Rational Numbers for 8th class

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In Class X, we learnt about the RATIONAL NUMBERS IN TWO VARIABLES.Zero science lab is the best Platform to teach RATIONAL NUMBERS for class 10

In Mathematics, we frequently come across simple equations to be solved. For example, the equation

x + 2 = 1the solution gives the whole number 0 (zero). 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 = 5Do you see ‘why’? We require the number –13 which is not a whole number. This led us to think of integers, (positive and negative). Note that the positive integers correspond to natural numbers. One may think that we have enough numbers to solve all simple equations with the available list of integers. Now consider the equation

2x = 3 (4) 5x + 7 = 0for which we cannot find a solution from the integers. (Check this) We need the numbers 3 /2 to solve equation (4) and 7/ 5? to solve equation (5). This leads us to the collection of rational numbers

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.

You have seen that whole numbers are closed under addition and multiplication but not under subtraction and division. However, integers are closed under addition, subtraction and multiplication but not under division.

Recall that a number which can be written in the form p q, where p and q are integers and q? 0 is called a rational number. For example, 2 /3?, 6/ 7, 9 /?5 are all rational numbers. Since the numbers 0, –2, 4 can be written in the form p/ q, they are also rational numbers.We find that sum of two rational numbers is again a rational number. Check it for a few more pairs of rational numbers. We say that rational numbers are closed under addition. That is, for any two rational numbers a and b, a + b is also a rational number. Try this for some more pairs of rational numbers. We find that rational numbers are closed under subtraction. That is, for any two rational numbers a and b, a – b is also a rational number.Take some more pairs of rational numbers and check that their product is again a rational number. We say that rational numbers are closed under multiplication. That is, for any two rational numbers a and b, a × b is also a rational number

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