1 / 10

Understanding Algebra: Variables, Expressions, and Writing Equations

This section introduces the basics of algebra, focusing on key concepts such as variables, algebraic expressions, factors, and exponents. Discover what makes a variable important and how to identify them in real-life scenarios. Learn how to write and evaluate algebraic expressions, as well as convert between verbal and algebraic forms. The lesson also covers the principles of multiplication and the meaning of exponents. By the end, students will be equipped to tackle algebraic problems and translate expressions effectively.

ata
Télécharger la présentation

Understanding Algebra: Variables, Expressions, and Writing Equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 1-1 Algebra: Variables and Expressions

  2. Why study algebra?

  3. Variable • 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 • 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?

  4. Algebraic Expression • “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. • 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.

  5. Factor • xy x(y) (x)y (x)(y) • Algebraic expression consist a raised dot or parentheses. This means multiplication. • Factor is quantities being multiplied • 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.

  6. Exponent • Exponent (or powers): repeated multiplication • xn= x· x· x· x· x·… x • variable x is the base and n is the 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”

  7. Writing Algebraic Expression • 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

  8. 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

  9. Writing Verbal 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

  10. 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”

More Related