Compare and order integers

key notes :

Understanding Integers

Integers are whole numbers (not fractions or decimals) that can be positive, negative, or zero. The further a number is to the right on the number line, the greater its value. The further a number is to the left on the number line, the smaller its value.

Key points:

• Positive integers are greater than zero.
• Negative integers are less than zero.
• Zero is neither positive nor negative.
• Positive integers are greater than negative integers.

=	When two values are equal, we use the “equals” sign	example: 2+2 = 4
<	When one value is smaller than another, we can use a “less than” sign.	example: 3 < 5
>	When one value is bigger than another, we can use a “greater than” sign	example: 9 > 6

Comparing Integers

Example 1: Comparing Positive Integers Compare 5 and 2. 5 is greater than 2, so we write: 5 > 2	Example 2: Comparing Negative Integers Compare -3 and -7. -3 is to the right of -7 on the number line. So, -3 is greater than -7, and we write: -3 > -7
Example 3: Comparing Positive and Negative Integers Compare 4 and -1. 4 is positive, and -1 is negative. Positive integers are always greater than negative integers. So, 4 > -1	Example 4: Comparing with Zero Compare -2 and 0. -2 is negative, and negative integers are always less than zero. So, -2 < 0

How to compare and order integers?

Integers on the left side of 0 on the number line get smaller as we move from right to left, whereas integers on the right side of 0 get greater as we move from left to right. Therefore, to compare two integers, we can use greater than (>) or less than (<) symbols.

How to order the integers from lowest to highest? Give an example.

The ordering of integers can be done from lowest to highest in ascending order. For example, if we integers such as, 5, -1, 0, 3, -4, -6, 1, 2, then the order of the given integers from lowest to highest will be:
-6 < -4 < -1 < 0 < 1 < 2 < 3< 5

Which is the smallest and largest integers among the ordered integers of -5 to 5?

If the integers are ordered from -5 to 5, then;
-5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5
Thus, from the above arrangement, we can say the smallest integer is -5, and the greatest integer is 5

Tips and Tricks

• Number Line Visualization: Always visualize the number line. This helps in understanding the relative positions of integers.
• Negative Integers: Remember that with negative integers, the larger the number, the smaller its value (e.g., -10 is smaller than -1).
• Zero as a Reference: Use zero as a reference point. Positive numbers are always greater than zero, and negative numbers are always less than zero.

Practice Problems

Compare the following integers using >, <, or =:

• a) -8 and 3
• b) 5 and -5
• c) -2 and -4

Order the following integers from least to greatest:

• a) -7, 2, -1, 5, -3

Order the following integers from greatest to least:

• a) 6, -4, 0, -2, 3

Summary

In this lesson, we learned how to compare and order integers. Understanding the number line and the relative positions of positive, negative, and zero is crucial for mastering integer operations. Remember to use the symbols >, <, and = correctly and to visualize the number line when ordering integers.

Learn with an example

let’s practice!