Commutative Property


 
 
Concept Explanation
 

Commutative Property

Commutative Property:

1. Addition of Rational Numbers : For any two rational numbers a and b, a + b = b+ a

Example: Verify commutative property for addition on large frac{-2}{3};and;frac{5}{7}

Solution: 

LHS  =  large frac{-2}{3};+;frac{5}{7}=frac{-14}{21};+;frac{15}{21}=frac{1}{21}

RHS  =  large frac{5}{7}+frac{-2}{3}=frac{15}{21};+;frac{-14}{21}=frac{1}{21}

LHS = RHS

We see that the two rational numbers can be added in any order. So addition is commutative for rational numbers.

2. Subtraction of Rational Numbers:  For any two rational numbers a and b, a – b ≠ b –  a.

Example: Verify commutative property for subtraction on large frac{-1}{3};and;frac{2}{7}

Solution

LHS  =  large frac{-1}{3};-;frac{2}{7}=frac{-7}{21};-;frac{6}{21}=frac{-13}{21}

RHS  =  large frac{2}{7}-frac{-1}{3}=frac{2}{7};+;frac{1}{3}=frac{6}{21};+;frac{7}{21}=frac{13}{21}

LHS large neq RHS

So subtraction is not commutative for rational numbers.

3. Multiplication of rational numbers : For any two rational numbers a and b, a × b = b × a

Example: Verify commutative property for multiplication on large frac{-1}{3};and;frac{5}{7}

Solution

LHS  =  large frac{-1}{3} times frac{5}{7}=frac{-5}{21}

RHS  =  large frac{5}{7} times frac{-1}{3}=frac{-5}{21}

LHS = RHS

We see that the two ratrional numbers can be multiplied in any order. So multiplication is commutative for ratioanl numbers.

4. Division of Rational Numbers : For any two rational numbers a and b, a ÷ b ≠ b ÷ a.

Example: Verify commutative property for multiplication on large frac{-1}{3};and;frac{5}{7}

Solution

LHS  =  large dpi{100} fn_jvn large frac{-1}{3} div frac{5}{7}=frac{-1}{3} times frac{7}{5}=frac{-7}{15}

RHS  =  large frac{5}{7} div frac{-1}{3}=frac{5}{7} times frac{-3}{1}=frac{-15}{7}

We see that the expressions on both the sides are not equal. So divsion is not commutative for rational numbers.

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

The commutative property of ADDITION states _____________________________

Right Option : C
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Explanation
Question : 2

Name the property of rational numbers illustrated by : (2/9 + 4/9) = (4/9 + 2/9)

Right Option : C
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Explanation
Question : 3

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

Right Option : C
View Explanation
Explanation
 
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