 Hello and welcome to the session. In this session we will discuss a question which says that the following table shows the freezing points of various items and the statement is given to us in which the first column shows the items as fuel, wax, butter, honey and mercury and in the second column the column's freezing points of the various items in degree synthesis are given as minus 42, 35, 25, minus 5 and minus 28. Now in the A part we have to arrange the items from lowest freezing point to the highest freezing point and tell which freezing point is lower, mercury or honey. Then in the B part compare the absolute values of items, fuel and wax and in the C part we have to check that is the freezing point of butter or mercury closer to the freezing point of water which is zero degree Celsius. Now before starting the solution of this question we should know some results. Firstly we should now write a number line that a number line is used to compare integers. In a number line numbers to the left are less than the numbers to the right and numbers to the right are greater than the numbers to the left. Now consider a number line, now here let us watch minus 1 is on the number line we have marked the points minus 1 and 2. Now here we can see that minus 1 is to the left of the number 2 therefore minus 1 is less than the number 2. Now we just compare the points 2 and 3. Now from the number 9 you can see that 3 is to the right of the number 2, 3 is greater than we can compare integers by using the number line. The absolute value of a number is the distance of that number from zero to a number line. In integers minus 2 and minus 3 we have to know that which integer is closer to zero then we will find the absolute value of both of these integers. Now the absolute value of minus 2 is written as absolute value of minus 2 which is equal to 2 is equal to now we know that absolute value of a number is its distance from zero on a number line. Now the value of minus 2 is 2 of minus 3 is 3 the distance of the point minus 2 from zero is less than the distance of the point minus 3 from zero on a number line therefore to zero. Now these two words they welcome to us a key idea for solving out the given question. And now we will start with the solution since of various items it is given to a freezing point to the highest freezing point and then we have to tell that the freezing point is lower, more than or less. The A part first of all let us construct a number line. Now here we have constructed a number line which is the value here large so we take the points at the distance of 10 even stick numbers are on the right side of zero and negative numbers are on the left side of zero. So we have the points minus 15, minus 40, minus 30, minus 20, minus 10, 0, 10, 20. Now in the question the freezing points of various items are given to us from lowest freezing point to the highest freezing point. We will plot the given freezing points on the others we will plot minus 42, 45, 25, 8 on the number line. Now we have plotted all the freezing points on the number line we can see that minus 42 is on the extreme left of all the numbers as we have discussed the integer which is on the integers is the smallest of all the integers. On the right of minus 42, 28 we can see from the number line minus 5 is the next freezing point and then comes 25, 45. Now let us make a table the freezing points of the given items from the lowest to have the item with the lowest freezing point that is fuel with the freezing point minus 32 degree Celsius. Then next we have mercury with the freezing point minus 28 degree Celsius and then we have butter with the freezing points minus 5 degree Celsius respectively as the item freezing point that is the degree Celsius. We can see that the freezing point in the v part we have to compare the absolute values of the items fuel and of fuel is minus 42 degree Celsius and that of wax is 45 degree Celsius of its freezing point that is the absolute value of minus 42 is equal to 42 per wax the absolute value of 45 is equal to 45. Now where we can see 32 therefore value wax is greater than the absolute value that we have to find that whose freezing point is closer to the freezing point of water it is the freezing point of water or the freezing point of mercury of the freezing points of mercury and butter by using the given idea from 0 of mercury is minus 28 degree Celsius and the freezing point of water is 25 degree Celsius. Now for mercury the absolute value of 28 will be equal to 28 for butter absolute value of 25. Now see that 25 is less than 28 into the definition of absolute value this means that the distance of 25 from 0 is less than the distance of minus 28 from 0 which means that the freezing point of butter that is 25 degree Celsius is closer to the freezing point of water that is 0 degree Celsius as compared to the freezing point of mercury which is minus 28 degree Celsius. 25 degree Celsius is closer to 0 degree Celsius hence the freezing point butter is closer to the freezing point solution of the given version and that's all for this session. Hope you all have enjoyed this session.