Lesson Objectives

- Learn how to create a number line for the whole numbers
- Learn how to write an inequality relationship with the "<" less than symbol
- Learn how to write an inequality relationship with the ">" greater than symbol

## How to Write Inequalities with Whole Numbers

In the place value lesson, we learned about a group of numbers known as the whole numbers. The whole numbers begin with a 0 and increase in increments of 1 indefinitely.

Whole Numbers: {0,1,2,3,4,5,…}

The three dots, known as an ellipsis, indicate our pattern continues forever, after 5 would come 6, then 7, so on and so forth. We can visually show the whole numbers using a number line. Our number line begins with a 0 in the leftmost position. Each additional notch moving right indicates an increase by 1 or the next whole number. No matter how big our number line, we can never show all of the whole numbers. For this reason, we place an arrow at the right end; it indicates that the whole numbers continue forever. There are numbers to the left of 0 and between each whole number. We will talk about those groups of numbers as we get further along. For now, we will focus on only the whole numbers, and keep things very simple.

The number line allows us to visually display two key properties:

Example 1: Replace the ? with "<" or ">".

12 ? 18 12 < 18

12 is to the left of 18 on the number line and represents a smaller number. Since 12 is on the left, we use the less than "<" symbol. Remember to always use the inequality symbol that points to the smaller number. If the problem had been reversed as: 18 ? 12, we would have used a greater than ">" symbol. In that case, the larger number 18 is on the left side.

18 > 12

Example 2: Replace the ? with "<" or ">".

21 ? 15 21 > 15

21 is to the right of 15 on the number line and represents a larger number. Since 21 is on the left, we use the greater than ">" symbol. Remember to always use the inequality symbol that points to the smaller number.

Whole Numbers: {0,1,2,3,4,5,…}

The three dots, known as an ellipsis, indicate our pattern continues forever, after 5 would come 6, then 7, so on and so forth. We can visually show the whole numbers using a number line. Our number line begins with a 0 in the leftmost position. Each additional notch moving right indicates an increase by 1 or the next whole number. No matter how big our number line, we can never show all of the whole numbers. For this reason, we place an arrow at the right end; it indicates that the whole numbers continue forever. There are numbers to the left of 0 and between each whole number. We will talk about those groups of numbers as we get further along. For now, we will focus on only the whole numbers, and keep things very simple.

The number line allows us to visually display two key properties:

- Numbers increase from left to right: →
- Numbers decrease from right to left: ←

- "=" : Equals, the two quantities are equal
- "≠" : Not Equal, the two quantities are not equal
- "<" : Less Than, the left quantity is less than the right quantity
- ">" : Greater Than, the left quantity is greater than the right quantity

- 6 ≠ 3 : 6 is not equal to 3
- 6 > 3 : 6 is greater than 3
- 3 < 6 : 3 is less than 6

Example 1: Replace the ? with "<" or ">".

12 ? 18 12 < 18

12 is to the left of 18 on the number line and represents a smaller number. Since 12 is on the left, we use the less than "<" symbol. Remember to always use the inequality symbol that points to the smaller number. If the problem had been reversed as: 18 ? 12, we would have used a greater than ">" symbol. In that case, the larger number 18 is on the left side.

18 > 12

Example 2: Replace the ? with "<" or ">".

21 ? 15 21 > 15

21 is to the right of 15 on the number line and represents a larger number. Since 21 is on the left, we use the greater than ">" symbol. Remember to always use the inequality symbol that points to the smaller number.

#### Skills Check:

Example #1

Replace the ? with "<" or ">".

29 ? 31

Please choose the best answer.

A

29 > 31

B

29 < 31

Example #2

Replace the ? with "<" or ">".

19 ? 14

Please choose the best answer.

A

19 > 14

B

19 < 14

Example #3

Replace the ? with "<" or ">".

55 < 51

Please choose the best answer.

A

true

B

false

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