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Properties of Rational Numbers - Commutative Property of Rational Numbers

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Commutative Property of Rational Numbers:

1. Commutativity of Addition of Rational Numbers:

`(-2)/3 + 5/7 = 1/21 and 5/7 + ((-2)/3) = 1/21`.

`(-2)/3 + 5/7 = 5/7 + (-2/3)`

`-6/5 + (-8/3) = -58/15 and (-8)/3 + (-6/5) = -58/15`

`(-6)/5 + ((-8)/3) = (-8)/3 + ((-6)/5)`

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.

2. Commutativity of Subtraction of Rational Numbers:

`2/3 – 5/4 = (-7)/12 and 5/4 – 2/3 = 7/12`

`1/2 - 3/5 = -1/10 and 3/5 - 1/2 = 1/10`

Subtraction is not commutative for integers and integers are also rational numbers. So, Subtraction will not be commutative for rational numbers too.

3. Commutativity of Multiplication of Rational Numbers:

`(-7)/3 xx 6/5 = (-42)/15 = 6/5 xx (-7)/3`

`- 8/9 xx (-4/7) = - 32/63 = (- 4)/7 xx (- 8/9)`

Multiplication is commutative for rational numbers.

In general, a × b = b × a for any two rational numbers a, and b.

4. Commutativity of Division of Rational Numbers:

`-5/4 ÷ 3/7 = - 35/12`

`3/7 ÷ (-5/4) = 12/-35`

`-5/4 ÷ 3/7 ≠ 3/7 ÷ (-5/4)`

You will find that expressions on both sides are not equal.

So division is not commutative for rational numbers.

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