This document discusses various properties of algebra, including: 1. The identity properties for addition and multiplication - adding or multiplying any number by 0 or 1, respectively, does not change the number. 2. The zero property of multiplication states that multiplying any number by 0 equals 0. 3. The inverse property states that two numbers whose product is 1 are multiplicative inverses (like 1/5 and 5). 4. The properties of equality, including reflexive, symmetric, and transitive properties are explained. The substitution property allows replacing equals with equals.

1. Algebra Properties Notes 1 - 4

2. Rules, Rules, Rules…… Identity and Equality Properties

3. Addition The additive identity property a + 0 = 0 + a = a (adding 0 to anything doesn’t change what it is!)

4. Multiplication Multiplication identity property a(1) = 1(a) = a (multiplying something by 1 doesn’t change what it is!)

5. BIG FAT ZERO! Multiplicative Property of Zero a • 0 = 0 • a = 0 (0 times any number equals 0!) “ Duh” property

6. INVERSE Multiplicative Inverse Property: Two numbers whose product is 1 are called multiplicative inverses or reciprocals (like 1/5 and 5, or 2/3 and 3/2: you just flip the fraction!)

7. Properties of Equality (=) Reflexive Property The reflexive property of equality says that any number equals itself. For any number a , a = a . Symmetric Property The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. For any numbers a and b , if a = b , then b = a .

8. MORE Properties of Equality…. Transitive Property For any numbers a , b , and c , if a = b and b = c , then a = c . Substitution If a = b , then a may be replaced by b in any expression.

9. Your Turn….. Name the multiplicative inverse of each number or variable: 3 2/7 4/x 2 ½ m

10. Pretty good….now try these: Name the property or properties illustrated: x • 1 = x 15/3 + 4 = 5 + 4 2/3 • 3/2 = 1 11 • 0 = 0 2 + 3 = 2 + 3 If 12 + 3 = 15 then 15 = 12 + 3 0 + m = m

11. Bet you can’t get this one! Which property is illustrated? If x + 5 = 9 and 9 = y, then x + 5 = y

12. Hmmmm….. What would the multiplicative inverse of __ 5 __ r – 7 look like?

13. Coming Soon…. To a classroom near you…… More Properties!! (It will be a real scream!)