Question

discuss the properties of rational numbers​

Answer 1

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The properties of rational numbers are:

• Closure Property.
• Commutative Property.
• Associative Property.
• Distributive Property.
• Identity Property.
• Inverse Property.

@MissValiant❤࿐

Answer 2

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$\huge \tt \red{QUESTION}$

Discuss the properties of rational numbers

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Closure Property :

Over Addition - Addition of two rational numbers is also a rational number.

$Example: \frac{7}{9} + \frac{( - 5)}{9} = \frac{2}{9}$

Over Subtraction - On subtracting two rational numbers, we get another rational number.

$Example : \frac{8}{10} - \frac{( - 7)}{10} = \frac{15}{10}$

Over multiplication - Multiplying two rational numbers, we get result as a rational number.

$Example : \frac{ - 3}{4} \times \frac{5}{7} = \frac{ - 3 \times 5}{4 \times 7} = \frac{ - 15}{28}$

Over division - When rational number (expect zero) divided by another rational number (expect zero) the quotient is always a rational number.

$Example : \frac{a}{b} \div \frac{c}{d} = \frac{ac}{bd}$

Commutative Property :

Over Addition - The sum of two rational numbers remains unchanged if they interchange their places.

$Example :\frac{1}{2} + \frac{1}{3} = \frac{1}{3} + \frac{1}{2}$

➜Addition of rational number is commutative.

Over Subtraction - The difference of two rational number does not remain unchanged if they interchange their places.

$Example : \frac{1}{2} - \frac{1}{3} ≠ \frac{1}{3} - \frac{1}{4}$

➜ Subtraction of rational number is not commutative.

Over multiplication - The product of two rational numbers remains unchanged if they interchange their places.

$Example: \frac{1}{3} \times \frac{1}{4} = \frac{1}{4} \times \frac{1}{3}$

➜ Multiplication of rational number is commutative.

Commutative property is not true for division.

$Example: \frac{4}{9} \div \frac{1}{2} ≠ \frac{1}{2} \div \frac{4}{9}$

➜Division of rational number is not commutative.

Associative Property :

Over Addition - For three or more rational numbers, it does not matter which two are added first and then their sum is added to the third rational number.

$Example: \frac{1}{3} + ( \frac{1}{4} + \frac{1}{5} ) = ( \frac{1}{3} + \frac{1}{4} ) + \frac{1}{5}$

➜ Addition of rational number is associative.

Over Subtraction - For any three or more rational numbers it matters which two are subtracted first and then third is subtracted from their difference.

$Example:( \frac{1}{2} - \frac{1}{3} ) - \frac{1}{4} ≠ \frac{1}{2} - ( \frac{1}{3} - \frac{1}{4} )$

➜ Subtraction of rational number is not associative.

Over multiplication - The product of any three or more rational numbers remains the same irrespective of the order in which the Multiplication is carried out.

$Example: \frac{1}{3} \times ( \frac{1}{4} \times \frac{1}{5} ) = ( \frac{1}{3} \times \frac{1}{4} ) \times \frac{1}{5}$

➜Multiplication of rational number is associative.

Division of rational numbers is not associative.

$Example: (\frac{6}{1} \div \frac{2}{1} ) \frac{3}{1} ≠ \frac{6}{1} \div ( \frac{2}{1} \div \frac{3}{1} )$

➜Division of rational number is not associative.

Identity Property :

If zero is added to any rational number, then the sum is equals to rational number itself.

$Example: \frac{7}{9} + 0 =\frac{7}{9}$

➜Additive Identity of rational number

The product of any rational number and 1 is always rational number itself.

Example : 7/9 x 1 = 7/9

➜Multiplicative Identity of rational number.

Inverse Property :

For every rational number, there exists an rational number such that their sum is zero. Each of such numbers is called additive inverse of the other.

Example : 4/1 + (-4)/1 = 0

➜Additive Inverse of rational number.

Hope It Helps You!!....

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