Free Online Maths Tutorials - Understanding Integers
In this article, I am explaining the basics of integers and their application in addition and subtraction which will greatly benefit students.
Positive and negative numbers, including zero, are known as integers. When the numbers are prefixed by a + sign, they are positive numbers. When the numbers are prefixed by a minus sign, they are known as negative numbers. It is a number that is not a decimal or a fraction. positive and negative numbers, including zero, are known as integers. When the numbers are prefixed by a + sign, they are positive numbers. When the numbers are prefixed by a minus sign, they are known as negative numbers. It is a number that is not a decimal or a fraction.Characteristics of positive numbers
They have a positive value and are written in the following manner, in increasing order: +1, +2, +3, +4, +5.......... All the positive numbers have a greater value than zero.Characteristics of negative numbers
They have negative values and are ordered in the following way in increasing order: -10, -9, -8, -7,-6, -5,-4, etc. All the negative numbers have a lesser value than zero.What are positive and negative numbers?
We apply a positive sign to numbers when we represent factors such as increasing weight, height, or mass, deposits, profits from business, temperatures above sea level, etc. We fix a negative sign to numbers under circumstances such as the representation of loss in business, decreasing weight, temperature below sea level, etc. One fine example of a positive integer is the profit of a business firm during the year, which is +300,000. One fine example of a negative integer is the temperature of Washington, DC, during the winter, which is -4 degrees, as it is below freezing point.When the numbers are represented on a number line
When the numbers are represented on a number line, they are represented as follows: Z = { -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5}Addition and subtraction of integers
When both the numbers are positive
When both numbers have a positive value, add the two numbers as follows: 23 + 22 = 45.When one number is positive and one number is negative
The greater number should be determined, and the symbol of greater value should be considered. These numbers should be subtracted to derive the output. For example, +50 -20= +30. Look at the below example to know the application when a greater number is denoted with a greater value: -50 + 20 = -30.
If the problem is: (-50) -(+20) = 0, then you should solve the problem in this manner: The - symbol and + symbol both result in a negative sign. So,When both the numbers are negative
When both the numbers are negative, place a negative sign and add both numbers. Look at the above example: -24-24 = -48.When the numbers are enclosed in a bracket
You should solve the problems in the following way when enclosed in a bracket: (+50) + (-30) = The number 50 has a positive value, whereas -30 has a negative value. So, considering the + sign outside the bracket and the - sign within the bracket, it becomes minus as + and - result in negative numbers. So, you should solve the problem in this way: +50 -30 = 50 -30 = 20.
When the problem is as follows: (+50)-(-20), then you should consider the - or negative sign outside the bracket and the - sign prefixed to 20. Both the negative numbers lead to positive symbols. So, you should add as follows: 50 + 20 = 70.
Integers are an interesting set of numbers. Each succeeding number is more in value by 1 from the earlier number. Integer numbers are the basic elements of the number train. There are various systems of numbers like binary, octal, or hexadecimal. In each system there are the basic notations like - only 0 and 1 in binary and all numbers thereafter are made with a combination of these two notations and all the succeeding numbers are 1 more than the earlier.
Coming to the octal we have only eight notation 0, 1, ..., 6 and 7 and all succeeding numbers are made with a combination of these, and each is 1 more than the earlier.
In hexadecimal we add some new notations and basic numbers become 0, 1, 2, ... 8, 9, a, b, c, d, e, and f - a total of 16 notations, following the same rule of succeeding 1 from the earlier.
So, in any system the basic elements are integers, the whole numbers.
All the fractional numbers are present within the chain of these integers and the integers are like a boundary to them. For example, in the common decimal system the numbers like 4.056, 4.973, 4.003, 4.527 all lie within the integers 4 and 5.
Integers are like the milestones of number path.