Grade 11 General Mathematics Properties of Equality.pptx

Senior High School Grade 11 General Mathematics - Quarter 1 Lesson 1 (Properties of Equality)

1. PROPERTIES OF EQUALITY NIKIE V. GOLONG Special Science Teacher I

2. OBJECTIVES: Define the properties of equality used in solving mathematical equations; Identify the different properties of equality through examples and mathematical expressions;

3. Addition Subtraction Multiplication Division Reflexive Symmetric Transitive Substitution PROPERTIES OF EQUALITY

4. Definition: Any quantity is equal to itself. Reflexive

5. If a is a real number, then a = a Example: 5 = 5, x = x Reflexive

6. Symmetric Definition: If one quantity equals a second quantity, then the second equals the first.

7. Symmetric If a = b , then: b = a Example: If x +2 = 7, then 7= x + 2

8. Transitive Definition: If one quantity equals a second quantity and the second equals a third quantity, then the first equals the third.

9. Transitive If a = b and b = c , then a = c Example: If x = y + 3 and y + 3 = 10, then x = 10

10. Substitution Definition: If two quantities are equal, one may be substituted for the other in any expression or equation.

11. Substitution If a = b , then b can be substituted for a (or vice versa) in any expression. Example: If x = 5 and 3 x = y , then 3(5) = y

12. Let’s Practice!

13. 1. Which property is shown by the statement: If P = Q, then Q = P? A. Symmetric Property B. Substitution Property C. Reflexive Property D. Transitive Property

14. 2. Identify the property: For any variable z, z = z. A. Transitive Property B. Symmetric Property C. Substitution Property D. Reflexive Property

15. 3. If x = 10 and 10 = y, then x = y. This is an example of the: A. Symmetric Property B. Reflexive Property C. Substitution Property D. Transitive Property

16. 4. Given A = B + C. If B + C = 5, then A = 5. What property justifies this step? A. Symmetric Property B. Transitive Property C. Reflexive Property D. Substitution Property

17. 5. When you replace ‘cost’ with ‘ ₱5.00’ in the sentence, ‘The total is the cost plus tax,’ assuming ‘cost = ₱5.00’, which property is used? A. Reflexive Property B. Transitive Property C. Substitution Property D. Symmetric Property

18. What property of equality is being shown? 6. If 10=x, then x=10 SYMMETRIC

19. What property of equality is being shown? 7. If c=2, then 2c=4. SUBSTITUTION

20. What property of equality is being shown? 8. xyz = xyz REFLEXIVE

21. What property of equality is being shown? 9. If x = 2, and 2 = y, then x = y. TRANSITIVE

22. What property of equality is being shown? 10. If 4d=r, then r=4d SYMMETRIC

23. Addition Definition: The same number may be added to both sides of an equation without changing the equality.

24. Addition If a = b , then a + c = b + c Example: x – 4 = 6 x – 4 + 4 = 6 + 4 x = 10

25. Subtraction Definition: The same number may be subtracted from both sides of an equation without changing the equality.

26. Subtraction If a = b , then a - c = b - c Example: x + 4 = 6 x + 4 - 4 = 6 - 4 x = 2

27. Multiplication Definition: Both sides of an equation may be multiplied by the same nonzero number without changing the equality.

28. Multiplication If a = b , then a • c = b • c Example:  

29. Division Definition: Both sides of an equation may be divided by the same nonzero number without changing the equality.

30. Division If a = b and c ≠ 0, then Example:  

31. Let’s Practice!

32. 1. When solving the equation x + 4 = 10, you subtract 4 from both sides. Which property of equality are you using? A. Addition C. Division B. Multiplication D. Subtraction

33. 2. If A = B, then A ⋅ C = B ⋅ C What property of equality is illustrated here? A. Addition C. Division B. Multiplication D. Subtraction

34. 3. The step from to y = 15 is an application of the: A. Division Property of Equality B. Addition Property of Equality C. Subtraction Property of Equality D. Multiplication Property of Equality  

35. 4. To change 8x = 24 into x = 3, you divide both sides by 8. This is an example of the: A. Subtraction Property of Equality B. Multiplication Property of Equality C. Addition Property of Equality D. Division Property of Equality

36. What property of equality is being shown? x + 10 = 6 x + 10 – 10 = 6 - 10 x = -4 subtraction

37. What property of equality is being shown?   multiplication

38. What property of equality is being shown?   division

39. What property of equality is being shown? x - 10 = 6 x - 10 + 10 = 6 + 10 x = 16 addition

40. REFERENCES 1. Department of Education. (2016) . K to 12 curriculum guide: General Mathematics. Department of Education, Republic of the Philippines. 2. Paul Dawkins. (n.d.). Algebra – Properties of Equality. Paul’s Online Math Notes. https://tutorial.math.lamar.edu

41. THANK YOU! I hope you learned something today. God bless us all!