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# Properties of Rational Numbers - Commutativity

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#### notes

1) Whole numbers -

 Operation Numbers Remarks Addition 0 + 7 = 7 + 0 = 7 ,2 + 3 = 3 + 2 = 5For any two whole numbers a and b, a + b = b + a Addition is commutative . Subtraction 3 - 2 = 1  but 2 - 3 = -1 For any teo whole numbers a and b , a-b ≠ b - a Subtraction is not commutative. Multiplication 2 × 3 = 6 and 3 × 2 = 6For any two whole numbers a and b, a × b = b × a Multiplication is commutative . Division 4 ÷ 2 = 2 but 2 ÷ 4 = 0.5For any two whole numbers a and b, a ÷ b ≠ b ÷ a Division is not commutative .

2 ) Integers :

 Operation Numbers Remarks Addition -2 + 3 = 1 and3 + (-2) = 1 Addiion is commutative. Subtraction (-2)-(1) = -3  but  (1) - (-2) = 3 Subtraction is not commutative. Multiplication -2 * (-7) = 14 and (-7) * (-2) = 14 Multiplication is commutative. Division -2 ÷ 3 = - 1.666... but 3 ÷ -2 = -1.5 Division  is not commutative .

3) Rational numbers :
example- -2/3 + 5/7 = 1/21 and 5/7+(-2/3)=1/21
We say that two rational numbers can be added in any order. We say that addition is commutative for rational numbers. That is, for any two rational numbers a and b,
a + b = b + a.

b. Subtraction :
Example - 2/3 - 5/4 =-7/12 and 5/4 - 2/3 = 7/12
Note  that subtraction is not commutative for integers and integers are also rational numbers. So, subtraction will not be commutative for rational numbers too.

c. Multiplication :
Example - -7/3 xx 6/5 = -42/15 = 6/5 xx -7/3
We say that  multiplication is commutative for rational numbers. In general, a × b = b × a for any two rational numbers a and b.

d. Division :
Example - -5/4 ÷3/7 = -35/12, 3/7 ÷ (-5/4) = (12/-35)
The expressions on both sides are not equal. So division is not commutative for rational numbers.

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Commutative Property of Rational Number [00:05:58]
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