This presentation is the property of its rightful owner.
1 / 16

# 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

Lesson 11

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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

• -72/ -24

• 12.1/ -11

• -5/6

• -2/9

### 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

• 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.