Complete lesson 1
Thursday 30 April 2020
Thursday 23 April 2020
Science
Nutrition in plants
Photosynthesis
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Wednesday 22 April 2020
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Monday 20 April 2020
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Monday 13 April 2020
Maths
Chapter 1 Integers
CLASS VII CHAPTER -1
CLASS VII CHAPTER -1
INTEGERS
integers:- together the positive numbers 0 and negative numbers are called integers
....,...,-3, - 2, -1,0,1,2,3.....
negative numbers go to the left of zero
positive Number go to the right of zero
the opposite of an integer is the integer which is at the same distance from zero but in the opposite
direction on the number line.
The integer pairs,(-6,6),(-5,5),(-4,4),(-3,3),(-2,2),(-1,1) are opposite of each other.
Also , for any integer a,
-(-a)=+a. -(+a)=-a
The numbers 2,-2,4,-5,0,-1 put in order from lowest to highest are -5,-2,-1,0,2,4.
The numbers -3,8,-4,-6,3,2 put in order from highest to lowest are 8,3,2,-3,-4,-6.
Absolute Value of an integer :-
The absolute value of a number is the distance between 0 and the number on the number line.
Distance is always a positive quantity.
Absolute value is represented by a vertical bars on each side of the number, I.e., absolute value of a
number
a is | a |.
Examples :- | -18|=18. |27|=27.
-| -615|=-615. -|100|=-100
properties of addition and subtraction of integers
1.Closure property: Integers are closed under addition and subtraction is the sum and difference of
integers is an integer
Addition. Subtraction
4+8=12 6-3=3
(-6)+(-8)=-14 4-8=-4
(-12)+16=4. (-6)-(-8)=2
24+(-40)=-16. (-7)-9=-16
2.Commutative property: addition is commutative for integers while subtraction is not commutative for
integers. If A and B are integers,then A+B =B+A but A-BB-A
addition
(-5)+(-10)=(-10)+(-5)=-15
(-4)+8=8+(-4) =4
11+(-19)=(-19)+11=-8
subtraction
6-55-6 as 1-1
(-4)-88-(-4) as -1212
(-11)-(-7)-7-(-11) as -44
3.Identity property: 0 is the additive identity for integers.
if a is an integer, then a + 0 = 0 + a =a
examples: 0+5=5+0=5 , 0+(-8)=(-8)+0=-8
4.Associative property: Associative property holds good for addition of integers whereas associative
property does not hold good for subtraction of integers.
If a,b and c are integers, then
a+(b+c)=(a+b)+c.
Examples,: (-6)+[5+(-3)]=(-6)+(2)=-4
[(-6)+5]+(-3)=(-1)+(-3)=-4
Hence, (-6)+[5+(-3)]=[(-6)+5]+(-3)
5.Additive inverse: The additive inverse of an integer a is the integer (-a),
such that a+(-a) (-a)+a=0.
Example: the additive inverse of 4 is -4 and -46 is 46.
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