What are Integers | Basic Arithematics | Properties of Integers

Integers | Bionomial Expression | Trinomial Expresion

Integers: 

    

    All Positive and negative Whole numbers including zero are integers. 

Examples: -349, -4, -1, 0, 1, 4, 77, 183 . 

    Therefore, some intergers are positive, some are negative. and interger 0 is neither poitve nor negative. 

    The difference between two consective integers is 1.Let suppose if x is an integer then the next consective integer is x+1 or (x-1). 

Sample Question: The sum of three consective integers is 18. What is the samllest of numbers?

Solution: x is the smallest integer, then next two consective integers are x+1 and x+2. nthe sum of these three numbers is:

                            x+ (x+1)+ (x+2) = 18

                                    3x+3=18

                                    3x = 15

                                      x=5

Properties of Integers

•     Sum of integers is also an integer.
•     Product (multiplication) of integers is also an integer.
•     Division of one integer by another integer not necessarly yields an integer. If you divide 6 by 3, the result is 2. Which is an integer, but if 5 is divided by 6, the answer is 5/6, which is not an integer.

Odd Integers.

Any number that cannot be divided by 2 is called an odd integer; therefore {. .. 5, - 3, - 1, 1, 3; 5, . . . } represents the set of all odd integers.

Examples: 3, 5, 7, 11, 33, 45 etc

Properties of Odd Integers

. The difference between two consecutive odd numbers is 2. If x is an odd number then next odd number is x + 2. Next to x + 2 is x + 4.

The sum of two odd integers is an even integer.

Product of two odd integers is an odd integer.

[9:42 pm, 08/04/2023] 𝙎𝙃𝙀𝙍 𝘿𝙀𝙑𝙀𝙇𝙊𝙋𝙀𝙍𝙎: Division of an odd integer by another odd integer may not be an integer (5 +3 is not an integer).

[9:43 pm, 08/04/2023] 𝙎𝙃𝙀𝙍 𝘿𝙀𝙑𝙀𝙇𝙊𝙋𝙀𝙍𝙎: integer).

Even Integers

Any number that can be divided by 2 or Integers that are multiples of 2 are called even integers, namely {. . , - 6, - 4, - 2, 0, 2, 4, 6, . . . }.

Example: 2, 4, 6, 80, 96, 110 etc

Propertiesof Even Integers

The difference between two even numbers is 2.

If x is an even number then next even number is x + 2. Next to x + 2 is x + 4.

The sum of even integers is an even integer.

Product of two even integers is an even integer.

Division of an even integer by another even integer may not be an even integer (6 + 2 is not an even integer).

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