Closure Property


 
 
Concept Explanation
 

Closure Property

Closure Property:

The closure property states that for any two rational numbers a and b, a – b is also a rational number. The result is a rational number. So the rational numbers are closed under subtraction.

1) Addition of Rational Numbers : The closure property states that for any two rational numbers a and b, a + b is also a rational number.

Example: Verify closure property for addition on large frac{1}{2};and;;frac{3}{5}

Solutionlarge frac{1}{2};+;;frac{3}{5}=frac{5}{10};+frac{6}{10}=frac{11}{10}

The result is a rational number. So we say that rational numbers are closed under addition.

2) Subtraction of Rational Numbers  :  The closure property states that for any two rational numbers a and b, a – b is also a rational number.

Example: Verify closure property for subtraction on  large frac{1}{3};and;;frac{3}{5}

Solution:  large frac{1}{3};-frac{3}{5}=frac{5}{15};-frac{9}{15}=frac{-4}{15}  Is also a rational numberThe result is a rational number. So the rational numbers are closed under subtraction.

3) Multiplication of Rational Numbers :  The closure property states that for any two rational numbers a and b, a × b is also a rational number.

Example: Verify closure property for multiplication on large frac{1}{4};and;;frac{8}{5}

Solution: large frac{1}{4};times ;frac{8}{5}=frac{8}{20}=frac{2}{5}The result is a rational number. So rational numbers are closed under multiplication.

4) Division of Rational Numbers :  The closure property states that for any two rational numbers a and b, a ÷ b is also a rational number.

Example: Verify closure property for multiplication on large frac{1}{10};and;;frac{8}{5}

Solutionlarge frac{1}{10};div frac{8}{5}=frac{1}{10};times frac{5}{8}=frac{5}{80}=frac{1}{16}The result is a rational number. But we know that any rational number a, a ÷ 0 is not defined. So rational numbers are not closed under division. But if we exclude 0, then all the rational numbers are closed under division.

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

The result of the following expression on simplification will be _______________.

frac{18}{3}+frac{9}{5}

Right Option : A
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