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(a) Find the additive inverse of each of \[2004\] (b) Arrange in ascending order: \[8,-3,9,-8,-5,1\] .

Last updated date: 14th Jul 2024
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Hint: Such types of problems are in general quite simple to understand and are easy to solve. We can solve such questions very efficiently once we understand the core concepts behind the problem. To solve it, we need to have a fair amount of idea of number systems and invertible integers for the first part, and some basic idea of greater and lesser numbers for the second part. According to the first part, we need to find the additive inverse of a particular rational number, which means we need to find such a number, if possible, such that on adding this number with our given number in the problem, the result turns out to be zero. By the second part, we need to arrange all the given numbers in such a way that the least one is kept first and the highest one at the last.

Complete step-by-step solution:
Now we start off with the solution to the given problem by trying to figure out a number which when added to the given number results in a value equal to zero. Let the number be equal to ‘x’. The given number here is \[2004\] which is equal to \[+2004\] . Now we add ‘x’ and this given number and equate it to zero. We then find the value of ‘x’.
  & x+2004=0 \\
 & \Rightarrow x=-2004 \\
Thus our required answer to the problem is \[-2004\] .
Now solving the second part, we realise that we need to keep the smaller numbers first and the larger numbers towards the end. We arrange them as,
\[-8,-5,-3,1,8,9\] . Here we can clearly see that, the least number is at the beginning and the highest number at the end.

Note: To solve this problem, we need to have a thorough knowledge of number systems and greater and lesser numbers and their comparisons. Here in the first part of the problem, we need to figure out what number we should add to the given number so that the net result becomes zero. A simple method will be just to revert the sign of the given number. In the second part we need to arrange the numbers from a lower value to a higher value.