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**

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

● **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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● **Rational Numbers - Worksheets**

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

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Subtracting Rational Numbers

Worksheet on Addition and
Subtraction of Rational Number

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Properties of Multiplication of Rational Numbers

Worksheet on Division of Rational Numbers

Worksheet on Properties of Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

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