An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
The set of integers is denoted by the letter 'Z'.
Z = {. . . . . . . . . . -3, -2, -1, 0, 1 , 2, 3 . . . . . . . . .} is the set of integers. i.e. both +ve and -ve.
Z^{+} = {+1, +2, +3, +4, +5, +6 . . . . . . . . .} is the set of +ve integers.
Z^{-}= {-1, -2, -3, -4, -5, -6 . . . . . . . . . } is the set of -ve integers.
In the above number line, the negative integers left to the zero are increasing.
i.e. -3< -2< -1< 0< 1< 2< 3< 4 and so on.
The absolute value of an integer is the numerical value without power to whether the sign is negative or positive. For example:
let A and B be two places in which A is -5 km left from zero and B is +5 km right from zero. Then, what can be the distance between A and B.
In simple sense,
Distance of A + Distance of B,
= -3 + 3
= 0, which is impossible.
But by using absolute value, we can write as:
Distance of (A + B) = |-3| + |3|
= 3 + 3
= 6 km.
In such case, the numerical value of either 3 or -3 will be same i.e. 3.
The fundamental operations of integers on number lines are:addition
Solution:
In addition, Here, (+4) + (+5)
= +(4+5) = +9 ans.
Again, In subtraction, Here, (+9) - (+4)
= + (5-4) = +5 ans.
Answer: The set of all the numbers both positive and negative including zero is called the set of integers.
Solution:
Here, (+5) + (-2)
= +(5-2) = +3
Solution:
In Addition, Here, (+3) + (-7)
= (-7) + (+3)
= -(7-3) = -4 ans.
Again, Here, (+5) - (-3)
= (+5) + (+3)
= +(5+3) = +8 ans.
The rules of multiplication of integers are:
Solution:
Here, (+3) × (+2)
= +6 ans.
The rules of dividing the integers are:
Solution:
Here, (+8) ÷ (+2)
= (+4)
Write the integers that lie 3 units right and 3 units left to -2.
write the integers that lie 5 units right and 5 unit left to -5.
Write the integers that lie 8 units right and 8 units left to +2.
Write the integers that lie 10 units right and 10 units left to +5.
What are the opposite integers of -2.
What are the opposite integers of +5.
What is the sum of (-8) and its additive inverse of (+3)?
What is the sum of (+6) and its additive inverse?
Subtract (-7) from the additive inverse of (-2).
Find the sum of (+5) and the additive inverse of (-12).
ASK ANY QUESTION ON Integers
No discussion on this note yet. Be first to comment on this note