[PDF] CLASS VII MATHEMATICS CHAPTER-I INTEGERS MODULE 4/8

949_6CLASS_7_1_MODULE_4_8_PDF.pdf

CLASS VII

MATHEMATICS

CHAPTER-I

INTEGERS

MODULE 4/8

In the previous modules we have discussed about the operations on Integers and their properties. In this module first we will discuss about all the properties under addition and subtraction and their application.

The different properties are

1. Closure property

2. Commutative property

3. Associative property

4. Additive identity.

1. a) Closure Property under addition. For any two integers ͚a͛ and ͚b͛ , a+ b is always an

integer. Ex. 4 and -3 are integers and 4 + (-3) = 4 - 3 = 1, 1 is always an integer.

b) Closure property under subtraction. For any two integers ͚a͛ and ͚b͛, a - b is always an

integer. Ex. 6 and -8 are integers and 6 - (-8) = 6 + 8 = 14 is also an integer. So integers are closed under addition and subtraction

2.a) Commutative property under addition:-for any two integers ͚a͛ and ͚b͛ , a н b с b н a

Ex. For the integers 5 and -9 ,

5 + (-9) = 5 - 9 = -4

(-9) + 5 = -9 + 5 = -4

5 + (-9) = (-9) + 5 = -4

b) Under subtraction For the integers 5 and -6

5 - (-6) = 5 + 6 = 11

(-6) - (5) = -6 -5 = -11

5 - (-6) ് (-6) - (5)

So integers are commutative under addition and they are not commutative under subtraction.

3. a)Associative property under addition:- For any three integers ͚a͛ ͚b͛ and ͚c͛

A + ( b + c ) = (a + b ) + c

Ex. For the integers 6 , -7 and 8

6 + [ (-7) + 8] = 6 + [-7 + 8] = 6 + (1) = 6 +1 = 7

[ 6 + (-7)] + 8 = [ 6 -7 } + 8 =(-1) + 8 = -1 +8 = 7 6 + [ (-7) + 8] = [ 6 + (-7) ] + 8 = 7 b) Under subtraction:- For the integers 6, -7 and 8

6 - [ (-7) - 8] = 6 - [-7 -8 ] = 6- [ - 15 ] = 6 + 15 = 21

[ 6 - (-7) ] - 8 = [ 6+ 7 ] - 8 = 13 - 8 = 5

6 - [ (-7) - 8] т ΀ 6 (-7) ] -8

So integers are associative under addition and not associative under subtraction.

4. Additive identity:- For any integer ͚a͛

a + 0 = 0 + a = a , 0 (zero) is called additive identity of integers.

Ex 5 + 0 = 0 + 5 = 5

-2 + 0 = 0 + ( -2) = -2

Applications :-

1) Verify a + b = b + a for

i) a =25 , b = -15 ii) a = -6 and b = 7 iii) a = -8 and b = -3 i) a + b = 25 + (-15) = 25 - 15 = + 10 b + a = (-15 ) + 25 -15 + 25 = +10 a + b = b + a similarly work out the other problems

2) verify a + ( b+ c ) = (a + b ) + c for

i) a = -2 b= -3 and c = 9 ii) a = 10 , b = 12 and c = -14 i) a + ( b + c ) = (-2) + [(-3) + 9] = -2 + [ -3 + 9] = -2 + (6) = -2 + 6 = +4 (a + b) + c = [(-2) + (-3) ] + 9 = [ -2 -3 ] + 9 = -5 + 9 = +4. a + ( b+ c ) = (a + b) + c work out the other problem.

ASSIGNMENT.

1 . Fill in the blanks.

a) -15 + ( ) = -80 + ( ) b) - 69 + ( ) = -69 c) 120 + ( ) = 0 d) [ 13 + ( -25 ) ] + ( ) = ( ) + [ (-25 ) + (-9) ]

2. Write a pair of positive integers whose difference is 10

3. write a positive and a negative integers whose sum is -8

4. Write a positive and a negative integers whose difference is -4

5. In a quiz , Team A scored -40 , 10 , 0 , 50 and Team B scored 10 ,20 , -30 , 15 in four

respective round. Which Team scored more points.

S.SAHADEVA RAO

TGT.SS

AECS-2 HYD.