Lesson 11
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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

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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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