Commutative Property


 
 
Concept Explanation
 

Commutative Property

Commutative property of addition in rational numbers:

The addition of rational numbers is commutative i.e. if large frac{a}{b};and;frac{c}{d}  are any two ratoinal numbers, then

                    large frac{a}{b}+frac{c}{d}=frac{c}{d}+frac{a}{b}

Verification:  In order to verify this property, let us consider two expressions

                 large frac{5}{6}+frac{-4}{9}=frac{-4}{9}+frac{5}{6}

We have,

                large frac{-4}{9}+frac{5}{6}=frac{-8+15}{18}=frac{7}{18} and, large frac{5}{6}+frac{-4}{9}=frac{15}{18}+frac{-8}{18}=frac{15+(-8)}{18}=frac{7}{18}

large therefore ;frac{5}{6}+frac{-4}{9}=frac{-4}{9}+frac{5}{6}

Similarly, it can be verified for others pairs of rational numbers.

Commutative property of subtraction in rational numbers:

The subtraction of rational numbers is not always commutative. That is, for any two rational numbers large frac{a}{b} and large frac{c}{d}, we have

                    large frac{a}{b}-frac{c}{d}neq frac{c}{d}-frac{a}{b}

For example, large frac{2}{3}-frac{1}{6}=frac{2}{3}+frac{-1}{6}=frac{2times 2+(-1)times 1}{6}=frac{3}{6}=frac{1}{2}

and,            large frac{1}{6}-frac{2}{3}=frac{1}{6}+frac{-2}{3}=frac{1+(-2)times 2}{6}=frac{1-4}{6}=frac{-3}{6}=frac{-1}{2}

large therefore ;frac{2}{3}-frac{1}{6}neq frac{1}{6}-frac{2}{3}

Commutative property of multiplication in rational numbers:

The multiplication of rational numbers is commutative. That is, if large frac{a}{b} and large frac{c}{d} are any two raitonal numbers, then

                  large frac{a}{b}times frac{c}{d}=frac{c}{d}times frac{a}{b}

Verification: We have,

                 (i)   large frac{3}{4}times frac{5}{7}=frac{3times 5}{4times 7}=frac{15}{28} and, large frac{5}{7}times frac{3}{4}=frac{5times 3}{7times 4}=frac{15}{28}

                     large therefore ;frac{3}{4}times frac{5}{7}=frac{5}{7}times frac{3}{4}

                 (ii)  large frac{-5}{12}times frac{-3}{4}=frac{-5times -3}{12times 4}=frac{15}{48}=frac{5}{16} and, large frac{-3}{4}times frac{-5}{12}=frac{-3times -5}{4times 12}=frac{15}{48}=frac{5}{16}

large therefore ;frac{-5}{12}times frac{-3}{4}=frac{-3}{4}times frac{-5}{12}

Commutative property of division in rational numbers:

For any rational  number large frac{a}{b}, we have

                              large frac{a}{b}div 1=frac{a}{b} and  large frac{a}{b}div (-1)=-frac{a}{b}=frac{-a}{b}

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

Name the property of multiplication illustrated by the following: -11/13 × -17/5 = -17/5 × -11/13

Right Option : C
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Explanation
Question : 2

Name the property illustrated by: (5/9 x 2/9) = (2/9 x 5/9)

Right Option : C
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Explanation
Question : 3

The commutative property of ADDITION states _____________________________

Right Option : C
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Explanation
 
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