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# Algebra Properties 1 4

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### Algebra Properties 1 4

1. 1. Algebra Properties Notes 1 - 4
2. 2. Rules, Rules, Rules…… <ul><li>Identity </li></ul><ul><li>and </li></ul><ul><li>Equality Properties </li></ul>
3. 3. Addition <ul><li>The additive identity property </li></ul><ul><li>a + 0 = 0 + a = a </li></ul><ul><li>(adding 0 to anything </li></ul><ul><li>doesn’t change what it is!) </li></ul>
4. 4. Multiplication <ul><li>Multiplication identity property </li></ul><ul><li>a(1) = 1(a) = a </li></ul><ul><li>(multiplying something by 1 doesn’t change what it is!) </li></ul>
5. 5. BIG FAT ZERO! <ul><li>Multiplicative Property </li></ul><ul><li>of Zero </li></ul><ul><li>a • 0 = 0 • a = 0 </li></ul><ul><li>(0 times any number equals 0!) </li></ul><ul><li>“ Duh” property </li></ul>
6. 6. INVERSE <ul><li>Multiplicative Inverse Property: </li></ul><ul><li>Two numbers whose product is 1 are called multiplicative inverses or reciprocals </li></ul><ul><li>(like 1/5 and 5, or 2/3 and 3/2: you just flip the fraction!) </li></ul>
7. 7. Properties of Equality (=) <ul><li>Reflexive Property The reflexive property of equality says that any number equals itself. For any number a , a = a . </li></ul><ul><li>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 </li></ul><ul><li>a = b , then b = a . </li></ul>
8. 8. MORE Properties of Equality…. <ul><li>Transitive Property </li></ul><ul><li>For any numbers a , b , and c , if a = b and </li></ul><ul><li>b = c , then a = c . </li></ul><ul><li>Substitution </li></ul><ul><li>If a = b , then a may be replaced by b in any expression. </li></ul>
9. 9. Your Turn….. <ul><li>Name the multiplicative inverse of each number or variable: </li></ul><ul><li>3 </li></ul><ul><li>2/7 </li></ul><ul><li>4/x </li></ul><ul><li>2 ½ </li></ul><ul><li>m </li></ul>
10. 10. Pretty good….now try these: <ul><li>Name the property or properties illustrated: </li></ul><ul><li>x • 1 = x </li></ul><ul><li>15/3 + 4 = 5 + 4 </li></ul><ul><li>2/3 • 3/2 = 1 </li></ul><ul><li>11 • 0 = 0 </li></ul><ul><li>2 + 3 = 2 + 3 </li></ul><ul><li>If 12 + 3 = 15 then 15 = 12 + 3 </li></ul><ul><li>0 + m = m </li></ul>
11. 11. Bet you can’t get this one! <ul><li>Which property is illustrated? </li></ul><ul><li>If x + 5 = 9 and 9 = y, then x + 5 = y </li></ul>
12. 12. Hmmmm….. <ul><li>What would the multiplicative inverse of </li></ul><ul><li>__ 5 __ </li></ul><ul><li>r – 7 look like? </li></ul>
13. 13. Coming Soon…. <ul><li>To a classroom near you…… </li></ul><ul><li>More Properties!! </li></ul><ul><li>(It will be a real scream!) </li></ul>