Math department

6TH PRIM.

Unit 1Integers

2-The set of Integers

3-Ordering and comparing Integers

1-Revision

Exit

Revision on sets

is a well-defined collection of objects.Each object of a set is called a member or an element of the set.

The set

If X= { 1 , 2 , 5 , 7 } , Y = { 2 , 5 , 9 }

Then Put ( , , , ): (a) 2……… X (b) 6………Y (c) Y……… X (d) { 2 , 9 } …. Y

Ex:

The set of Counting numbers = { 1 , 2 , 3 , …………}

The set of Natural numbers = { 0 , 1 , 2 , 3 , ………}

In the Venn diagram, U is the universal set.a) U =

b) M =

c) N =

d) M \ =

e) N \ = f) M U N =

h) M – N = g) M ⋂ N =

i) N – M =Answer

Try Again

The set of Counting numbers = { 1 , 2 , 3 , …………}

The set of Natural numbers = { 0 , 1 , 2 , 3 , ………}

In the Venn diagram, U is the universal set.a) U = { 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 }b) M = { 3 , 4 , 7 , 9 }c) N = { 4 , 6 , 7 }d) M \ = { 2 , 5 , 6 , 8 }e) N \ = { 2 , 3 , 5 , 8 , 9 }f) M U N = { 3 , 4 , 6 , 7 , 9 }h) M – N = { 3 , 9 } g) M ⋂ N = { 4 , 7 } i) N – M = { 6 } Answer

Try Again

a) 65…… ∉ …….. Nb) 0 …… ∈ ……… Nc) { 1 , 2 } .... ⊂... Nd) { 0 } …… ⊄..… Ne) { 2.3 , 4 } . ⊄... Nf) 8.4 …… ∈ ……. Ng) Ø ……. ⊂ ………N

Mark (true ) or (false) such that N is the set of natural numbers :

Contents

T

T

F

T F

T F

T

T

F

T F

F

F

a) 65…… ∉ …….. Nb) 0 …… ∈ ……… Nc) { 1 , 2 } .... ⊂... Nd) { 0 } …… ⊄..… Ne) { 2.3 , 4 } . ⊄... Nf) 8.4 …… ∈ ……. Ng) Ø ……. ⊂ ………N

Mark (true ) or (false) such that N is the set of natural numbers :

Contents

T

T

F

T F

T

T

T

F

T F

F

F

F

TRY AGAIN

V . GOOD

The set of integers is an infinite set and extends without limit from both sides. * Zero is neither positive nor negative.

•One is the smallest positive integer number.

•(-1) is the greatest negative number.

The set of Integers

N ⊂ Z , Z+ ⊂ Z , Z- ⊂ Z , { 0 } ⊂ Z The Set of Positive Integers : Z+ = { 1 , 2 , 3 , 4 , 5 , . . . }

The Set of Negative Integers : Z- = { -1 , -2 , -3 , -4 , -5 , . . . }

The Set of Integers : Z = { . . . , -3 , -2 , -1 , 0 , 1 , 2 , 3 , . . . }

Notice that :-

Z= Z+

U {0 }UZ- Z - Z- = N

Z= N U Z- N – Z+ = {0}

Z+ ⋂ Z- =Ø Z ⋂ Z- =Z-

Z ⋂ Z+ = Z+ Z ⋂ N = N

Z+ U N = N

Mark (true) or (false) and give the reason :

(a) Zero ∈ Z- ( ) because :……………………………………

(b) φ = Z- ⋂ Z+ ( ) because : ……………………………………

(c) Z+ ⋂ N = Z+ ( ) because :……………………………………

(d) {-17} ⊂ Z ( ) because : ……………………………………

Ex:1

Find the value of ( x ) to get a true statement :

(a) -5 ∈ {-1, 0, -3, x} then …………………

(b) x ∈ {2, 5, -3} ∩ {5, -2, -3} then

…………………

(c) {2, x} U {-4, 0, 4} = {0, -2, 2, -4, 4} then

…………………

Ex:2

The absolute value of the

integerThe absolute value of the integer (a) is the distance between the location of (a) and the location of Zero on the number line . It is always positive and denoted by the symbol │a│

Find the absolute value of : 4 , -4 , 0 , -8 the solution : l 4 l = 4 , l-4l = 4 , l 0 l = 0 , l-8l = 8

Ex:1

Complete the following :(a)│-102 │= (b) - │-15 │ =

(c) │-5 │+ │ 7 │ =

(d) the relation between │b │, │-b │ is

Ex:2

Write the inverse of each of the numbers :

113 ( ……………… ) -9 ( …………… ) 0 ( ……………… ) 7 ( …………… ).

Ex:3

AnswerTry

Again

Complete the following :(a)│-102 │= 102 (b) - │-15 │ = - 15(c) │-5 │+ │ 7 │ = 12(d) the relation between │b │, │-b │ is Equal

Ex:2

Write the inverse of each of the numbers :

113 ( ……………… ) -9 ( …………… ) - 113

9 0 ( ……………… ) 7 ( …………… ). 0

-7

Ex:3

Try Again

Answer

H.W.BOOKLE

T P. 5

Contents

Ordering and Comparing Integers

This means that :……. -3 < -2 < -1 < 0 < 1 < 2 < 3 < … (ascending order).….…. 3 > 2 > 1 > 0 > -1 > -2 > -3 … (descending order).

Arrange the following numbers in an ascending order : -1 , 3 , 1 , -5 , 7

The ascending order is : -5 , -1 , 1 , 3 , 7

Ex1

Put the correct sign (>, < or =) :(a) -7 -9 (b) 3 -13 (c) -4 0

(d) │-11 │ 11 (e) -7 - │-5 │ (f) 30 103

Ex2

1-Arrange the following integers :(a) 6 , -60 , 2 , -17 , -22 , 0 (ascendingly).

…… , ……. , …… , ……. , …… , …….

(b) 1, -11, 3, -1, -8, 5 (descendingly).

…… , ……. , …… , ……. , …… , …….

2-Complete the space using the correct sign (>, < or =) :

(b) 3 …. -6 (b) -7 … 17 (c) │-13 │…. 3

(d) │-5 │ ….. 5 (e) 3 + │-3 │ …. 8 (f) - │-4 │ ….. 2

Exerc ise

3-Write the previous integer and the next integer for each of the following integers :

(a)…. , -9 , …. (b) …. , 13, …. (c) …. , 3 , ….

4-Write the integers between each two integers of the following:

(b)-4, ( ……. ), 2 (b) -1, ( ……. ), 5 (c) -7, ( ……. ), 0

5-Determine the Constant value by which the following integers increase, then complete the next three numbers :

(c) -7, -6, -5, …., …., ….

(b) -50, -40, -30, …, .…, ….

AnswerTry

Again

3-Write the previous integer and the next integer for each of the following integers :

(a)…. , -9 , …. (b) …. , 13, …. (c) …. , 3 , ….

-10 -8 12 14 2 44-Write the integers between each two integers of the following:

(b)-4, ( ……. ), 2 (b) -1, ( ……. ), 5 (c) -7, ( ……. ), 0

-3,-2,-1,0,1 0,1,2,3,4 -6,-5,-4,-3,-2,-1

5-Determine the Constant value by which the following integers increase, then complete the next three numbers : -4 , -3 , -2(c) -7, -6, -5, …., …., …. -20, -10, 0(b) -50, -40, -30, …, .…, ….

AnswerTry

Again

H.W.BOOKLET P.

6,7

Contents