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Algebra Properties 1 4

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  • 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!)
  • 14.