• Identify integers
• Compare positive and negative integers using a number line
• Understand absolute value
• Add, subtract, multiply, and divide integers

Opposite and Integers

The video below shows more examples of how to find the opposite of an integer.

You can view the transcript for “Ex: Determine the Opposites of Integers” here (opens in new window).

Integers on a Number Line

In the video below we show more examples of how to plot integers on a number line.

You can view the transcript for “Plot Integers on the Number Line” here (opens in new window).

Order Positive and Negative Numbers

Order each of the following pairs of numbers using [latex]<[/latex] or [latex]\text{>}[/latex] .

1. [latex]14[/latex] and [latex]6[/latex]
2. [latex]-1[/latex] and [latex]9[/latex]
3. [latex]-1[/latex] and [latex]- 4[/latex]
4. [latex]2[/latex] and [latex]- 20[/latex]

Show Solution

Begin by plotting the numbers on a number line as shown in the number line below.

 

1. Compare [latex]14[/latex] and [latex]6[/latex].	[latex]14[/latex] and [latex]6[/latex]
[latex]14[/latex] is to the right of [latex]6[/latex] on the number line.	[latex]14>6[/latex]

2. Compare [latex]−1[/latex] and [latex]9[/latex].	[latex]-1[/latex] and [latex]9[/latex]
[latex]−1[/latex] is to the left of [latex]9[/latex] on the number line.	[latex]-1<9[/latex]

3. Compare [latex]−1[/latex] and [latex]−4[/latex].	[latex]-1[/latex] and [latex]- 4[/latex]
[latex]−1[/latex] is to the right of [latex]−4[/latex] on the number line.	[latex]-1>-4[/latex]

4. Compare [latex]2[/latex] and [latex]−20[/latex].	[latex]2[/latex] and [latex]- 20[/latex]
[latex]2[/latex] is to the right of [latex]−20[/latex] on the number line.	[latex]2>-20[/latex]

In the video below we show more examples of how to use inequality symbols to compare integers.

You can view the transcript for “Ex: Compare Integers Using An Inequality Symbol” here (opens in new window).

Absolute Value

Simplify:

1.  [latex]|3|[/latex]
2.  [latex]|-44|[/latex]
3.  [latex]|0|[/latex]

Show Solution

1.
	[latex]|3|[/latex]
[latex]3[/latex] is [latex]3[/latex] units from zero.	[latex]3[/latex]

2.
	[latex]|-44|[/latex]
[latex]−44[/latex] is [latex]44[/latex] units from zero.	[latex]44[/latex]

3.
	[latex]|0|[/latex]
[latex]0[/latex] is already at zero.	[latex]0[/latex]

In the video below we show another example of how to find the absolute value of an integer.

You can view the transcript for “Ex 1: Determine the Absolute Value of an Integer” here (opens in new window).

Simplify Absolute Values

Watch the following video to see more examples of how to simplify expressions that contain absolute value.

You can view the  transcript for “Simplify Absolute Value Expressions” here (opens in new window).

Adding Integers

In the following video we present more examples of using color counters to model addition of integers.

You can view the transcript for “Adding Integers with the Same Sign Using Color Counters” here (opens in new window).

Model each addition.

1. [latex]3 + 4[/latex]
2. [latex]−1 + 4[/latex]
3. [latex]4 + (−6)[/latex]
4. [latex]−2 + (−2)[/latex]

Show Solution

1. [latex]7[/latex]

    

2. [latex]3[/latex]

    

3. [latex]-2[/latex]

    

4. [latex]-4[/latex]

You can view the transcript for “Adding Integers | How to Add Positive and Negative Integers” here (opens in new window).

Subtracting Integers

Watch the video below to see more examples of modeling integer subtraction with color counters.

You can view the transcript for “Subtracting Integers with Color Counters (No Extra Zeros Needed)” here (opens in new window).

Model each subtraction.

1. [latex]7 - (-8)[/latex]
2. [latex]-7 - (-2)[/latex]
3. [latex]4 - 1[/latex]
4. [latex]-6 - 8[/latex]

Show Solution

1. [latex]15[/latex]

    

2. [latex]-5[/latex]

    

3. [latex]3[/latex]

    

4. [latex]-14[/latex]

You can view the transcript for “Subtracting Integers | How to Subtract Positive and Negative Integers” here (opens in new window).

Multiplying Integers

You can view the transcript for “Multiplying Integers | How to Multiply Positive and Negative Integers” here (opens in new window).

Watch the following video for more examples of how to multiply integers with different signs, and the same sign.

You can view the transcript for “Ex: Multiplying Integers” here (opens in new window).

Dividing Integers

You can view the transcript for “Dividing Integers | How to Divide Positive and Negative Integers” here (opens in new window).

Watch the following video for more examples of how to divide integers with the same and different signs.

You can view the transcript for “Ex: Dividing Integers” here (opens in new window).

Simplifying and Evaluating Expressions With Integers That Use all Four Operations

Watch the following video to see another example of how to use the order of operations to simplify an expression that contains integers.

You can view the transcript for “Ex: Simplify an Expression With Integers Using the Order of Operations” here (opens in new window).