Section 1-1Section 1-1Section 1-1Section 1-1Algebra: Variables and Algebra: Variables and

ExpressionsExpressions

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 25-10 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+3xIs 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– xn= x· x· x· x· x·… x– variable x is the base and n is the exponent.

Exponent

Ex: Evaluate expression 33. (3 · 3· 3 = 27)What is the base number? What is the exponent?How do we read 33 ? “3 to the power of 3”, “3 to the third power,” or “3 cubed”

Ex: Evaluate expression 22. (2 · 2= 4)What is the base number? What is the exponent?How do we read 22 ? “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; 2a3

-Ex: the sum of 11 and x to the third power; 11+x3

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+x3

• the sum of 11 and x to the third power

– Ex: c2 +x3

• 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”