Expressions

• Associative property


  • a+(b+c)=(a+b)+c
• Commutative property


  • a+b=b+a
• Associative property


  • (a*b)*c=a*(b*c)
• Commutative property


  • a*b=b*a
• Zero product property


  a*b=0 if either a=0 or b=0 or both a and b=0
• Each of friends purchase 2 cans of soda and 3 hot dogs
• 6 (2) + 3 = 12 + 18 = 30
• Generate Equivalent Expressions


  1. Commutative Property: Order of addends/factors does not change sum/product

  2. Associative Property: Grouping of addends/factors does not change sum/product

  3. Distributive Property: a*(b+c)=a*b+a*c
• Equivalent expressions


  • 6+x=x+6
  • (6+3x)+y=6+(3x+y)
  • 5(x+7)=5*3x+5*7=15x+35
• Subtraction: add the opposite
• 1. P=P+(-P), P-N=P+(-N), N-P=N+(-P), N-N=N+(-N)
• The student council has spent $337.50 on the supplies needed to sponsor a dance concert fundraiser. Three council members wrote the following expressions to represent the total amount raised for tickets sold: 6.75t-337.50, 6.75(t-50)-337.50, 6.75-337.50
• They were all correct because the expressions are equivalent
• Write 2 equivalent expressions for -5.5(x+2)


  1. -5.5x+(-5.5*2)

  2. -5.5(x+2)
• Write equivalent expressions by combining like terms


  1. -5.25x+3.5x+2.75=-1.75x+2.75

  2. x+(x+y)=2x+y
• Write two expressions that are equivalent to x-2

  1. 3x+1-21=-3x-2

  2. 2-3x=-3x+2
• Write two expressions that are equivalent to -x-3/4

  1. -x-3/4

  2. -3/4-x
• Write an expression equivalent to -3y+3+[(3)-4]


  • 3y+3+(-1)=-3y-1
• The property used to make the expressions equivalent was the Distributive Property
• Write an expression equivalent to 3.5x+2.5x-3


  (3.5+2.5)x+(-3)=6x-3