Properties Of Mathematics 2007

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Properties Of Mathematics 2007

  1. 1. Properties of Mathematics<br />Everything you need to know and more……<br />
  2. 2. Properties of Mathematics<br />Operations and Properties<br />
  3. 3. Properties of Mathematics<br />No, not these operations!!!<br />
  4. 4. Properties of Mathematics<br />These operations….of NUMBERS!!!!<br />Addition<br />Subtraction<br />Multiplication<br />Division<br />
  5. 5. Properties of Mathematics<br />No, not these properties!!!<br />
  6. 6. Properties of Mathematics<br />These properties…….of NUMBERS!!!!<br />Associative Property of Multiplication<br />Commutative Property of Multiplication<br />Identity Property of Multiplication<br />Inverse Property of Multiplication<br />Multiplicative Property of Zero<br />Multiplicative Property of -1<br />Associative Property of Addition<br />Commutative Property of Addition<br />Identity Property of Addition<br />Inverse Property of Addition<br />Substitution Property Distributive Property<br />Reflexive Property<br />Symmetric Property<br />Transitive Property<br />Addition Property<br />Subtraction Property<br />Multiplication Property<br />Division Property<br />
  7. 7. Properties of Mathematics<br />Hmmmmm….…What’s the<br /> difference between……<br /> operations of NUMBERS and<br /> properties of NUMBERS ????<br />and<br />OPERATION of numbers….<br />is the WAY we calculate numbers…… <br />(add, subtract, multiply, & divide)<br />PROPERTIES of numbers….<br />are the METHODS we use to calculatenumbers……<br />WAY<br />METHODS<br />
  8. 8. Properties of Mathematics<br /> So Let’s get started.…<br />PROPERTIES <br />OF<br />NUMBERS<br />
  9. 9. Properties of Mathematics<br />Addition, Subtraction, Multiplication & Division Properties<br />
  10. 10. Properties of Mathematics<br /> When you have each side of an expression equal <br /> to the other side, you can add, subtract, multiply <br /> or divide the SAME number on each side and <br />not change the equalities.<br />Addition Property<br />a = b<br />a + c = b + c<br />Subtraction Property<br />a = b<br />a - c = b - c<br />Multiplication Property<br />a = b<br />a ∙ c = b ∙ c<br />Division Property<br />a = b, (c ≠ 0)<br />=<br />
  11. 11. Properties of Mathematics<br />Addition Property<br />Subtraction Property<br />1 = 1<br />1 +5= 1 +5<br />6 = 6<br />1 = 1<br />1 - 5= 1 - 5<br />-4 = -4<br />Multiplication Property<br />Division Property<br />2 = 2<br />2 ∙ 5= 2 ∙ 5<br />10 = 10<br />10 = 10<br />10 ÷ 5= 10 ÷ 5<br />6 = 6<br />
  12. 12. Properties of Mathematics<br />IDENTITY PROPERTIES<br />
  13. 13. Properties of Mathematics<br />The Identity Property<br />Addition<br />a + 0 = a<br />Multiplication<br />a ∙ 1 = a<br />
  14. 14. Addition<br />5 + 0 = 5<br />Multiplication<br />5 ∙ 1 = 5<br />Properties of Mathematics<br />The Identity Property<br />
  15. 15. Properties of Mathematics<br />REFLEXIVE PROPERTY<br />
  16. 16. Properties of Mathematics<br />a = a<br />Reflexive Property<br />1=1<br />9x=9x<br />x + y=x + y<br />3(x-2)= 3(x-2)<br />
  17. 17. Properties of Mathematics<br />SYMMETRIC PROPERTY<br />
  18. 18. The Symmetric property is an equality <br /> relationship that switches one expression on <br /> one side of an equation to the other side. <br />(note: keep expressions exactly “as is” .)<br />a + b = c <br />c = a + b<br />Properties of Mathematics<br />Symmetric Property<br />9 - 5=4<br />5=9 - 4<br />5=9 - 4<br />9-4=5<br />
  19. 19. Properties of Mathematics<br />COMMUTATIVE PROPERTY<br />
  20. 20. The Commutative property of addition or multiplication changes the “position of a term” on one side of an expression. <br />AdditionMultiplication<br />Properties of Mathematics<br />Commutative Property<br />a<br />∙ = ∙<br />b<br />b<br />a<br />b<br />+ = +<br />b<br />a<br />a<br />a<br />b<br />b<br />a<br />
  21. 21. ADDITION3 + 8=11<br />8 + 3=11<br />11=11<br />MULTIPLICATION2∙5∙ 4 =40<br />5 ∙ 2∙ 4 =40<br />40=40<br />Properties of Mathematics<br />Commutative Property<br />
  22. 22. Properties of Mathematics<br />ASSOCIATIVE PROPERTIES<br />
  23. 23. Properties of Mathematics<br />The Associative property ASSOCIATES (groups) <br /> terms of numbers or variables with other terms <br /> using parentheses. (notice: original term positions never change)<br />ADDITIONa+(b+ c)=(a+b)+ c <br />MULTIPLICATION(a∙b) c =a (b∙ c)<br />Associative Property<br />
  24. 24. Properties of Mathematics<br /> ADDITION<br />MULTIPLICATION<br />Associative Property<br />1+(7+ 5)=( 1+5)+ 7<br />1+(12)=(6)+ 7<br />13=13<br />(1∙7) 5 =1 (7∙ 5)<br /> (7) 5 =1 (35)<br />35=35<br />
  25. 25. Properties of Mathematics<br />INVERSE PROPERTY<br />OF ADDITION<br />
  26. 26. Properties of Mathematics<br />The Inverse property of multiplication cancels out a number or variable by the using the “inverse” or “opposite” operation of the number or variable. <br />a + -a = 0<br />Inverse Property of Addition<br />= 0<br />1 +<br />-1<br />-7 +<br /> 7<br />
  27. 27. Properties of Mathematics<br />INVERSE PROPERTY<br />OF MULTIPLICATION<br />
  28. 28. Properties of Mathematics<br />The Inverse property of multiplication “cancels out”<br /> a number or variable by the using the “inverse” or “opposite” operation of the number or variable and gives a new value of “1”. <br />Inverse Property of Multiplication<br />a ∙<br />= 1<br />
  29. 29. Properties of Mathematics<br />Inverse Property of Multiplication<br />= = 1<br />3x∙<br />5∙<br />= = 1<br />∙.52<br />= = 1<br />∙ = = 1<br />a ∙<br />= 1<br />
  30. 30. Properties of Mathematics<br />Multiplicative Property of Zero<br />Multiplicative Property of -1<br />
  31. 31. Any number or variable multiplied by zero will become zero.<br /> Any number or variable multiplied by -1 will become the “opposite sign” of that number or variable. <br />Properties of Mathematics<br />Multiplicative Property of Zero<br />a ∙ 0 = 0<br />7 ∙ 0 = 0<br />0 x = 0<br />0 = 0 ∙ 5y<br />Multiplicative Property of -1<br />a ∙ -1 = -a<br /> 7 ∙ -1 = -7<br />-5y ∙ -1 = 5y<br />-1 ∙ 3= -3<br />
  32. 32. Properties of Mathematics<br />DISTRIBUTIVE PROPERTY<br />
  33. 33. The distributive property “distributes”(multiplies) a number or variable “among” the other terms in the parentheses. (multiply)<br />a(b + c) = ab + ac<br />Or reverse…..<br />ab + ac = a(b + c)<br />Properties of Mathematics<br />Distributive Property<br />
  34. 34. 5(x + 2) = 5(x) + 5(2)<br />5(x + 2) = 5x + 10<br />Or reverse…..<br /> 3x + 3y = 3(x+ y)<br />Properties of Mathematics<br />Distributive Property<br />
  35. 35. Properties of Mathematics<br />SUBSTITUTION PROPERTY<br />
  36. 36. Properties of Mathematics<br />The Substitution property “takes the place of” some number, variable or term for something else in your mathematical expression.<br />Substitution Property<br />=b<br />a<br />b<br />+ c = d<br />a<br />
  37. 37. Properties of Mathematics<br />Substitution Property<br />x = 4<br />4<br />2x + 5 = ?<br />2<br />( )<br />4<br />+ 5 = ?<br />8 + 5 = ?<br />13 = 13<br />
  38. 38. Properties of Mathematics<br />TRANSITIVE PROPERTY<br />
  39. 39. The Commutative property of addition or multiplication changes the “position of a term” on one side of an expression. <br />Properties of Mathematics<br />Transitive Property<br />c<br />a<br />c<br />b<br />a<br />=<br />=<br />=<br />b<br />
  40. 40. Properties of Mathematics<br />Transitive Property<br />=<br />17<br />8 + y<br />=<br />Z - 5<br />17<br />8 + y<br />Z - 5<br />=<br />
  41. 41. http://streaming.discoveryeducation.com/images/assetDetail/button_download.gif<br />http://streaming.discoveryeducation.com/images/assetDetail/button_download.gif<br />Properties of Mathematics<br />Acknowledgements<br />

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