Introduction
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In Mathematics, we frequently come across simple equations to be solved. For example, the equation:
x + 2 = 13 (1)
is solved when x =
The solution 11 is a
x + 5 = 5 (2)
the solution gives the
If we consider only natural numbers, equation (2) cannot be solved. To solve equations like (2), we added the number zero to the collection of natural numbers and obtained the whole numbers.
Even whole numbers will not be sufficient to solve equations of type:
x + 18 = 5 (3)
Do you see ‘why’? We require the number
This led us to think of
Now consider the equations:
2x = 3 (4)
5x + 7 = 0 (5)
for which we cannot find a solution from the integers. (Check this) We need the numbers
This leads us to the collection of
We have already seen basic operations on rational numbers. We now try to explore some properties of operations on the different types of numbers seen so far.