1 / 13

Understanding the Multiplication Property of Equality and Reciprocals in Algebra

This lesson covers the Multiplication Property of Equality and the concept of reciprocals in algebra. It explains that two numbers are reciprocals when their product equals 1, and highlights properties of reciprocals concerning positive and negative numbers, including that the reciprocal of 0 does not exist. The lesson also addresses solving equations using the Multiplication Property of Equality, emphasizing the importance of multiplying both sides by the reciprocal of a number to isolate variables. Homework exercises are included for practice.

catori
Télécharger la présentation

Understanding the Multiplication Property of Equality and Reciprocals in Algebra

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. MTH 10905Algebra The Multiplication property of equality CHAPTER 2 Section 3

  2. Identity Reciprocals • Reciprocal – two numbers are reciprocals when their product equals 1. • If a is a non-zero number the reciprocal is • The reciprocal of a positive is positive and the reciprocal of a negative is a negative

  3. Identity Reciprocals • The reciprocal of 0 does not exist. first we cannot have a zero on the bottom of a fraction second zero divided by zero is zero. • Exp: the reciprocal of 3 is because • Exp: the reciprocal of -2 is because

  4. Identity Reciprocals • Exp: the reciprocal of is because • Exp: the reciprocal of is because

  5. Multiplication Property to Solve Equation • Multiplication Property of Equality if a = b then a · c = b · c for any real number a, b, and c • We can multiply any non-zero number to both sides without changing the solution. • We can solve equations in the form of ax = b using the multiplication property • To isolate the variable we will multiply by the reciprocal of the numerical coefficient .

  6. Multiplication Property to Solve Equation • Exp: Exp:

  7. Multiplication Property to Solve Equation • Exp: Division is defined in the term of multiplication this allows is to divide both sides by a non-zero number Exp:

  8. Multiplication Property to Solve Equation • Exp: Exp:

  9. Multiplication Property to Solve Equation Exp: Exp:

  10. Multiplication Property to Solve Equation When solving an equation in the form of ax = b: • for a fractions multiply both sides by the reciprocal of a • for whole numbers divide both sides by a Exp: Exp:

  11. Solve Equation in the form of –x = a • Remember that x = a is the same as 1x = a Therefore, -x = a is the same as -1x = a Exp: Exp:

  12. Do some steps Mentally to Solve Equations • As you become comfortable you can do some of the steps mentally Exp: Exp:

  13. HOMEWORK 2.3 • Page 118 – 119 #9, 11, 19, 25, 31, 35, 49, 57

More Related