Properties of equality
Download as PPTX, PDF6 likes11,730 views
This document discusses the properties of equality, including addition, subtraction, multiplication, and division properties. It explains how to use these properties to solve literal equations by adding, subtracting, multiplying, or dividing the same term on both sides of the equation. Examples are provided to demonstrate solving equations using each property step-by-step. The document also covers the substitution, reflexive, symmetric, and transitive properties of equality.
Properties of equality
- 2. OBJECTIVES: • Illustrate and model the different properties of equality. • Use the different properties of equality to solve literal equations.
- 3. PROPERTIES OF EQUALITY: • Addition Property of Equality (APE) • Subtraction Property of Equality (SPE) • Multiplication Property of Equality (MPE) • Division Property of Equality (DPE) • Substitution Law • Reflexive Property • Symmetric Property • Transitive Property (TPE)
- 4. ADDITION PROPERTY: If x = y, then x + z = y + z Equals may be added on both sides of the equation
- 5. SOLVE EACH EQUATION USING ADDITION PROPERTY x – 7 = 10
- 6. THIS IS HOW IT WORKS: x – 7 = 10 WRITE THE ORIGINAL EQUATION
- 7. THIS IS HOW IT WORKS: x – 7 = 10 WRITE THE ORIGINAL EQUATION x – 7 + 7 = 10 + 7 ADD 7 ON BOTH SIDES
- 8. THIS IS HOW IT WORKS: x – 7 = 10 WRITE THE ORIGINAL EQUATION x – 7 + 7 = 10 + 7 ADD 7 ON BOTH SIDES x = 17 SIMPLIFY
- 9. ADDITION PROPERTY IN PROBLEM SOLVING: The water level fell 12.5 feet from a high tide to a low tide. The water level at the pier was 9.25 feet at low tide. Find the water level at the pier at high tide.
- 10. REPRESENT EACH GIVEN BY THE USE OF VARIABLES Let x = be the high tide water level in feet 12.5 = drop in water level 9.25 = low tide water level
- 11. FORMULATE YOUR EQUATION x – 12.5 = 9.25
- 12. SOLVE EACH EQUATION USING ADDITION PROPERTY x – 12.5 = 9.25
- 13. THIS IS HOW IT WORKS: x – 12.5 = 9.25 WRITE THE ORIGINAL EQUATION
- 14. THIS IS HOW IT WORKS: WRITE THE ORIGINAL EQUATION x – 12.5 + 12.5 = 9.25 + 12.5 ADD 12.5 ON BOTH SIDES x – 12.5 = 9.25
- 15. THIS IS HOW IT WORKS: WRITE THE ORIGINAL EQUATION x – 12.5 + 12.5 = 9.25 + 12.5 ADD 12.5 ON BOTH SIDES x – 12.5 = 9.25 x = 21.75 SIMPLIFY
- 16. SUBTRACTION PROPERTY: If x = y, then x - z = y - z Equals may be subtracted from both sides of the equation
- 17. SOLVE EACH EQUATION USING SUBTRACTION PROPERTY x + 5 = 11
- 18. THIS IS HOW IT WORKS: x + 5 = 11 WRITE THE ORIGINAL EQUATION
- 19. THIS IS HOW IT WORKS: x + 5 = 11 WRITE THE ORIGINAL EQUATION x + 5 - 5 = 11 - 5 SUBTRACT 5 ON BOTH SIDES
- 20. THIS IS HOW IT WORKS: x + 5 = 11 WRITE THE ORIGINAL EQUATION x + 5 - 5 = 11 - 5 SUBTRACT 5 ON BOTH SIDES x = 6 SIMPLIFY
- 22. MULTIPLICATION PROPERTY: If x = y, then xz = yz Both sides of the equation may be multiplied by equals
- 23. SOLVE EACH EQUATION USING MUTIPLICATION PROPERTY 8x = 72
- 24. THIS IS HOW IT WORKS: 8x = 72 WRITE THE ORIGINAL EQUATION
- 25. THIS IS HOW IT WORKS: 8x = 72 WRITE THE ORIGINAL EQUATION 8x/8 = 72/8 DIVIDE 8 ON BOTH SIDES
- 26. THIS IS HOW IT WORKS: 8x = 72 WRITE THE ORIGINAL EQUATION 8x/8 = 72/8 DIVIDE 8 ON BOTH SIDES x = 9 SIMPLIFY
- 27. DIVISION PROPERTY: If x = y and z ≠ 0 then 𝒙 𝒛 = 𝒚 𝒛 Both sides of the equation may be divided by a non-zero real number
- 28. SUBSTITUTION PROPERTY: If x + y = z and x = y, then 𝒚 + 𝒚 = 𝒛 𝒐𝒓 𝒙 + 𝒙 = 𝒛 Equals may be substituted for equals
- 29. REFLEXIVE PROPERTY: x = x, y = y, z = z Any number or expressions is equal to itself
- 30. SYMMETRIC PROPERTY: x = y then, y = x The expressions on both sides of an equation may be interchanged
- 31. TRANSITIVE PROPERTY: x = y and y = z, then x = z If two quantities are both equal to a third quantity, then they are equal to each other
- 32. COPY AND ANSWER ON YOUR NOTEBOOK 1. w – 4 = 36 2. 5t + 5 = 20 3. 3k – 4 = 30 4. n + 25 = -723 5. 9c + 1 = 82
- 33. COPY AND ANSWER ON YOUR NOTEBOOK 1. w – 4 = 36 (w = 40) 2. 5t + 5 = 20 3. 3k – 4 = 30 4. n + 25 = -723 5. 9c + 1 = 82
- 34. COPY AND ANSWER ON YOUR NOTEBOOK 1. w – 4 = 36 (w = 40) 2. 5t + 5 = 20 (t = 3) 3. 3k – 4 = 30 4. n + 25 = -723 5. 9c + 1 = 82
- 35. COPY AND ANSWER ON YOUR NOTEBOOK 1. w – 4 = 36 (w = 40) 2. 5t + 5 = 20 (t = 3) 3. 3k – 4 = 30 (k = 34/3) 4. n + 25 = -723 5. 9c + 1 = 82
- 36. COPY AND ANSWER ON YOUR NOTEBOOK 1. w – 4 = 36 (w = 40) 2. 5t + 5 = 20 (t = 3) 3. 3k – 4 = 30 (k = 34/3) 4. n + 25 = -723 (n = -748) 5. 9c + 1 = 82
- 37. COPY AND ANSWER ON YOUR NOTEBOOK 1. w – 4 = 36 (w = 40) 2. 5t + 5 = 20 (t = 3) 3. 3k – 4 = 30 (k = 34/3) 4. n + 25 = -723 (n = -748) 5. 9c + 1 = 82 (c = 9)