Rational Numbers In Expressions

       
           

When we have the Rational Numbers in Expressions then we need to solve the expressions using the rules of Hierarchy of operations. Now we will learn the hierarchy of operations to be followed. The hierarchy is denoted by B O D M A S, where ‘B’ stands for Bracket, ‘o’ stands for “of operation“, ‘D’ stands for Division operation, ‘M’ stands for multiplication operation, ‘A’ stands for Addition operation, ‘S’ stands for subtraction operation.

Now we will look at the addition and subtraction operation, first we check the denominators and make the two rational numbers as the like rational numbers. For this we find the LCM of the denominators and then convert the rational number into their equivalent forms such that the denominator is equal to its HCF. In case we have the two rational numbers in the expression as the like rational numbers, then simple addition or subtraction of the numerators is to be performed. Once the addition or the subtraction is done, we will simply convert the resultant rational number into its standard form.

In order to perform the multiplication and the division of the rational expression, we say that we need not to have the denominators same. When we have the multiplication operation, then the two numerators are multiplied and the denominators are also multiplied.

The resultant rational number is converted into its standard form and we should remember that if the two rational numbers are negative, then the products are positive rational numbers. In case one rational number is positive and another is negative, then the product is always negative.

When we have a division expression, then while solving the rational expression, the divisor is changed to its reciprocal and the operation of division is changed to the multiplication operation. Now the result is taken as simple product of two rational numbers. 

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