Understand Integers

Key Concepts

• Define integers and opposites.
• Compare and order integers.
• Use integers to represent quantities.

Introduction: 

Integers: 

Integers are whole numbers that consist of zero, positive and negative numbers. 

Application of integers in real life: 

• The sea level is always indicated by zero. 
• The above sea level is indicated with a positive integer. 
• The below sea level is indicated with a negative integer. 

2.1.1 Define integers and opposites 

Numbers greater than 0 are called positive numbers. Numbers less than 0 are called negative numbers. 

– 4 indicates “negative four.” 

4 and +4 both indicate “positive four.” 

The number 0 is neither positive nor negative. 

Some signed numbers are integers. Integers consist of the numbers labeled on the number line below. 

The integers are 

{…, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, …} 

Opposite numbers: 

Two numbers that are the same distance from 0 on the number line but are on the opposite sides of 0 are called opposites. 

Example 1: 

What is the opposite of -5? 

Solution: 

Step 1  

On a number line, opposite integers are the same distance from 0 but in opposite directions. Let’s look at a number line to see what’s on the other side of -5. 

Step 2  

It’s exactly 5 from 0. So, move 5 in the other direction to find its opposite. 

Step 3) The opposite of -5 is 5.  

2.1.2 Compare and order integers 

We compare integers just as we compare whole numbers.  For any two numbers graphed on a number line, the number to the right is the greater number and the number to the left is the smaller number. 

< 

means 

“is less than” 

> 

means 

“is greater than” 

Example 2: 

Let us compare -5 with -3. 

The graph of – 5 is to the left of – 3, so 

– 5 is less than – 3,  

written as  

5 < – 3. 

 We can also write  

– 3 > – 5.  

Since – 3 is to the right of – 5, 

– 3 is greater than – 5. 

Example3: 

The display at the right shows the daily low temperatures for several consecutive days in a New England city. Write the temperatures in order from least to greatest. On which day was it the coldest? Which was the warmest day? Write the temperatures from least to greatest. 

Solution: 

2.1.3 Use integers to represent quantities 

Example 4: 

Linda found the following facts interesting while surfing the internet. 

Which integer represents sea level? Explain. 

Use a negative integer to represent the depth to which a dolphin may swim.  

Which of these animals can travel at the greatest distance from sea level?  

Order the elevations of the animals as integers from least to greatest. 

Solution: 

Exercise:

1. Find the opposite of each number.
   a.5         b. −9             c. 2    
2. Find the opposite of each number.
   a. 7.3 b. -200        c. – 1/3                    
3. Graph the following integers on the number line: −6, 7, −3, and 1.

4. Which of the following are integers? Circle your answers.
6         – 4       – 2 ¾              – 3       0         – 9.5

5. What two numbers have an absolute value of 9?

6. Order the integers from least to greatest.
a.−4, 5, 0, 2               b.  −38, −26, −19, −55          c.  0, 13, −13, −7, 7

7. Name five integers between −6 and 3. Order them from least to greatest.

8. Graph the number 3 and its opposite.

9. Kyle kept track of the number of points he scored each time he played a video game. Sometimes the score is less than zero.
a. Order the negative plays from least to greatest.
b. Order the positive plays from greatest to least.

10. The table below shows a number of places from around the world. These places are listed in order from least elevation to greatest elevation. Use the elevations from the scattered boxes to complete the table.

Concept Map: 

What have we learned:

• Understand integers and their applications in real life.
• Understand opposites of integers.
• Compare and order integers on a number line.
• Use integers to represent quantities and analyze the situation.