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Properties of Rational Numbers

We will learn some useful properties of rational numbers.


Property 1:

If a/b is a rational number and m is a nonzero integer, then

ab = a×mb×m

In other words, a rational number remains unchanged, if we multiply its numerator and denominator by the same non-zero integer. 

For examples:

25 = (2)×25×2 = 410(2)×35×3 =  615(2)×45×4 = 820 and so on ……

Therefore, 25 = (2)×25×2 = (2)×35×3 = (2)×45×4 and so on ……

Property 2:

If ab is a rational number and m is a common divisor of a and b, then

ab = a÷ma÷m

In other words, if we divide the numerator and denominator of a rational number by a common divisor of both, the rational number remains unchanged.

For examples:

3240 = 32÷840÷8 = 45

 

Property 3:

Let ab and cd be two rational numbers.

Then ab = cda×db×c.

Properties of Rational Numbers





a × d = b × c

For examples:

If 23 and 46 are the two rational numbers then, 23 = 46 ⇔ (2 × 6) = (3 × 4).

Note:

Except zero every rational number is either positive or negative. 

Every pair of rational numbers can be compared.

 

Property 4:

For each rational number m, exactly one of the following is true:

(i) m > 0                (ii) m = 0               (iii) m < 0

For examples:

The rational number 23 is greater than 0.

The rational number 03 is equal to 0.

The rational number 23 is less than 0.

 

Property 5:

For any two rational numbers a and b, exactly one of the following is true:

(i) a > b                 (ii) a = b                                (iii) a < b

For examples:

If 13 and 15 are the two rational numbers then, 13 is greater than 15.

If 23 and 69 are the two rational numbers then, 23 is equal to 69.

If 27 and 38 are the two rational numbers then, 27 is less than 38.

 

Property 6:

If a, b and c be rational numbers such that a > b and b > c, then a > c.

For examples:

If 35, 1730 and 815 are the three rational numbers where 35 is greater than 1730 and 1730 is greater than 815, then 35 is also greater than 815.


So, the above explanations with examples help us to understand the useful properties of rational numbers.

Rational Numbers

Introduction of Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers






8th Grade Math Practice 

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Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Equivalent Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Adding Rational Numbers

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Worksheet on Properties of Multiplication of Rational Numbers

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Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers