Lesson 8-Properties of Numbers.notebook
Lesson 8Properties of Numbers.notebook
September 13, 2012
Aim: What are some properties of numbers?
DO Now: Tell whether each sentence is true or false 1. 357+19 = 19+357 2. 30-9 = 9-30 3. (19-8)-5=19-(8-5) 4. (19*8)*5=19*(8*5)
Aug 245:49 PM
Commutative Property of Addition
Commutative Property of Multiplication
When we add rational numbers, we assume that we can change that order in which two numbers are added without changing the sum.
When we multiply rational numbers, we assume that we can change that order in which two numbers are added without changing the product. multiplied a ● b = b ● a
a + b = b + a Ex.: 3 + 5 = 5 + ?
Ex.: 2 ● 7 = 7 ● ?
Associative Property of Addition:
Associative Property of Multiplication
Addition is a binary operation; that is, we add two numbers at a time. If we wish to add three numbers, we find the sum of ANY two and add that sum to the third.
If we wish to multiply three numbers, we find the product of ANY two and multiply that product by the third.
(a + b) + c = a + (b + c)
(a ● b) ● c = a ● (b ● c) Ex.: (4 ● 5) ● 8 = 4 ● (5 ● ?)
Ex.: (2 + 5) + 8 = 2 + (? + 8)
Sep 88:29 AM
1
Lesson 8Properties of Numbers.notebook
September 13, 2012
Sep 2412:44 PM
Sep 2412:49 PM
2
Lesson 8Properties of Numbers.notebook
September 13, 2012
The Distributive Property: a (b + c) = ab + ac AND a (b c) = ab ac Examples: a) 5 (4 + 7) = b)
3 (2 1) =
c)
9 (8 3) =
d)
4 (a + b) = Sep 89:34 AM
Additive Inverses (opposites): In general, for every rational number a and its opposite, or additive inverse, a: a + (a) = 0 Examples: 5 + (5) = 0 (7) + 7 = 0 9 + (9) = 0
Addition Property of Zero and the Additive Identify Element. 1. The addition property of zero states that for every number a: a + 0 = a 0 + a = a 2. The identity element of addition, or the additive identity element, is 0.
Sep 66:42 PM
3
Lesson 8Properties of Numbers.notebook
September 13, 2012
Multiplicative Inverses: (reciprocals) The product of a number and its reciprocal is 1. i.e.
a ● 1 = 1 a
Multiplication Property of One and the Multiplicative Identity Element: 1.
The multiplication property of one states that for every number a: a ● 1 = a and 1 ● a = a
2.
The identity element of multiplication, or the multiplicative identity element, is 1.
Multiplication Property of Zero: In general, for every number a: a ● 0 = 0 AND 0 ● a = 0 Sep 810:03 AM
Sep 2412:53 PM
4
Lesson 8Properties of Numbers.notebook
September 13, 2012
Sep 2412:54 PM
Examples: 1.
Name the number that is the additive identity element
2.
Name the identity element of multiplication.
3.
Replace each question mark with the number that makes the sentence true: a)
8 + 6 = 6 + ?
b)
(3 x 9) x 15 = 3 x (9 x ?)
c)
3 (x + 5) = 3x + 3(?)
d)
17 x 5 = ? x 17
e)
6(5 + 8) = 6(5) + ?(8)
f)
4 + 0 = ?
4. Identify the properties in example 3
Aug 306:11 PM
5
Lesson 8Properties of Numbers.notebook
4.
5.
September 13, 2012
Name the additive inverse (opposite) of each number: a)
5
b)
½
c)
¾
d)
0
e)
8
Name the multiplicative inverse for each entry: a)
3
b)
½
c)
8 5
d)
2 3
e)
1 5
Sep 810:09 AM
8.
Which is an illustration of the commutative property of addition? a) ab = ba b) a + 0 = a c) a + b = b + a d) (a + b) + c = a + (b + c)
9.
Which is an illustration of the distributive property? a) a + b = b + a b) a (b + c) = ab + ac c) (a + b) + c = a + (b + c) d) a (b + c) = ab + c
10. Which is an illustration of the associative property of multiplication? a) ab = ba b) a (0) = 0 c) a(1) = a d) (ab)c = a(bc) 11. What is the additive inverse for the real number represented by n?
12. What is the multiplicative inverse for the real number represented by n?
Sep 810:11 AM
6
Attachments
addingsubtracting signed numbers.url
September 13, 2012
Aim: What are some properties of numbers?
DO Now: Tell whether each sentence is true or false 1. 357+19 = 19+357 2. 30-9 = 9-30 3. (19-8)-5=19-(8-5) 4. (19*8)*5=19*(8*5)
Aug 245:49 PM
Commutative Property of Addition
Commutative Property of Multiplication
When we add rational numbers, we assume that we can change that order in which two numbers are added without changing the sum.
When we multiply rational numbers, we assume that we can change that order in which two numbers are added without changing the product. multiplied a ● b = b ● a
a + b = b + a Ex.: 3 + 5 = 5 + ?
Ex.: 2 ● 7 = 7 ● ?
Associative Property of Addition:
Associative Property of Multiplication
Addition is a binary operation; that is, we add two numbers at a time. If we wish to add three numbers, we find the sum of ANY two and add that sum to the third.
If we wish to multiply three numbers, we find the product of ANY two and multiply that product by the third.
(a + b) + c = a + (b + c)
(a ● b) ● c = a ● (b ● c) Ex.: (4 ● 5) ● 8 = 4 ● (5 ● ?)
Ex.: (2 + 5) + 8 = 2 + (? + 8)
Sep 88:29 AM
1
Lesson 8Properties of Numbers.notebook
September 13, 2012
Sep 2412:44 PM
Sep 2412:49 PM
2
Lesson 8Properties of Numbers.notebook
September 13, 2012
The Distributive Property: a (b + c) = ab + ac AND a (b c) = ab ac Examples: a) 5 (4 + 7) = b)
3 (2 1) =
c)
9 (8 3) =
d)
4 (a + b) = Sep 89:34 AM
Additive Inverses (opposites): In general, for every rational number a and its opposite, or additive inverse, a: a + (a) = 0 Examples: 5 + (5) = 0 (7) + 7 = 0 9 + (9) = 0
Addition Property of Zero and the Additive Identify Element. 1. The addition property of zero states that for every number a: a + 0 = a 0 + a = a 2. The identity element of addition, or the additive identity element, is 0.
Sep 66:42 PM
3
Lesson 8Properties of Numbers.notebook
September 13, 2012
Multiplicative Inverses: (reciprocals) The product of a number and its reciprocal is 1. i.e.
a ● 1 = 1 a
Multiplication Property of One and the Multiplicative Identity Element: 1.
The multiplication property of one states that for every number a: a ● 1 = a and 1 ● a = a
2.
The identity element of multiplication, or the multiplicative identity element, is 1.
Multiplication Property of Zero: In general, for every number a: a ● 0 = 0 AND 0 ● a = 0 Sep 810:03 AM
Sep 2412:53 PM
4
Lesson 8Properties of Numbers.notebook
September 13, 2012
Sep 2412:54 PM
Examples: 1.
Name the number that is the additive identity element
2.
Name the identity element of multiplication.
3.
Replace each question mark with the number that makes the sentence true: a)
8 + 6 = 6 + ?
b)
(3 x 9) x 15 = 3 x (9 x ?)
c)
3 (x + 5) = 3x + 3(?)
d)
17 x 5 = ? x 17
e)
6(5 + 8) = 6(5) + ?(8)
f)
4 + 0 = ?
4. Identify the properties in example 3
Aug 306:11 PM
5
Lesson 8Properties of Numbers.notebook
4.
5.
September 13, 2012
Name the additive inverse (opposite) of each number: a)
5
b)
½
c)
¾
d)
0
e)
8
Name the multiplicative inverse for each entry: a)
3
b)
½
c)
8 5
d)
2 3
e)
1 5
Sep 810:09 AM
8.
Which is an illustration of the commutative property of addition? a) ab = ba b) a + 0 = a c) a + b = b + a d) (a + b) + c = a + (b + c)
9.
Which is an illustration of the distributive property? a) a + b = b + a b) a (b + c) = ab + ac c) (a + b) + c = a + (b + c) d) a (b + c) = ab + c
10. Which is an illustration of the associative property of multiplication? a) ab = ba b) a (0) = 0 c) a(1) = a d) (ab)c = a(bc) 11. What is the additive inverse for the real number represented by n?
12. What is the multiplicative inverse for the real number represented by n?
Sep 810:11 AM
6
Attachments
addingsubtracting signed numbers.url
