Subject: Compulsory Maths

- The positive integers are always added holding the positive (+) sign in resulting value. For example,

(+5) + (+6) = 11 or (+11) - The negative integers are always added holding the negative (-) sign in the resulting value. For example,

(-5) + (-6) = -11 - The positive and negative integers are always added holding the negative (-) sign in the resulting value. For example,

(+6) + (-5) = 1 or (+1)

(-6) + (+5) = -1

**Closure property**

Closure property states that the sum of any two integers is also integers. For example,

(+2) + (+3) = +5, which is an integer

(+3) + (-2) = +1, which is an integer

(-3) + (+2) = -1, which is an integer

Thus, if x and y be any two integers and z is the set of integers then x + y∈ z.**Commutative property**

Commutative property states that thesum of any two integers remains unchanged if their places are interchanged. If x and y are two integers, then x + y = y + z

For example,

(+2) + (+3) = (+3) + (+2) = +5

(-3) + (+2) = (+2) + (-3) = -1**Associative property**

Associative property states that the sum of any three integers remains unchanged if the order in which they are grouped is altered. If x, y and z are three integers, then (x + y) + z = x + (y + z)

For example,

(+3) + (+4) + (+5) = (+3) + [(+4) + (+5)] = (+3) + (+9) = +12

(+3) + (-4) + (+5) = (+3) + [(-4) + (+5)] = (+3) + (+1) = +4**Additive property of zero (0)**

If zero (0) is added +0 any integers, the sum is equal to the integer itself. So, zero (0) is known as the identity element of addition. If a is any integer, then a + 0 = a

For example,

(+2) + 0 = (+2) or 2

(-3) + 0 = (-3)**Additive inverse**

Each integer is said to the additive inverse of the other if the sum of any two integer is zero (0). If a is any integer, then (+a) + (-a) = 0, where (+a) is the additive inverse of (-a) and (-a) is te additive inverse of (+a).

- The positive integers are always added holding the positive (+) sign in resulting value.
- Commutative property states that the sum of any two integers remains unchanged if their places are interchanged.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

What are the signs rules for the addition and subtraction of integer? Mention.

The sign rules for the addition and subtraction of integers are:

- The positive integers are always added.
- The negative integers are always added.
- The positive and negative integers are always subtracted.

Add: (+2) + (+5)

Solution:

Here, (+2) + (+5)

= +7 or 7 ans.

Add: (-3) + (-2)

Solution:

Here, (-3) + (-2)

= -5 (The sum holds the negative (-) sign.)

Add: (+4) + (-1) and (+4) + (-7)

Solution

Here, (+4) + (-1)

= +3 or 3

Similarly, (+4) + (-7)

= -7 (The difference holds the sign of the bigger integer.)

Add: (+4) + (+5)

Solution:

Here, (+4) + (+5)

= +9 or 9 (The sum holds the positive sign.)

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