Properties of Subtraction of Rational Numbers

We will learn how to use the properties of subtraction of rational numbers to find the difference of two rational numbers.

In subtraction of rational numbers a/b and c/d, we define:

(a/b - c/d) = a/b + (-c/d) = a/b + (additive inverse of c/d)


How to use the properties to solve the subtraction of two rational numbers?

Solved examples using the properties of subtraction of rational numbers:

1. Find the additive inverse of:

(i) 2/3

(ii) -17/9

(iii) 6/-19

(iv) -5/-13

Solution:

(i) Additive inverse of 2/3 is -2/3

(ii) Additive inverse of -17/9 is 17/9.

(iii) In standard form, we write 6/-19 as 6/19.

Hence, its additive inverse is 6/19.

(iv) We may write, -5/-13 = (-5) × (-1)/(-13) × (-1) = 5/13

Hence, its additive inverse is -5/13


2. Subtract 5/7 from 4/5

Solution:

Subtract 5/7 from 4/5

= (4/5 – 5/7)

= 4/5 + (additive inverse of 5/7)

= (4/5 + -5/7)

= {28 + (-25)}/35

= 3/35


3. Subtract -3/5 from -3/4

Solution:

Subtract -3/5 from -3/4

= {-3/4 - (-3/5)}

= -3/4 + (additive inverse of -3/5)

= {-3/4 + 3/5)}, [since, additive inverse of -3/5 is 3/5]

= (-15 + 12)/20

= -3/20


4. The sum of two rational numbers is -7. If one of them is -11/3, find the other.

Solution:

Let the other number be x. Then,

x + -11/3 = -7

⇒ x = -7 + (additive inverse of -11/3)

⇒ x = (-7 + 11/3), [since, additive inverse of -11/3 is 11/3]

⇒ x = (-7/1 + 11/3)

⇒ x = (-21 + 11)/3

⇒ x = -10/3

Hence, the required number is -10/3.


5. What number should be added to -5/6 to get 13/15?

Solution:

Let the required number to be added be x. Then,

-5/6 + x = 13/15

⇒ x = 13/15 + (additive inverse of -5/6)

⇒ x = (13/15 + 5/6), [since, additive inverse of -5/6 is 5/6]

⇒ x = (26 + 25)/30

⇒ x = 51/30

⇒ x = 17/10

Hence, the required number is 17/10.

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 Properties of Subtraction of Rational Numbers to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



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. Fraction as a Part of Collection | Pictures of Fraction | Fractional

    Feb 24, 24 04:33 PM

    Pictures of Fraction
    How to find fraction as a part of collection? Let there be 14 rectangles forming a box or rectangle. Thus, it can be said that there is a collection of 14 rectangles, 2 rectangles in each row. If it i…

    Read More

  2. Fraction of a Whole Numbers | Fractional Number |Examples with Picture

    Feb 24, 24 04:11 PM

    A Collection of Apples
    Fraction of a whole numbers are explained here with 4 following examples. There are three shapes: (a) circle-shape (b) rectangle-shape and (c) square-shape. Each one is divided into 4 equal parts. One…

    Read More

  3. Identification of the Parts of a Fraction | Fractional Numbers | Parts

    Feb 24, 24 04:10 PM

    Fractional Parts
    We will discuss here about the identification of the parts of a fraction. We know fraction means part of something. Fraction tells us, into how many parts a whole has been

    Read More

  4. Numerator and Denominator of a Fraction | Numerator of the Fraction

    Feb 24, 24 04:09 PM

    What are the numerator and denominator of a fraction? We have already learnt that a fraction is written with two numbers arranged one over the other and separated by a line.

    Read More

  5. Roman Numerals | System of Numbers | Symbol of Roman Numerals |Numbers

    Feb 24, 24 10:59 AM

    List of Roman Numerals Chart
    How to read and write roman numerals? Hundreds of year ago, the Romans had a system of numbers which had only seven symbols. Each symbol had a different value and there was no symbol for 0. The symbol…

    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