Download HW Section 1

Section 1 – 1:
The Real Number System
Selected Worked Homework Problems
4
1 2
⎧
,
,
⎨ − 8 , − π , − , − .75 , − .333... , 0 ,
5
10 3
⎩
1a) List all the negative integers.!
1b) List all the negative rational numbers.
Negative Counting numbers!
!
!
!
{ − 8 }!
Negative Fractions or negative decimals
that terminate or repeat.
4
⎧
⎫
⎨ − 8 , − , − .75 , − .333... ⎬
5
⎩
⎭
!
1c) List all the negative irrational numbers.!
1d) List all the negative real numbers. !
Negative decimals that!
DO NOT terminate or repeat.
{ − π }!
⎫
3 , 6 , 81 = 9 ⎬
⎭
Any negative number.
4
⎧
⎫
⎨ − 8 , − π , − , − .75 , − .333... ⎬
5
⎩
⎭
!
1e) List all the positive integers. !
1f) List all the positive rational numbers.
Positive Counting numbers!
!
!
!
Positive Fractions or decimals
that terminate or repeat.
⎧ 1 2
⎫
,
, 6 , 81 = 9 ⎬
⎨
⎩ 10 3
⎭
{6 ,
81 = 9
}!
!
1g) List all the positive irrational numbers. !
1h) List all the positive real numbers.
Positive decimals that!
DO NOT terminate or repeat.
{
}
3 ! !
Any positive number
⎧ 1 2
,
,
⎨
⎩ 10 3
!
1i) List all the integers.!
1j) List all the whole numbers.
Positive or Negative Counting !
numbers and zero!
{−8 , 0 , 6
, 81 = 9
}
!
⎫
3 , 6 , 81 = 9 ⎬
⎭
Counting numbers and zero
{
0 , 6 , 81 = 9
}
1k) List all the irrational numbers. !
1l) List a number that is not positive or negative.
{ −π ,
{ 0}
3
Math 100 !
}
!
!
Section 1 – 1 HW WKD!
© 2016 Eitel
3. What is the additive inverse of 7 ?!
4. What is the multiplicative inverse of 7 ?
The additive inverse adds to give zero!
the multiplicative inverse multiplies to give 1
7−7= 0
so − 7 is the additive inverse of 7 !
1
=1
7
1
so is the multiplicative inverse of 7
7
7•
2
?!
3
The additive inverse adds to give zero!
7. What is the additive inverse of
2 2
− =0
3 3
2
2
so − is the additive inverse of !
3
3
2 3
• =1
3 2
3
2
so is the multiplicative inverse of
2
3
−3
?!
5
The additive inverse adds to give zero!
9. What is the additive inverse of
−3 3
+ =0
5 5
3
−3
so + is the additive inverse of
!
5
5
Math 100 !
2
?
3
the multiplicative inverse multiplies to give 1
8. What is the multiplicative inverse of
−3
?
5
the multiplicative inverse multiplies to give 1
10. What is the multiplicative inverse of
−3 −5
•
=1
5 3
−5
−3
so
is the multiplicative inverse of
3
5
Section 1 – 1 HW WKD!
© 2016 Eitel
Select the property the justifies each statement:
A: Commutative property of multiplication!
B: Distributive property of multiplication
C: Identity property of multiplication!
D: Identity property of addition
E: Commutative property of addition!
F: Inverse property of multiplication!
11. 5 + 3 = 3 + 5 ____!
!
The order of addition has been changed so!
E: Commutative property of addition!
12. 5 •1 = 5 ____
the product of 5 and this number stays 5
D: Identity property of multiplication
1 3
• = 1 ____!
3 1
1
the product of and this number gives 1!
3
F: Inverse property of multiplication!
14. 2 • 6 = 6 • 2 ____
15. 7 + 0 = 7 ____!
16. 2(x + 4) = 2x + 8 ____
the sum of 7 and this number stays 7!
Each term in the brackets are multiplied by 2
D: Identity property of addition!
B: Distributive property of multiplication
13.
The order of multiplication has been changed
A: Commutative property of multiplication
17. Does a ÷ b = b ÷ a for all real numbers?!
18. Does a − b = b − a for all real numbers:
Give an example that proves that !
Give an example that proves that
division is not commutative for!
subtraction is not commutative for all
all real numbers?!
real numbers?
6 ÷ 2 ≠ 2 ÷ 6!
Math 100 !
!
6−2≠ 2−6
Section 1 – 1 HW WKD!
© 2016 Eitel