Ordering Integers

In ordering integers we will learn how to order the integers on a number line.

All integers can be represented on a number line. The convention followed to compare two integers represented on the number line is similar to that followed for the whole numbers marked on the number line. So the integer occurring on the right is greater than that on the left and the integer on the left is smaller than that on its right.

Ordering Integers

An integer on a number line is always greater than every integer on its left. Thus, 3 is greater than 2, 2 > 1, 1 > 0, 0 > -1, -1 > -2 and so on.

Similarly, an integer on a number line is always lesser than every integer on its right. Thus, -3 is less than -2, -2 < -1, -1 < 0, 0 < 1, 1 < 2 and so on.

Thus, we have the following examples:

(i) 3 > 2, since 3 is to the right of 2

(ii) 2 > 0, since 2 is to the right of 0

(iii) 0 > -2, since 0 is to the right of -2

(iv) -1 > -2, since -1 is to the right of -2


Integers obey the same Rule of Whole Numbers in their Ordering:

Rule I: Every positive integer is greater than every negative integer.

i.e., Since every positive integer is to the right of every negative integer, therefore, every positive integer is greater than every negative integer.


Rule II: Zero is less than every positive integer and is greater than every negative integer.

i.e., Since zero is to the left of every positive integer, therefore, zero is smaller than every positive integer.

Again, since zero is to the right of every negative integer, therefore, zero is greater than every negative integer.


Rule III: The greater the number, the lesser is its opposite.

i.e., The farther a number is from zero on its right, the larger is its value

For Example:

8 is greater than 5, but -8 is less than -5; similarly, -9 > -15 or, 9 < 15 and so on


Rule IV: The lesser the number, the greater is its opposite.

i.e., The farther a number is from zero on its left, the smaller is its value.

For Example:

6 is less than 7, but -6 is greater than -7; similarly, -8 < -5 or 8 > 5 and so on.


Rule V: The greater a number is the smaller is its opposite.

In general, if x and y are two integers such that

x > y, then -x < - y , and if x < y, then -x > - y

For Example:

(i) 6 > 4 and -6 < -4

(ii) 18 > 13 and -18 < -13.


Note: The symbol (-) is used to denote a negative integer as well as for subtraction.

(i) The temperature at an Everest is -10°C. Here the symbol (-) indicates the negative integer (-10) and no subtraction is involved.

(ii) On the other hand, 23 - 7 indicates the subtraction of 7 from 23.


Solved examples on ordering integers:

1. Arrange the integers from greater to lesser:

(i) 9, -2, 3, 0, -5, -7, 7, -1

(ii) -11, 17, -2, 2, -6, -15, 0, 1

(iii) 12, -21, -18, 14, -5, -1, 1, 10


Solution:

1. (i) 9, 7, 3, 0, -1, -2, -5, -7

(ii) 17, 2, 1, 0, -2, -6, -11, -15

(iii) 14, 12, 10, 1, -1, -5, -18, -21


2. Arrange the following integers in decreasing order.

(i) -3, 12, 7, 0, -8, 6

(ii) 0, -9, -15, 15, 9, -6, - 18, 29

(iii) -25, 0, -1, 8, - 6, - 13, 24, 6

(iv) -706, 409, 170, 109, -75, -555


Solution:

2. (i) 12, 7, 6, 0, -3, -8

(ii) 29, 15, 9, 0, -6, -9, -15, -18

(iii) 24, 8, 6, 0, -1, -6, -13, -25

(iv) 409, 170, 109, -75, -555, -706


3. Arrange the integers from lesser to greater:

(i) 0, 4, -4, 9, -10, -7, 12, -13

(ii) -14, 7, -25, -17, 20, 5, -9, -3

(iii) -6, 4, -18, 21, 29, -8, -16, 19


Solution:

3. (i) -13, -10, -7, -4, 0, 4, 9, 12

(ii) -25, -17, -14, -9, -3, 5, 7, 20

(iii) -18, -16, -8, -6, 4, 19, 21, 29


4. Arrange the following integers in increasing order.

(i) -3, 8, 6, 0, -7, 10

(ii) -17, 0, 9, 6, 10, -5, 8, -7

(iii) 0, -8, 6, -19, 65, -3, 38

(iv) -805, 508, -170, 108, 170, -85, -515


Solution:

4. (i) -7, -3, 0, 6, 8, 10

(ii) -17, -7, -5, 0, 6, 8, 9, 10

(iii) -19, -8, -3, 0, 6, 38, 65

(iv) -805, -515, -170, -85, 108, 170, 508

You might like these




Numbers Page

6th Grade Page

From Ordering Integers 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.



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.




Share this page: What’s this?

Recent Articles

  1. Writing Money in Words and Figure | Rules for Writing Money in Words

    Feb 11, 25 12:36 PM

    Rules for writing money in words and figure: 1. Abbreviation used for a rupee is Re. and for 1-rupee it is Re. 1 2. Rupees is written in short, as Rs., as 5-rupees is written as Rs. 5

    Read More

  2. Worksheet on Money | Conversion of Money from Rupees to Paisa

    Feb 11, 25 09:39 AM

    Amounts in Figures
    Practice the questions given in the worksheet on money. This sheet provides different types of questions where students need to express the amount of money in short form and long form

    Read More

  3. Worksheet on Measurement | Problems on Measurement | Homework |Answers

    Feb 10, 25 11:56 PM

    Measurement Worksheet
    In worksheet on measurement we will solve different types of questions on measurement of length, conversion of length, addition and subtraction of length, word problems on addition of length, word pro…

    Read More

  4. Worksheet on Subtraction of Capacity | Word Problems on Capacity | Ans

    Feb 10, 25 09:36 AM

    Subtraction of Volume Worksheet
    Practice the third grade math worksheet on subtraction of capacity. This sheet provides different types of questions where you need to arrange the values of capacity under

    Read More

  5. Practice Test on Circle | Quiz on Circle | Question and Test on Circle

    Feb 10, 25 09:08 AM

    Geometry practice test on circle, the questions we practiced and discussed under worksheets on circle are given here in geometry practice test.

    Read More