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Lesson 11. Multiplying and dividing real numbers. Properties of real numbers. 1. multiplication property of -1 For every real number a, a x -1 = -1 x a = -a 2. multiplication property of 0 For every real number a, a x 0 = 0

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lesson 11

Lesson 11

Multiplying and dividing real numbers

properties of real numbers
Properties of real numbers
  • 1.multiplication property of -1
  • For every real number a,
  • a x -1 = -1 x a = -a
  • 2. multiplication property of 0
  • For every real number a,
  • a x 0 = 0
  • 3. Inverse property of multiplication
  • For every real number a, where a is not equal to 0,
  • a x 1/a = 1/a x a = 1
multiplying signed numbers
Multiplying signed numbers
  • The product of 2 numbers with the same sign is a positive number
  • The sign of 2 numbers with different signs is a negative number
raising a number to a power
Raising a number to a power
  • (-3)4 = (-3)(-3)(-3)(-3)= 81
  • (-3)3 = (-3)(-3)(-3)= - 27
  • -34= - 3 3 3 3= - 81
  • -53 = - 5 5 5 = -125
  • (-5)3 = (-5)(-5)(-5)= -125
dividing signed numbers
Dividing signed numbers
  • 1. The quotient of 2 numbers with the same sign is positive.
  • 2. the quotient of 2 numbers with different signs is negative
simplify
simplify
  • -72/ -24
  • 12.1/ -11
  • -5/6
  • -2/9
lesson 12 using the properties of real numbers to simplify expressions
Lesson 12using the properties of real numbers to simplify expressions
  • The properties of real numbers are used to simplify expressions and write equivalent expressions.
properties of addition and multiplication
Properties of addition and multiplication
  • IDENTITY PROPERTY OF ADDITION
  • For every real number a,
  • a + 0 = a
  • IDENTITY PROPERTY F MULTIPLICATION
  • For every real number a,
  • a x 1 = a
  • COMMUTATIVE PROPERTY OF ADDITION
  • For every real number a and b,
  • a + b = b + a
  • COMMUTATIVE PROPERTY OF MULTIPLICATION
  • For every real number a and b,
  • a x b = b x a
properties cont
Properties cont.
  • ASSOCIATIVE PROPERTY OF ADDITION
  • For every real number a, b, and c,
  • (a + b) + c = a + ( b+ c)
  • a + b + c = a + b + c
  • ASSOCIATIVE PROPERT OF MULTIPLICATION
  • For every real number a, b and c,
  • (a b) c= a (b c)
  • a b c= a b c
identifying properties
Identifying properties
  • 1. 1 x 8 = 8
  • 2. 6 + 9 = 9 + 6
  • 3. (2 x 5) x 4 = 2 x ( 5 x 4)
  • 4. (7 + 1) + 3 = (1 + 7) + 3
  • 5. 0 + 10 = 10
  • 6. 17 x 1 = 17
true or false
True or false
  • d x 0 = d
  • (e r )b= (r e )b
  • x (y + z) = (x +y )z
  • d + ( e + f) = ( d + e) + f
  • How can you be sure???
lesson 15 distributive property
Lesson 15distributive property
  • For all real numbers a, b, and c
  • a (b + c) = a b + ac
  • And a (b - c) = a b - ac
distributing positive and negative numbers
Distributing positive and negative numbers
  • Simplify:
  • 6(4+8)= 6(4) + 6(8)
  • = 24 + 48 = 72
  • 6(2-7) = 6(2) + 6(-7)= 6(2) -6(7)
  • =12 + -42 = 12 -42 = -30
  • -(9+ 4)= -1(9) + -1 ( 4)
  • = -9 + -4 = -13
  • -20(12+8)= -20(12) + -20(8)
  • = -240 + -160= -400
simplifying algebraic expressions
Simplifying algebraic expressions
  • m n( m x + n y+ 2p)= mnmx+mnny+mn2p
  • = m2nx + mn2y +2mnp
  • (m x +2ny +z) m n= m n m x + mn2ny +m n z
  • = m2nx + 2mn2y + m n z
  • (y3-zx3)(-yz) = (-yz)y3 +(-yz)(-zx3)
  • = -y4z + x3yz2
check for understanding
Check for understanding
  • 1. Give an example of an expression that can be simplified using the distributive property.
  • 2.How do properties help you to simplify expressions?
  • 3. Explain the difference in finding the solution to (-2)2 and -22.
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