**INTEGERS**

Hi friends and my dear students! In this post, I have covered **Andhra Pradesh ****class-7 Maths integers (chapter-1) important points** After Reading **Mathematics ****integers**** ****Notes With important points**, Please do share it with your friends. You can **Learn Maths for All Classes here.**

**Natural Numbers: ****The counting numbers
1,2,3,4,5,6.....are called Natural numbers. It is represented by 'N'. N=
(1, 2, 3, 4, 5, 6 ....}The smallest a natural number is 1 and the greatest natural number does not exist **

**Whole Numbers: ****Natural numbers including zero are
called whole numbers. It is Represented by W. W= {0,1,2,3,4,5,6,... } The least
whole number is 0 and the greatest whole number does not exist. **

**Integers: ****The set containing the positive numbers, the
negative numbers together with zero is called the set of integers. Whole
numbers including negative numbers are called Integers. It is represented by Z.
The set of integers is represented by Z.**

**Z = {... - 4, -3, -2, -1, 0,1,2,3,4.....}**

**(or)**

**All the whole numbers together with
negative of counting numbers form the set of all integers. Z or I=
{...-5,-4,-3,-2,-1, 0, 1,2, 3..****}**** is the set of all integers. **

*** Each time you add a positive
integer, you move right on the number line. **

*** Each time you add a negative integer,
you move left on the number line. **

*** -a' is called the additive inverse
of a. **

**Note:**

**1{ 1.2,3,............} is called Set of positive integers.**

**2. { -1,-2,-3,...............} is called Set
of negative integers. ,**

**3. Zero is considered neither positive nor
negative.**

**4. In the number line all negative integers are on
the left side of zero, all positive integers are on the right side of zero.**

**5. Set of positive integers and zero considered as
Non – negative integers. {0,1,2,3,.......} is set of non – negative integers.**

**6. Set of negative integers and zero considered as
Non - positive integers. (0,-1,-2,....} is set of non - positive integers.**

**7. The differences between any two consecutive
integers is 1.**

**8. The absolute value of an integer is the numerical value of the integer regardless of its sign.**

**Also Check**

**Introduction to Knowing Our Numbers Key Points**

**Trigonometry Do This & Try this solution**

**SSC (10th class) Trigonometry Exercise - 11.1 Solution**

**SSC(10th class) Trigonometry Exercise - 11.1 Solutions**

**9. ****Properties of Addition
of Integers:**

** Let a € Z, b € Z, c € Z, then**

**i)****Associative
Law:**

** (a+ b) +c= a+ (b+c)**

**ii) ****Existence
of Additive Identity:**

** 0+a=a+0 = a. 0' is the additive identity on integers**

**iii) ****Existence
of Additive Inverse:**

**For each a € l there exist -a € l
such that a + (-a) = (-a) +a=0.**

**10. i) The product of two integers
with same sign is a positive integer.**

** ii) The product of two integers with unlike
signs is a negative integer.**

**11. ****Properties of
Multiplication of Integers:**

**Associative Law:**

** (a x b) x c =a x (b x c) for all integers a, b, c.**

**Distributive Law: **

**For all a,b,c € Z, we have a. (b+c)=
a b+ a c and (a +b).c=a.c+b.c**

**Existence of Multiplicative Identity: **

**Clearly, 1 is an integer such that
1-a = a 1=a. Thus, 1 is the multiplicative identity. . **

**Multiplicative property of 0: For
every integer a, we have a.0=0.a=0**

**☆**** On a number line when you add a
positive integer you move right side on the number line and if a negative
integer is added you move to the left side on the number line. **

**☆**** On the number line if you subtract a
positive integer you move to the left side and if you subtract a negative
integer you move to the right side.**

** ****☆**** Product of any two
positive integers or any two negative integers is always a positive
integer. **

** ****☆**** Product of a
positive integer and a negative integer is always a negative integer two integers with opposite signs always give a negative product. **

** ****☆**** Product of even number of negative integers is always a positive integer. **

** ****☆**** Product of odd
number of negative integers is always a negative integer**

**
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