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Integer Comparison on a Number Line

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Integer Comparison on a Number Line
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This number line shows the integers from -5 to 5.

Have you ever wondered how to compare negative numbers? This number line will be helpful in this Concept, but first look at the dilemma that Carmen is working on.

Carmen's Uncle lives in Bombay Beach California. When she did a little research, she discovered that Bombay Beach is below sea level. In fact, it is -226 feet below sea level.

Her Aunt lives in Salton Sea Beach California which is -220 feet below sea level.

Which place closest to sea level?

This Concept is all about comparing and ordering integers. By the end of the Concept you will know how to help Carmen answer this question.

Guidance

Now that you know about positive and negative integers, you can learn about comparing them. When we compare and order positive and negative integers, we use greater than, less than or equal to, or we write them in order from least to greatest or from greatest to least. Let’s start by learning about comparing integers.

How do we compare integers?

There are a couple of important things to consider when comparing integers.

1. A positive number is ALWAYS greater than a negative number.

The more positive a number, the greater it is.

-6 ____ 2

Negative six is below zero. Two is above zero. Two is greater than negative six.

-6 < 2

2. If two numbers are positive, the larger number is greater. 17____10

Seventeen is greater than 10.

17 > 10

3. If two numbers are negative, the number closer to zero is greater than the other.

For two negative numbers, you have to think backwards. The larger the number the greater the loss is. The greater the loss, the smaller the number. Think about the number and its relationship to zero. This will help you determine whether it is greater than or less than.

-25 ____ -36

Negative 25 is closer to zero than -36. It is the greater number.

-25 > -36

It does seem a bit backwards, but that is the way it is. You can think of it another way by looking at a number line.

-9 ____ -3

Let’s look at a number line to compare these values.

If you look at where negative nine is compared with negative three, you can see that negative three is closer to zero. Negative three is greater than negative nine.

-9 < -3

Use greater than, less than or equal to and compare each pair of values.

Example A

-6 ____ 8

Solution: <

Example B

-99 ____ -9

Solution: <

Example C

12 ____ 6

Solution: >

Now back to Carmen and her questions about sea level. Here is the original problem once again.

This number line shows the integers from -5 to 5.

Have you ever wondered how to compare negative numbers? This number line will be helpful in this Concept, but first look at the dilemma that Carmen is working on.

Carmen's Uncle lives in Bombay Beach California. When she did a little research, she discovered that Bombay Beach is below sea level. In fact, it is -226 feet below sea level.

Her Aunt lives in Salton Sea Beach California which is -220 feet below sea level.

Which place closest to sea level?

This can be a tricky question. Sea level would be considered 0 in this situation. Salton Sea Beach California is closest to 0.

Therefore, it is also closest to sea level.

Bombay Beach is -226 feet below sea level. It has the lowest sea level so it is the farthest away from zero.

Vocabulary

Here are the vocabulary words in this Concept.

Integers
the set of whole numbers and their opposites
Negative Numbers
numbers that are less than zero
Positive Numbers
numbers that are greater than zero
Zero
is a part of the set of integers, but is neither positive or negative

Guided Practice

Here is one for you to try on your own.

Jessie has a loss of fifteen dollars. Carmen has a loss of twenty - five dollars. Write integers and compare each loss is greater?

Answer

Written this way, you can figure out that a loss of twenty - five is a greater loss than a loss of fifteen. However, this is a trick question because you are going to write integers and compare them.

Let's see how this works.

First, write two integers to represent the situation.

-15 and -25

Now a negative fifteen is greater than a negative twenty - five because it is closer to zero.

Do you see how this is a tricky question?

Here is the answer.

-15 > -25

This is the answer.

Video Review

Here are videos for review.

Khan Academy, Locate Integers on a Number Line

James Sousa, Introduction to Integers

James Sousa, Example of Ordering Integers from Least to Greatest

James Sousa, Integer Application: Feet Below Sea Level

Practice

Directions: Compare each pair of integers using the symbols for greater than and less than.

1. 18 ____ 22

2. -12 ____ 12

3. -14 ____ -16

4. -20 ____ -33

5. 19 ____ -1

6. 0 ____ -3

7. -27 ____ -28

8. -233 ____ -300

9. -765 ____ -745

10. -234 _____ -300

Directions : Write integers and then use inequality symbols to compare each pair of values.

11. A loss of 16 and a loss of 29

12. A loss of 18 and a gain of 28

13. A loss of 27 and a loss of 10

14. A loss of 16 and a gain of 12

15. A loss of 90 and a loss of 99

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