

“expression” means what? consists of one or more numbers and variables and with one or more arithmetic operations. string of numbers and operators that can be placed on one side of an equation like 2+3. Algebraic Expression Ex. 1: Is x + 2 =3 an algebraic expression? Ex. 2: Is 3x-7 an algebraic expression? Ex. 3: Is an algebraic expression? Ex. 3: Come up with your own algebraic expression.

xy x(y) (x)y (x)(y) Algebraic expression consist a raised dot or parentheses. This means multiplication. Factor is quantities being multiplied Factor Ex 1: Is 5x a factor? Ex 2: Is (y+3) a factor? Is y a factor?; x(y+3) = xy+3x Is there anything unusual on the right side of the equation? There is a ‘common factor.’ Is xy + 3x equal to x(y+3)? Why? It is commutative. 2 – 3 =?= 3-2 What do we think of when we hear the term ‘product’? Multiplication! The result is called the product.

Exponent (or powers): repeated multiplication –x n = x· x· x· x· x·… x –variable x is the base and n is the exponent. Exponent Ex: Evaluate expression 3 3. (3 · 3· 3 = 27) What is the base number? What is the exponent? How do we read 3 3 ? “3 to the power of 3”, “3 to the third power,” or “3 cubed” Ex: Evaluate expression 2 2. (2 · 2= 4) What is the base number? What is the exponent? How do we read 2 2 ? “2 to the power of 2”, “2 to the second power”

Write each expression algebraically. –Ex: the product of 2 and a to the third power; 2a 3 -Ex: the sum of 11 and x to the third power; 11+x 3 Writing Algebraic Expression

Write an algebraic expression for each verbal expression. –Ex: five more than a number n 5+n –Ex:7 less than the product of 4 and a number x 7-4x –Ex: one third of the size of the original area a 1/3a or a/3 Writing Algebraic Expression

Write a verbal expression for each algebraic expression –Ex: 11+x 3 the sum of 11 and x to the third power –Ex: c 2 +x 3 the sum of c squared and 21 times d Writing Verbal Expression

Conclusion Conclusion: What have we learned today? –Variables –Algebraic expression –Factors and product –Exponent, power, base –Translating algebraic expression to verbal expression and vice-versa –What else? Homework: * Review notes * Read p. 8 “Translating from English to Algebra”