Properties of Division of Rational Numbers
We will learn the three properties of division of rational numbers.
Property 1 (Closure Property of division of rational numbers):
If a/b and c/d are any two rational numbers such that c/d ≠ 0 then
(a/b ÷ c/d) is also a rational number.
For example:
(i) 2/3 and 4/9 are any two rational numbers and clearly 4/9 ≠ 0 then
(2/3 ÷ 4/9) = (2/3 × 9/4) = (2 × 9)/(3 × 4) = 18/12 = 3/2 is also a rational number.
(ii) 6/7 and -5/7 are any two rational numbers and clearly -5/7 ≠ 0 then
(6/7 ÷ -5/7) = (6/7 × 7/-6) = (6 × 7)/(7 × -6) = 42/-42 = 1/-1 is also a rational number.
Property 2 (Property of 1 of division of rational numbers):
For every rational number a/b we have:
(a/b ÷ 1) = a/b
For example:
(i) 5/8 ÷ 1 = 5/8
(ii) -4/9 ÷ 1 = -4/9
(iii) 5/-2 ÷ 1 = 5/-2
Property 3:
For every nonzero rational number a/b, we have:
{a/b ÷ a/b} = 1
For example:
(i) 4/7 ÷ 4/7 = 4/7 × 7/4 = (4 × 7)/(7 × 4) = 28/28 = 1
(ii) -3/11 ÷ -3/11 = -3/11 × 11/-3 = (-3 × 11)/(11 × -3) = -33/-33 = 1
(iii) 3/-2 ÷ 3/-2 = 3/-2 × -2/3 = (3 × -2)/(-2 × 3) = -6/-6 = 1
● Rational Numbers
Introduction of Rational Numbers
Is Every Rational Number a Natural Number?
Is Every Rational Number an Integer?
Is Every Rational Number a Fraction?
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
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
Properties of Multiplication of Rational Numbers
Rational Expressions Involving Addition, Subtraction and Multiplication
Reciprocal of a Rational Number
Rational Expressions Involving Division
Properties of Division of Rational Numbers
Rational Numbers between Two Rational Numbers
8th Grade Math Practice
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