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Integers

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Integers The set of whole numbers and

their opposites

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The set of numbers used on the number line

is called the set of integers

This set can be written

{, -3, -2, -1, 0, 1, 2, 3, }

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The number line is made up of 3 sets ofnumbers

Natural numbers 1, 2, 3, 4,

Whole numbers 0, 1, 3, 4, Integers , -2, -1, 0, 1, 2,

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We can use a Venn Diagram torepresent thee 3 sets of numbers

and their relationship to one

another

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Operations with

Integers

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Addition

Subtraction

Multiplication

Division

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Addition of Integers

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When the signs of the numbers being added

are the same, add their absolute values--The

sign of the answer is the same as the sign of

the numbers added together

When the signs of the numbers being added

are different, subtract their absolute values--The sign of the answer is the same as the

number with the largest absolute value

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Rules for

Addition

Positive + Positive = Positive

Positive + Negative = Depends

Negative + Positive = Depends

Negative + Negative = Negative

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How to solve positive + negative or

negative +positi

ve

Absolute Value: This is the number of

spaces from zero on the number line.

Example: the absolute value of 10 is 10

the absolute value of -10 is 10

Once you find the absolute value of eachnumber you subtract and take the sign of the

greater number.

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Subtraction ofIntegers

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Add the opposite and refer to the addition

rules (change the subtraction to addition and

change the sign of the number being

subtracted)

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Examp

le

Here is another problem: -2 8 = x

Switching the problem to an addition

problem, it becomes -2 + (-8) = x, which isequal to -10.

6 - (-20) = x is equal to 6 + 20, which is 26.

-7 - (-1) = x is the same as -7 + 1, which is -

6.

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Multiplication ofIntegers

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When the sign of the numbers being

multiplied are the same, multiply the

numbers--The sign of the answer is positive

When the sign of the numbers being

multiplies are different, multiply the

numbers--The sign of the answer is negative

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Rules for

Multip

lication

Positive x Positive = Positive

Positive x Negative = Negative

Negative x Positive = Negative

Negative x Negative = Positive

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Ex

ample

The fourth rules follows the pattern that when twonumbers of the same sign are multiplied theanswer is always positive.

-8 x 3 = -24

-8 x 2 = -16

-8 x 1 = -8

-8 x 0 = 0 -8 x -1 = 8

-8 x -2 = 16

-8 x -3 = 24

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D

iv

ision of Integers

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Same as the rules for multiplication of

Integers

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Rules for

D

ivision with Integers

Positive Positive = Positive

Positive Negative = Negative

Negative Positive = Negative

Negative Negative = Positive

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Ex

ample

-9 3 = -320 (-4) = -5

-18 (-3) = 6