Computation with Integers

This course will cover the basic computation with integers.  You will learn the rules of adding, subtracting, multiplying, and dividing integers.

Understanding Integers

What are integers?

What are integers?

Integers are the set of whole numbers that can be positive, negative, or zero.

Examples

Examples of integers include: 

0

3

-5

7

-15

200

-1,746

Number Line

Positive numbers, negative numbers, and zero can be shown on a number line.

Zero is neither positive nor negative.  

All numbers to the right of zero are positive and all numbers to the left of zero are negative.

Opposite Numbers - Absolute Value

When numbers are the same distance from zero, they are considered opposites.  For example, 2 and -2 are opposites because they are each 2 units from zero.

Distance from zero also describes a number's absolute value.  In this example, the absolute value of 2 is 2 and the absolute value of -2 is 2.

|2| = 2      AND      |-2| = 2

Please note: The absolute value of a number cannot have a negative value because it only describes the number's distance from zero.  So |-2| is not -2 because -2 is 2 units from zero, not -2 units.

In other words, the solution to an absolute value problem cannot be negative.


Is it an Integer?

Before concluding the section on understanding integers, it is important to know that not all positive or negative numbers are integers.  

Decimal numbers, such as 0.5 and -3.24, can have positive or negative values.  However, they are not integers.

Fractions can also have positive or negative values.  But, 1/3 and -5/8 are not integers.

Test Your Knowledge - True or False

  • Integers are the set of whole, decimal, or fraction numbers that can be positive or negative.
  • Absolute value represents a number's distance from zero on a number line.
  • -5 and 5 are opposite numbers.
  • Zero can be either positive or negative.
  • -1/2 is NOT an integer.
  • 0.325 is an integer.
  • |-7| = -7 units from zero.
  • |3| = 3 units from zero.
  • -2.01 is an integer.
  • -50, 0, and 38 are all integers.

Addition of Integers

Adding Integers with the Same Sign

Positive + Positive = Positive

When adding two positive numbers, simply add the numbers and keep the answer positive.  Why? - the answer will be positive because both given numbers are positive.

3 + 2 = 5

6 + 7 = 13

2 + 6 = 8

Negative + Negative = Negative

When adding two negative numbers, simply add the numbers and keep the answer negative.  Why? - the answer will be negative because both given numbers are negative.

-3 + -2 = -5

-6 + -7 = -13

-2 + -6 = -8

-3 + -2 = ?

  • 1
  • -5
  • -1
  • 5

5 + 8 = ?

  • 3
  • 13
  • -3
  • -13

-2 + -7 = ?

  • 5
  • 9
  • -5
  • -9

9 + 5 = ?

  • -4
  • 4
  • 14
  • -14

-7 + -5 = ?

  • 12
  • 2
  • -12
  • -2

Adding Integers with Different Signs

Subtract and Use the Sign of the Largest Number

How do you add integers with different signs?  Take a look at the following problem:

-4 + 7 = ?

To solve this, you need to follow these steps:

1) Subtract the numbers:  7-4 = 3

2) Which number (7 or 4) is larger?     7 is larger.

3) Is the 7 in the original problem positive or negative?     It's positive.

So, since 7 is the larger number, and it is positive, the answer is going to be positive.

Therefore, -4 + 7 = 3.

When the larger number is negative . . .

Take a look at this one:

3 + -8 = ?

We follow the same steps as before:

1) Subtract the numbers:   8 - 3 = 5

2) Which number (8 or 3) is larger?    8 is larger.

3) Is the 8 in the original problem positive or negative?     It's negative.

Since 8 is negative, the solution will also be negative.

Therefore, 3 + -8 = -5.

3 + -2 = ?

  • 5
  • -1
  • 1
  • -5

-6 + 5 = ?

  • -1
  • -11
  • 1
  • 11

9 + -4 = ?

  • 13
  • -5
  • -13
  • 5

-8 + 12 = ?

  • -4
  • 4
  • -20
  • 20

4 + -9 = ?

  • -13
  • 5
  • -5
  • 13

Subtraction of Integers

Subtracting Integers

Always remember - Keep Change Change

The phrase "Keep Change Change" will help you remember the steps to solve a subtraction problem with integers.


Let's look at the steps to solve the following problem:

-3 - 2 = ?

Step 1 - KEEP

The first number in the problem is -3.  We will do nothing to it.  So we keep it as is:

-3

Step 2 - CHANGE

The current arithmetic operation is subtraction.  We will change it to addition:

+

Step 3 - CHANGE

The next number in the problem is 2.  It is positive.  So, we need to change it's sign to negative:

-2

Step 4 - Apply addition rules to solve

After following the Keep Change Change steps, our new problem looks like this:

-3 + -2 = ?

We have an addition with like signs problem.  Solve it!

-3 + -2 = -5

We add 3 and 2, which is 5.  Since both numbers are negative, the answer is negative!

5 - -4 =?

  • 1
  • 9
  • -1
  • -9

-2 - 7 = ?

  • -9
  • -5
  • 9
  • 5

3 - 1 = ?

  • -2
  • 2
  • -4
  • 4

9 - 12 = ?

  • -3
  • 3
  • -21
  • 21

- 5 - -5 = ?

  • -10
  • 10
  • 0
  • None of the Above

Multiplication & Division of Integers

Rules of Multiplying/Dividing Integers

The Rules are the Same

Multiplying and Dividing integers share the same rules.  Just remember the rules and you are well on your way to mastering the multiplication and division of integers.

Multiplication

Positive x Positive = Positive

Positive x Negative = Negative

Negative x Positive = Negative

Negative x Negative = Positive

Division

Positive / Positive = Positive

Positive / Negative = Negative

Negative / Positive = Negative

Negative / Negative = Positive

Let's see it in action

-2 x 8 = ?

Since we are multiplying a negative and a positive, our answer will be negative:

2 x 8 = 16

It is -2 times 8 in the original problem.  Therefore we end up with -16 for our solution.

-2 x 8 = -16

Try another

-6 x -3 = ?

We have a negative times a negative! Our answer will be positive!

-6 x -3 = 18

6 x 3 is 18.  Since both numbers are negative, our answer will be positive.

-2 x 5 = ?

  • 10
  • -10

16 / -4 = ?

  • -4
  • 4

-15 / -3 = ?

  • 5
  • -5

8 x 4 = ?

  • 36
  • 32

7 / -1 = ?

  • -7
  • 7

-4 x -3 = ?

  • -12
  • 12

Course Assessment

-5 + -3 = ?

  • -2
  • -8
  • 8
  • 2

4 - -2 = ?

  • 2
  • -6
  • -2
  • 6

-7 - 3 = ?

  • -10
  • 10
  • -4
  • 4

-9 / 3 = ?

  • -3
  • 3
  • 27
  • -27

6 + -5

  • 11
  • -1
  • -11
  • 1

9 x -4 = ?

  • 32
  • -36
  • -32
  • 36

21 / 7 = ?

  • 4
  • -3
  • -4
  • 3

-5 - 5 = ?

  • 0
  • -10
  • 10
  • None of the above

5 x - 7 =

  • -35
  • 12
  • 35
  • -12

-2 + -9 = ?

  • 11
  • 7
  • -11
  • -7