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Commutative Property

Rational Numbers I - Concepts

Rational Numbers

Addition of Rational Numbers

Closure Property

Commutative Property

Distributive Property

Additive Inverse

Equivalent Rational Numbers

Comparison of Rational Numbers

Representation of Rational Numbers on Number Line

Standard Form of Rational Numbers

Rational Numbers between Two Rational Numbers

Absolute Value of Rational Numbers

Class - 7th IMO Subjects

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 _____________________________
A. that you can multiply the factors in any order.	B. that you can divide the numbers in any order.	C. that up can add the numbers in any order.	D. that you can group the numbers in any order.
Right Option : C
View Explanation

Question : 2

Name the property of rational numbers illustrated by : (2/9 + 4/9) = (4/9 + 2/9)
A. Distributive property	B. Associative property	C. Commutative property	D. Closure property
Right Option : C
View Explanation

Question : 3

7a + 2 = a(7) + 2, is explained by which property?
A. Associative over addition	B. Associative over multiplication	C. Commutative over multiplication	D. Commutative over Addition
Right Option : C
View Explanation