Integers In Math

Introduction to integers in math:

The number line in the figure below is a helpful visual devic to associate the set of whole numbers with evenly spaced points on a line. For each nonzero whole number, we can associate its negative to the left of zero. The set of whole numbers, along with -1, -2, -3 and so on, is called the set of integers in math. The integers in math are basic for mathematics solving numbers. Let us see about the integers in math.

     

The following terminology is used with reference to the integers:
{…, -3, -2, -1, 0, 1, 2, 3,…} Integers
{1, 2, 3,…} Positive Integers
{0, 1, 2, 3,…} Non-negative Integers
{…, -3, -2, -1} Negative Integers
{…, -3, -2, -1, 0} Non-positive Integers
The symbol -1 can be read as “negative one,” “opposite of one,” or “additive inverse of one.

Integers in math:

PROPERTY 1. If a is any integer, then - (-a) = a. The opposite of the
opposite of any integer is the integer itself.

Addition of Integers
      The number line is also a convenient visual aid for interpreting the addition of integers in math.The absolute value of a number is the distance between the number and zero on the number line. 
For example, the absolute value of 8 is 8. The absolute value of 18 is 18. Vertical bars on either side of a number denote absolute value. Thus we write |6| = 6 |-6| = 6 |0| = 0

Note that the absolute value of a positive number is the number itself, but the absolute value of a negative number is its opposite. Thus the absolute value of any number except 0 is positive, and the absolute value of 0 is 0.

We can describe the process of adding integers precisely by using the concept of absolute value.

Two Positive Integers in math

The sum of two positive integers is the sum of their absolute values.(The sum of two positive integers is a positive integer)
For example,
43+ 54 = |43| + |54| = 43+ 54 = 97

Two Negative Integers:
The sum of two negative integers is the opposite of the sum of their absolute values. (The sum of two negative integers is a negative integer)
For example,
(-67) + (-93) = (|-67| +|-93|) = -(67 + 93) = -160

One Positive and One Negative Integer:
The sum of a positive and negative integer can be found by subtracting the smaller absolute value from the larger absolute value
and give the result the sign of the original number that has the larger absolute value.
For example,
82 + (-40) = |82| - |-40| = 82 - 40 = 42

Zero and Another Integer
The sum of zero and any integer is the integer itself.
For example,
0 + (- 46) = - 46

Subtraction of Integers
A general description for the subtraction of integers follows:
Subtraction of Integers
If a and b are integers, then a – b = a + (-b)
a – b = a + (-b) can be read as “a minus b is equal to a plus the opposite of b. Every subtraction problem can be changed to an equivalent addition problem.

Integers in math:

Example 1:

Add – 5 and – 3,

Solution :
Step 1 : 5 + 3 = 8
Step 2 : – 8
Thus – 5 + (– 3) = – 8

Example 2 :

Subtract 4 from 7.

Solution :
                  Subtract 4 from 7 means, what should be added to 4 to give 7. The result  is 3.

Example 3 :

Subtract – 2 from 8.

Solution :
                 To subtract – 2 from 8, we should find what should be added to – 2 to give 8.

Example 4 :

Subtract  – 4 from – 10

Solution :

                 – 10 – (– 4) = – 10 + (additive inverse of – 4)
                                       
                                       = – 10 + 4

                                       = – 6 (see addition of two integers)