Division of Rational Numbers



In division of rational numbers, if a/b and c/d are two rational numbers such that c/d ≠ 0. We define, { a/b ÷ c/d} = {a/b × d/c}

When a/b is divided by c/d , then a/b is called the dividend; c/d is called the divisor and the result is known as quotient.



Examples on division of rational numbers;

1. Divide:

(i) 9/16 by 5/8

(ii) -6/25 by 3/5

(iii) 11/24 by -5/8

(iv) -9/40 by -3/8


Solution:

(i) 9/16 ÷ 5/8

= 9/16 × 8/5

= (9 × 8)/(16 × 5)

= 72/80

= 9/10


(ii) -6/25 ÷ 3/5

= -6/25 × 5/3

= {(-6) × 5}/(25 × 3)

= -30/75

= -2/5


(iii) 11/24 ÷ (-5)/8

= 11/24 × 8/(-5)

= (11 × 8)/{24 × (-5)}

= 88/-120

= -11/15


(iv) -9/40 ÷ (-3)/8

= (-9)/40 × 8/(-3)

= {(-9) × 8}/(40 × (-3))

= -72/-120

= 3/5



2. The product of two numbers is -28/27. If one of the numbers is -4/9, find the other.

Solution:

Let the other number be x.

x × (-4)/9 = -28/27

⇒ x = (-28)/27 ÷ (-4)/9

⇒ x = (-28)/27 × 9/-4

⇒ x = {(-28) × 9}/{27 × (-4)}

⇒ x = -(28 × 9)/-(27 × 4)

⇒ x = (287 × 91 )/(273 × 41 )

⇒ x = 7/3

Hence, the other number is 7/3.



3. Fill in the blanks: 27/16 ÷ (_____) = -15/8

Solution:

Let 27/16 ÷ (a/b) = -15/8.

27/16 × b/a = -15/8

⇒ b/a = -15/8 × 16/27 = -10/9

⇒ a/b = 9/-10 = -9/10

Hence, the missing number is -9/10.

Properties of division of rational numbers;

 Property 1 (Closure Property):

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.


Property 2 (Property of 1):

For every rational number a/b we have:

(a/b ÷ 1) = a/b


Property 3:

For every nonzero rational number a/b, we have:

{a/b ÷ a/b} = 1



Rational Numbers
  • What is Rational Numbers?
  • Representation of Rational Numbers on the Number Line
  • Addition of Rational Numbers
  • Subtraction of Rational Numbers
  • Multiplication of Rational Numbers
  • Division of Rational Numbers
  • To Find Rational Numbers

    • Rational Numbers - Worksheets
  • Worksheet on Rational Numbers
  • Worksheet on Representation of Rational Number on a
       Number Line
  • Worksheet on Addition and Subtraction of Rational
       Number
  • Worksheet on Multiplication of Rational Number
  • Worksheet on Division of Rational Numbers
  • Worksheet on Word Problems on Rational Numbers
  • Objective Questions on Rational Numbers




    • 8th Grade Math Practice

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