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. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More