2. Edit the text with your own short phrases. To change a sample image, select a picture and delete it. Now click the Pictures icon in each placeholder to insert your own images. The animation is already done for you; just copy and paste the slide into your existing presentation. Sample pictures courtesy of Bill Staples. Properties of Equality Adapted from Walch Education

3. Properties of equality are rules that allow you to balance, manipulate, and solve equations. PropertyIn symbolsIn words Reflexive property of equality a = aA number is equal to itself. Symmetric property of equality If a = b, then b = a. If numbers are equal, they will still be equal if the order is changed. Transitive property of equality If a = b and b = c, then a = c. If numbers are equal to the same number, then they are equal to each other. Addition property of equality If a = b, then a + c = b + c. Adding the same number to both sides of an equation does not change the equality of the equation.

4. Properties of Equality, continued PropertyIn symbolsIn words Subtraction property of equality If a = b, then a – c = b – c. Subtracting the same number from both sides of an equation does not change the equality of the equation. Multiplication property of equality If a = b and c ≠ 0, then a c = b c. Multiplying both sides of the equation by the same number, other than 0, does not change the equality of the equation. Division property of equality If a = b and c ≠ 0, then a ÷ c = b ÷ c. Dividing both sides of the equation by the same number, other than 0, does not change the equality of the equation. Substitution property of equality If a = b, then b may be substituted for a in any expression containing a. If two numbers are equal, then substituting one in for another does not change the equality of the equation.

5. Properties of Operations PropertyGeneral ruleSpecific example Commutative property of addition a + b = b + a3 + 8 = 8 + 3 Associative property of addition (a + b) + c = a + (b + c)(3 + 8) + 2 = 3 + (8 + 2) Commutative property of multiplication a b = b a3 8 = 8 3 Associative property of multiplication (a b) c = a (b c)(3 8) 2 = 3 (8 2) Distributive property of multiplication over addition a (b + c) = a b + a c3 (8 + 2) = 3 8 + 3 2

6. Edit the text with your own short phrases. To change a sample image, select a picture and delete it. Now click the Pictures icon in each placeholder to insert your own images. The animation is already done for you; just copy and paste the slide into your existing presentation. Sample pictures courtesy of Bill Staples. Key Concepts: When operations are performed on one side of the equation, the properties of operations are generally followed When an operation is performed on both sides of the equation, the properties of equality are generally followed The properties of equality, as well as the properties of operations, justify our reasoning

7. Edit the text with your own short phrases. To change a sample image, select a picture and delete it. Now click the Pictures icon in each placeholder to insert your own images. The animation is already done for you; just copy and paste the slide into your existing presentation. Sample pictures courtesy of Bill Staples. Let’s Practice: Which property of equality is missing in the steps to solve the equation –7x + 22 = 50? EquationSteps –7x + 22 = 50Original equation –7x = 28 x = –4Division property of equality

8. Edit the text with your own short phrases. To change a sample image, select a picture and delete it. Now click the Pictures icon in each placeholder to insert your own images. The animation is already done for you; just copy and paste the slide into your existing presentation. Sample pictures courtesy of Bill Staples. Refer to the table of Properties of Equality The subtraction property of equality tells us that when we subtract a number from both sides of the equation, the expressions remain equal The Missing Step Is… “Subtraction property of equality”

9. Edit the text with your own short phrases. To change a sample image, select a picture and delete it. Now click the Pictures icon in each placeholder to insert your own images. The animation is already done for you; just copy and paste the slide into your existing presentation. Sample pictures courtesy of Bill Staples. Thanks for Watching!!!! ~ Dr. Dambreville