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Properties of Rational Numbers - Closure Property of Rational Numbers

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Closure Property of Rational Number:

1. Closure Property of Addition of Rational Numbers:

`3/8 + (-5)/7 = (21 + (-40))/56 = -19/56`.

`(-3)/8 + (-4)/5 = (-15 + (-32))/40 = -47/40`

`4/7 + 6/11 = (44 + 42)/77 = 86/77`

We find that sum of two rational numbers is again a rational number.

We say that rational numbers are closed under addition. That is, for any two rational numbers a, and b, a + b is also a rational number.

2. Closure Property of Subtraction of Rational Numbers:

`(-5)/7 – 2/3 = (-5 xx 3 – 2 xx 7)/21 = (-29)/21`.

`5/8 – 4/5 = (25 – 32)/40 = -7/40`.

The difference of the two rational numbers be again a rational number.

We find that rational numbers are closed under subtraction. That is, for any two rational numbers a, and b, a – b is also a rational number.

3. Closure Property of Multiplication of Rational Numbers:

`-2/3 xx 4/5 = - 8/15`

`3/7 xx 2/5 = 6/35`.

`-4/5 xx -6/11 = 24/55`.

Both the products are rational numbers.

We say that rational numbers are closed under multiplication. That is, for any two rational numbers a, and b, a × b is also a rational number.

4. Closure Property of Division of Rational Numbers:

`-5/3 ÷ 2/5 = -25/6`

`-3/8 ÷ 2/9 = -27/16`

Any rational number a, a ÷ 0 is not defined.
So rational numbers are not closed under division.

However, if we exclude zero then the collection of, all other rational numbers is closed under division.

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