Division of Rational Numbers
To learn division of rational numbers let us recall how to divide a fraction by another fraction. We know division of fractions is the inverse of multiplication.
Similarly, in case of rational number also, division is the inverse of multiplication as defined below:
Division: If m and n two rational numbers such that n ≠ 0, then the result of dividing m by n is the rational number obtained on multiplying m by the reciprocal of n.
When x is divided by y, we write m ÷ n. Thus m ÷ n = m × 1/n.
If w/x and y/z are two rational numbers such that y/z ≠ 0, then
w/x ÷ y/z = w/x × (y/z)^-1 = w/x × z/y
Dividend: The number to be divided is called the dividend.
Divisor: The number which divides the dividend is called the divisor.
Quotient: When dividend is divided by the divisor, the result of the division is called the quotient.
If w/x is divided by y/z, then w/x is the dividend, y/z is the divisor and w/x ÷ y/z = w/x × z/y is the quotient.
Note: It should be noted that division by 0 is not defined.
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.
● 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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