Lesson 11

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# Lesson 11 - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Lesson 11' - paley

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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
• 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
• 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
• (-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
• 1. The quotient of 2 numbers with the same sign is positive.
• 2. the quotient of 2 numbers with different signs is negative
simplify
• -72/ -24
• 12.1/ -11
• -5/6
• -2/9
• The properties of real numbers are used to simplify expressions and write equivalent expressions.
• For every real number a,
• a + 0 = a
• IDENTITY PROPERTY F MULTIPLICATION
• For every real number a,
• a x 1 = a
• 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.
• 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
• 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
• 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 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
• 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
• 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
• 1. Give an example of an expression that can be simplified using the distributive property.