Simplification of Rational Numbers


 
 
Concept Explanation
 

Simplification of Rational Numbers

Simplification of Rationla Numbers: simplification of rational numbers involves using various properties to simplify the rational number.

Example: Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) 2/5 + 7/3 + - 4/5 + (-1/3)

Solution: Firstly group the rational numbers with same denominators:  2/5 + -4/5 + 7/3 +  (-1/3)

Now the denominators which are same can be added directly.

(2+(-4))/5 + (7+(-1))/3 = (2-4)/5 + (7-1)/3  = -2/5 + 6/3

By taking LCM for 5 and 3 we get, 15

large frac{-2}{5} + frac{6}{3}=frac{-6+30}{15}=frac{24}{15}=frac{8}{5}

Example: Re-arrange suitably and find the sum in each of the following:  11/12 + ( -17/3) + 11/2 + (- 25/2)

 

Solution: Firstly group the rational numbers with same denominators: 11/12 + (- 17/3) + (11 - 25)/2 =  11/12 + (- 17/3) +  (-14/2)

By taking LCM for 12, 3 and 2 we get, 12

large frac{11}{12}+frac{-17}{3}+frac{-14}{2}=frac{11-68-84}{12}=frac{-141}{12}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If a=7, then the value of large large -left ( frac{1-2a}{a-5} right ) is ______

Right Option : C
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Question : 2

What is the reciprocal of left ( frac{3}{2}times frac{1}{3} right )+left ( frac{1}{3}times 9 right ) ?

Right Option : D
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Explanation
Question : 3

2-frac{11}{39}+frac{5}{26}=_________ .

Right Option : B
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Explanation
 
 
 
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