How to Order Integers and Numbers

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The term integers represent the meaning “intact” or “whole”. So, you can generally refer an integer as a whole number, except integers can be negative also!

What is an Integer?

An integer is a whole number (not any decimal or fraction numbers) which can be zero, positive or negative numbers. Some examples of integers can be \(6 \ , \ 2 \ , \ 0 \ , \ -7 \ , \ -19,\) etc. Moreover, we can represent integers by the denotation \(Z\) which comprises of:
Positive Integers: As the name suggests, any integer that is greater than zero is termed as a positive integer.
Negative Integer: As from the name, any integer that is less than zero is termed as a negative integer.
Zero: Zero is neither a positive integer or a negative integer. It is just a whole number.
So, we can write \(Z = \{…… \ ,-3 \ , \ -2 \ , \ -1 \ , \ 0 \ , \ 1 \ , \ 2 \ , \ 3 \ , \ ……\}\)
Also, we can place all integers on a number line where the negative ones are placed on the left of \(“0”\) and the positive ones on the right. Moreover, we can perform the 4 basic mathematic properties with integers. They are:

Addition
Subtraction
Multiplication
Division

We often see that negative integers are always written as \(-7 \ , \ -19\), and so on. But it’s not generally considered necessary to write positive integers like \(+7 \ , \ +19\), and so on. So, when we write just \(7,\) we mean \(+7\).
Another thing to note is, that an absolute value of any integer is always positive. So, \(\lvert -3 \rvert=3\) and \(\lvert 3 \rvert\) is also \(3\).

How to Order Integers and Numbers

To order integers and numbers, follow these steps:

First, you should identify the negative numbers from the set. Remember, the farthest the negative number is from zero, the smaller it gets. In other words, the bigger the negative integer, the smaller it is.
If the set contains a zero, then it should be written and ranked above all negative numbers.
Finally, place the positive numbers higher than zero. A greater positive number always has a greater value.

Example: \(-15< -9< -7<0<2<5<7<19\) (This is an ascending order of all integers in the set).

Free printable Worksheets

Exercises for Ordering Integers and Numbers

1) \(-12, \ -7, \ 12, \ -9, \ -3, \ 4\) \( \Rightarrow \ \)

2) \(16, \ 27, \ 4, \ -12, \ -10, \ 2\) \( \Rightarrow \ \)

3) \(8, \ 34, \ -18, \ 32, \ 20, \ 6\) \( \Rightarrow \ \)

4) \(8, \ 10, \ -17, \ 20, \ 5, \ -10\) \( \Rightarrow \ \)

5) \(-6, \ -3, \ 24, \ 27, \ 19, \ -24\) \( \Rightarrow \ \)

6) \(1, \ -1, \ -3, \ 13, \ 10, \ -8\) \( \Rightarrow \ \)

7) \(12, \ -6, \ -14, \ 20, \ 13, \ -2\) \( \Rightarrow \ \)

8) \(-3, \ 27, \ 21, \ 17, \ -8, \ 24\) \( \Rightarrow \ \)

9) \(9, \ 13, \ 11, \ -11, \ -9, \ -5\) \( \Rightarrow \ \)

10) \(5, \ 1, \ -15, \ -18, \ 20, \ -6\) \( \Rightarrow \ \)

Answers

1) \(-12, \ -7, \ 12, \ -9, \ -3, \ 4\) \( \Rightarrow \ \color{red}{12, \ 4, \ -3, \ -7, \ -9, \ -12} \)

Solution:
Step 1: Find the smallest negative integer (farthest from zero): \(-12\)

- 32

and the largest positive integer: \(33\)

33

Step 2: Order the numbers from the lagest one to the smallest one: \(12, \ 4, \ -3, \ -7, \ -9, \ -12\)

2) \(16, \ 27, \ 4, \ -12, \ -10, \ 2\) \( \Rightarrow \ \color{red}{27, \ 16, \ 4, \ 2, \ -10, \ -12} \)

3) \(8, \ 34, \ -18, \ 32, \ 20, \ 6\) \( \Rightarrow \ \color{red}{34, \ 32, \ 20, \ 8, \ 6, \ -18} \)

4) \(8, \ 10, \ -17, \ 20, \ 5, \ -10\) \( \Rightarrow \ \color{red}{20, \ 10, \ 8, \ 5, \ -10, \ -17} \)

5) \(-6, \ -3, \ 24, \ 27, \ 19, \ -24\) \( \Rightarrow \ \color{red}{27, \ 24, \ 19, \ -3, \ -6, \ -24} \)

6) \(1, \ -1, \ -3, \ 13, \ 10, \ -8\) \( \Rightarrow \ \color{red}{13, \ 10, \ 1, \ -1, \ -3, \ -8} \)

7) \(12, \ -6, \ -14, \ 20, \ 13, \ -2\) \( \Rightarrow \ \color{red}{20, \ 13, \ 12, \ -2, \ -6, \ -14} \)

8) \(-3, \ 27, \ 21, \ 17, \ -8, \ 24\) \( \Rightarrow \ \color{red}{27, \ 24, \ 21, \ 17, \ -3, \ -8} \)

9) \(9, \ 13, \ 11, \ -11, \ -9, \ -5\) \( \Rightarrow \ \color{red}{13, \ 11, \ 9, \ -5, \ -9, \ -11} \)

10) \(5, \ 1, \ -15, \ -18, \ 20, \ -6\) \( \Rightarrow \ \color{red}{20, \ 5, \ 1, \ -6, \ -15, \ -18} \)

How to Order Integers and Numbers