# 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

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

Representation of 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 Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

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

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as:

2. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 13, 24 02:23 AM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

3. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 13, 24 01:20 AM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

4. ### Comparison of Two-digit Numbers | Arrange 2-digit Numbers | Examples

Sep 12, 24 03:07 PM

What are the rules for the comparison of two-digit numbers? We know that a two-digit number is always greater than a single digit number. But, when both the numbers are two-digit numbers

5. ### Worksheet on Two Digit Numbers | Numbers in Words | Two-Digit Numbers

Sep 12, 24 02:09 AM

In worksheet on 2-digit numbers we will write the number which come before, after and in between, write the numerals, write the number names, place value and face value of 2-digit numbers, numbers in…

Rational Numbers - Worksheets

Worksheet on 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 Properties of Addition of Rational Numbers

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers