 Hello and welcome to the session. In this session, we shall study the concept of absolute value and make out the comparison of absolute value from the statements about order. We also know about integers. Now, integers are a set of four numbers with their opposites. For example, three of these are very number, then a set of three, that is the negative of the given number. Now, we will need the use of number line to represent the integers. Now, here we have drawn a number line and we have marked a point as zero. Now, the integers on the right side of zero are positive integers and the opposites, that is on the left side of zero, we are having the negative integers. Now, opposite of zero, opposite of one, minus one, then opposite of two is minus two, opposite of three is minus three and so on. If and positive numbers are used in real life situation, the positive and negative numbers are used to describe the quantities having opposite direction of values. These integers are used to write the values of temperature above or below the freezing point, elevation above or below the sea level, credit and debit, positive and negative charge, etc. This with the help of an example, this example is a cliff and reaches 20 feet above the sea level, goes 20 feet below the sea level, while the integers have a position of mountaineer and the scuba diameter related to sea level. Think of the given example representing the sea level, the point zero. Now, a vertical number nine, then points above zero will be positive and the points below zero will be negative. Above zero, it will be positive and for the scuba diameter, depth will lie below zero, so it will be a negative integer. We will write the following table in which it will write the particular integer for the mountaineer and scuba diameter position related to the sea level. Now, as the mountaineer has 20 feet above the zero point, it will be given a positive integer, that is, the integer 20, the integer minus this position is 20 feet below the sea level, that is, 20 feet below the point zero. Now to compare our other integers, now our number line is used to compare and order integers. Numbers to the left are less than numbers to the right and numbers to the right are greater than numbers to the left. For a number line, now here we have drawn a number line. Now here we want to know that if minus three is less than minus two, now if we have to compare, then let's compare root number line. Now for the number line, you can see that minus three is to the left, numbers to the numbers to the right on the number line. For example, we have to plot these two points on the number line. Now here it is to the right of minus four. Numbers to the right are greater than numbers to the left on the number line. An example for discussing the application of compare and order of integers in zero word. And the example says that the temperature of a city A is minus four degrees and temperature of city B is minus six degrees. Root setting is warmer. Start with its solution. Now here we have drawn the number line and we have to mark the points minus four and minus six the points minus four and minus six on the number line. Now as to the right, the temperature of city A which is minus four degrees is greater than the temperature of city B which is minus six degrees. Hence is warmer than city B. Now let us discuss the concept of absolute value. Absolute value of a number between the number that is the given number zero on the number line. Now the absolute value of any number A is written as absolute value of A. That is like this we will write the absolute value of any number between the value of two. Then it is written as is equal to two value of minus two which is written as absolute value of minus two is equal to therefore absolute value of a number is the minimum value of the number without giving regard to its sign. Now from the number line we can see that the distance of minus two from zero is two units and also the distance of absolute value of a number is the distance of the given number from zero on the number line. Now let us discuss an example and the example says find the absolute value of minus ten and the absolute value of six at this solution. Then we have to find this we will plot minus ten on the number line that the distance of minus ten from zero on a number line is minus ten is equal to ten. If we plot six on a number line then the distance of six from zero on a number line is of six is equal to some of the embedded remarks the opposite integers distance from zero on the number line. Second is unit value of zero unit value of a number is never negative it means absolute value is always a positive number. Next is minus mu of minus a negative or negative of the absolute value of minus five will be equal to mu of minus five is five. I am solving this will be equal to minus five and we have absolute value of minus five is equal to five. Absolute value of minus five is five which is positive and its negative or opposite is minus five. Now let us discuss how to compare values. Now if we have to compare mu of minus four now we have every rent how to compare two integers so we will follow the same procedure here on the number line. Now we know that absolute value of minus four is equal to four. Now here we have four that is four on the number line absolute value of minus four absolute value of minus four. How to compare the absolute values from the statement about order. For this let us consider an example which will help us. And the example says our statement shows she has an account balance less than minus twenty dollars that date has of minus twenty dollars which is equal to twenty dollars. P and twenty on the number line this is the point minus twenty and this is the point twenty on the number line. Now less than minus twenty means the value is less than minus twenty on the left of minus twenty on the number line that is minus twenty five minus thirty and so on. Now many are not taken as negative so we have taken the absolute value of minus twenty dollars which is equal to twenty dollars and we have plotted this on a number line. Now as we have already discussed that the values less than minus twenty means the values twenty five minus thirty and so on. Twenty five new value greater than twenty dollars it means her debit shows that she has an account balance less than minus twenty dollars means she owes more than to the bank. So in this session we have learnt about the concept of absolute value the comparison of absolute values from the statements about order. This completes our session hope you all have enjoyed the session.