Subtraction of Rational Number with Different Denominator

We will learn the subtraction of rational number with different denominator. To find the difference of two rational numbers which do not have the same denominator, we follow the following steps:

Step I: Let us obtain the rational numbers and see whether their denominators are positive or not. If the denominator of one (or both) of the numerators is negative, re-arrange it so that the denominators become positive.

Step II: Obtain the denominators of the rational numbers in step I.

Step III: Find the lowest common multiple of the denominators of the two given rational numbers.

Step IV: Express both the rational numbers in step I so that the lowest common multiple of the denominators becomes their common denominator.

Step V: Write a rational number whose numerator is equal to the difference of the numerators of rational numbers obtained in step IV and denominators is the lowest common multiple obtained in step III.

Step VI: The rational number obtained in step V is the required difference (simplify if required).

Following examples will illustrate the above procedure.

1. Subtract 9 from 4/5

Solution:

We have, 9 = 9/1

Clearly, denominators of the two rational numbers are positive. We now re-write them so that they have a common denominator equal to the LCM of the denominators.

In this case the denominators are 1 and 5.

The LCM of 1 and 5 is 5.

We have, 9 = 9/1 = 9 × 5/1 × 5 = 45/5

Therefore, 4/5 - 9

            = 4/5 - 9/1

            = 4/5 - 45/5

            = (4 - 45)/5

            = -41/5

Therefore, 4/5 - 9 = -41/5


2. Find the difference of: -3/4 - 5/6

Solution:

The denominators of the given rational numbers are 4 and 6 respectively.

LCM of 4 and 6 = (2 × 2 × 3) = 12.

Now, -3/4 = (-3) × 3/4 × 3 = -9/12

and 5/6 = 5 × 2/6 × 2 = 10/12

Therefore, -3/4 - 5/6

          = -9/12 - 10/12

            = (-9 - 10)/12

            = -19/12

Therefore, -3/4 - 5/6 = -19/12

 

3. Simplify: 3/-15 - 7/-12

Solution:

First we write each of the given numbers with positive denominator.

3/-15 = 3 × (-1)/(-15) × (-1) = -3/15, [Multiplying the numerator and denominator by -1]

⇒ 3/-15 = -3/15

7/-12 = 7 × (-1)/(-12) ×  (-1) = -7/12, [Multiplying the numerator and denominator by -1]

⇒ 7/-12 = -7/12

Therefore, 3/-15 - 7/-12 = -3/15 - (-7)/12

Now, we find the LCM of 15 and 12.

The LCM of 15 and 12 = 60

Rewriting -3/15 in the form in which it has denominator 60, we get

-3/15 = -3 × 4/15 × 4 = -12/60

Rewriting -7/12 in the form in which it has denominator 60, we get

-7/12 = -7 × 5/12 × 5 = -35/60

Therefore, 3/-15 - 7/-12

            = -3/15 - (-7)/12

            = -12/60 - (-35)/60

            = (-12) - (-35)/60

            = -12 + 35/60

            = 23/60

Thus, 3/-15 - 7/-12 = 23/60.


4. Simplify: 11/-18 - 5/12

Solution:

First we write each one of the given rational numbers with positive denominator.

Clearly, denominator of 5/12 is positive.

The denominator of 11/-18 is negative.

The rational number 11/-18 with positive denominator is -11/18.

Therefore, 11/-18 - 5/12 = -11/18 - 5/12

The LCM of 18 and 12 is 36.

Rewriting -11/18 in forms having the same denominator 36, we get

-11/18 = (-11) × 2/18 × 2, [Multiplying the numerator and denominator by 2]

⇒ -11/18 = -22/36

Rewriting 5/12 in forms having the same denominator 66, we get

5/12 = 5 × 3/12 × 3, [Multiplying the numerator and denominator by 3]

⇒ 5/12 = 15/36

Therefore, 11/-18 - 5/12

           = -11/18 - 5/12

           = -22/36 - 15/36

           = -22 - 15/36

           = -37/36

Therefore, 11/-18 - 5/12 = -37/36


If a/b and c/d are two rational numbers such that b and d do not have a common factor other than 1, i.e., HCF of b and d is 1, then

a/b - c/d = a × d - c × b/b × d

For example, 5/18 - 3/13 = 5 × 13 - 3 × 18/18 × 13 = 65 - 54/234 = 11/234

and -2/11 - 3/14 = (-2) × 14 - (3 × 11)/11 × 14 = -28 - 33/154 = -61/154

Rational Numbers

Introduction of 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

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

Addition of Rational Numbers

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

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers





8th Grade Math Practice

From Subtraction of Rational Number with Different Denominator to HOME PAGE




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.



Share this page: What’s this?

Recent Articles

  1. Relation between Diameter Radius and Circumference |Problems |Examples

    Apr 22, 24 05:19 PM

    Relation between Radius and Diameter of a Circle
    Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

    Read More

  2. Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

    Apr 22, 24 01:35 PM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  3. Preschool Math Activities | Colorful Preschool Worksheets | Lesson

    Apr 21, 24 10:57 AM

    Preschool Math Activities
    Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

    Read More

  4. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Apr 20, 24 05:39 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  5. What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

    Apr 20, 24 05:29 PM

    Examples of Parallel Lines
    In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

    Read More

Rational Numbers - Worksheets

Worksheet on Rational Numbers

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

Worksheet on Operations on Rational Expressions

Objective Questions on Rational Numbers