Properties of Equality and Inequality PDF

NUMBER THEORY PROPERTIES OF EQUALITY  OBJECTIVES 1. state the properties of equality and inequality; 2. identify the properties of equality and inequality applied in the given statement; and 3. solve equations and inequalities applying the different properties.  Equatio...

NUMBER THEORY PROPERTIES OF EQUALITY  OBJECTIVES 1. state the properties of equality and inequality; 2. identify the properties of equality and inequality applied in the given statement; and 3. solve equations and inequalities applying the different properties.  Equatio For example, ; ,, the value n of A statement of is still 2. They look different but the equality between two numbers, two equation is still mathematical expressions equivalent. This gives and a number and a us a couple of properties mathematical expression. that hold true for all equations. An equation is when So we will use properties you have the left side of equality to produce equal to the right side. equivalent equation so We state that equal with that we can solve for the equal sign. our variable. PROPERTIES OF EQUALITY  01 REFLEXIVE PROPERTY Any number or expression is equal to itself. Examples: 6=6, 5=5, 7=7  02 SYMMETRIC The sides of an equation may PROPERTY be interchanged. If Examples: If  03 TRANSITIVE PROPERTY If two quantities are equal to a third quantity, then they are all equal to each other. If Examples:  04 ADDITION PROPERTY OF EQUALITY If we add the same quantity to both sides of an equation, then the equation remains the same. The formula is if Examples: Add 4 on both sides of the equation  05 SUBTRACTION PROPERTY OF EQUALITY If we subtract the same quantity to both sides of an equation, then the differences are equal. The formula is if Examples: Subtract 2 on both sides of the equation  06 MULTIPLICATION PROPERTY OF EQUALITY If we multiply the same quantity to both sides of an equation, the sides remain equal. The formula is if. Examples: Multiply 2 on both sides of the equation  07 DIVISION PROPERTY OF EQUALITY If we divide by a non-zero number to both sides of an equation, the two sides remain equal. The formula is if. Examples: Divide each side by 5  08 SUBSTITUTION PROPERTY OF EQUALITY If two quantities are equal, then either can replace the other in any equation or expression. That is, one can substitute for the other at any time.The formula is if. Examples:  Check your Understanding Directions: Choose the letter of your best answer. ______1. If , then A. Addition Property of Equality ______2. If , then B. Subtraction Property of Equality ______3. C. Multiplication Property of Equality ______4. If , then D. Division Property of Equality ______5. If , then E. Reflexive Property ______6. If and , then F. Symmetric Property G. Transitive Property ______7. If and H. Substitution Property of Equality ______8. If , then can be substituted I. Distributive Property for in any expression. ______9. If and ______10.  Check your Understanding Directions: Choose the letter of your best answer. ____F__1. If , then A. Addition Property of Equality ____C__2. If , then B. Subtraction Property of Equality ____E__3. C. Multiplication Property of Equality ____B__4. If , then D. Division Property of Equality ____A__5. If , then E. Reflexive Property ____H__6. If and , then F. Symmetric Property G. Transitive Property ___G___7. If and H. Substitution Property of Equality ____H__8. If , then can be substituted I. Distributive Property for in any expression. ____D__9. If and ___ I___10. Example Problem Find the value of x and identify the property of equality that justifies each step. 2. APE MPE DPE 3. 4. Distributive P. Distributive P. SPE SPE APE APE DPE Symmetric Property DPE 5. Combine like terms Subtraction Property of Equality Directions: Identify the property that justifies each step. 1. _____________________ _____________________ 2. _______________________ _______________________ _______________________ _______________________ Quiz 1 Directions: Identify the property that justifies each step. 1. 2. 5 _________ __________ __________ _________ 3. _______________________ _______________________ ______________________ _______________________ 4. ________________________ ________________________ 5. 8 _______________________ 7 ______________________ 7 7 ______________________ 7 7 ___________________ 6. ____________________ ____________________ ____________________ 7. ____________________ ____________________