Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5, ... . Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5, … . We do not consider zero to be a positive or negative number. For each positive integer, there is a negative integer, and these integers are called opposites. For example, -3 is the opposite of 3, -21 is the opposite of 21, and 8 is the opposite of -8. If an integer is greater than zero, we say that its sign is positive. If an integer is less than zero, we say that its sign is negative.

Example: Integers are useful in comparing a direction associated with certain events. Suppose I take five steps forwards: this could be viewed as a positive 5. If instead, I take 8 steps backwards, we might consider this a -8. Temperature is another way negative numbers are used. On a cold day, the temperature might be 10 degrees below zero Celsius, or -10°C.

The Number Line

The number line is a line labeled with the integers in increasing order from left to right, that extends in both directions:

For any two different places on the number line, the integer on the right is greater than the integer on the left. Examples: 9 > 4, 6 > -9, -2 > -8, and 0 > -5

Absolute Value of an Integer

The number of units a number is from zero on the number line. The absolute value of a number is always a positive number (or zero). We specify the absolute value of a number n by writing n in between two vertical bars: |n|. Examples: |6| = 6

|-12| = 12

Adding Integers

1) When adding integers of the same sign, we add their absolute values, and give the result the same sign. Examples: 2 + 5 = 7

(-7) + (-2) = -(7 + 2) = -9

(-80) + (-34) = -(80 + 34) = -114 2) When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value. Example: 8 + (-3) = ?

The absolute values of 8 and -3 are 8 and 3. Subtracting the smaller from the larger gives 8 - 3 = 5, and since the larger absolute value was 8, we give the result the same sign as 8, so 8 + (-3) = 5. Example: 8 + (-17) = ?

The absolute values of 8 and -17 are 8 and 17.

Subtracting the smaller from the larger gives 17 - 8 = 9, and since the larger absolute value was 17, we give the result the same sign as -17, so 8 + (-17) = -9.

Subtracting Integers

Subtracting an integer is the same as adding its opposite.

Examples: In the following examples, we convert the subtracted integer to its opposite, and add the two integers.

7 - 4 = 7 + (-4) = 3

12 - (-5) = 12 + (5) = 17

-8 - 7 = -8 + (-7) = -15

-22 - (-40) = -22 + (40) = 18 Note that the result of subtracting two integers could be positive or negative.

Multiplying Integers

To multiply a pair of integers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opposite signs, their product is oppositeof the product of their absolute values (their product is negative). If one or both of the integers is 0, the product is 0.

Dividing Integers

To divide a pair of integers both integers have the same sign, divide the absolute value of the first integer by the absolute value of the second integer.

To divide a pair of integers if both integers have different signs, divide the absolute value of the first integer by the absolute value of the second integer, and give this result a negative sign.

The following video shows more examples of multiplying and dividing negative numbers:

Positive integers are all the whole numbers greater than zero: 1, 2, 3, 4, 5, ... . Negative integers are all the opposites of these whole numbers: -1, -2, -3, -4, -5, … . We do not consider zero to be a positive or negative number. For each positive integer, there is a negative integer, and these integers are called opposites. For example, -3 is the opposite of 3, -21 is the opposite of 21, and 8 is the opposite of -8. If an integer is greater than zero, we say that itsPositive and Negative Integerssignis positive. If an integer is less than zero, we say that itssignis negative.Example:

Integers are useful in comparing a direction associated with certain events. Suppose I take five steps forwards: this could be viewed as a positive 5. If instead, I take 8 steps

backwards, we might consider this a -8. Temperature is another way negative numbers are used. On a cold day, the temperature might be 10 degrees below zero Celsius, or -10°C.

The number line is a line labeled with the integers in increasing order from left to right, that extends in both directions:The Number LineFor any two different places on the number line, the integer on the right is greater than the integer on the left.

Examples:

9 > 4, 6 > -9, -2 > -8, and 0 > -5

The number of units a number is from zero on the number line. The absolute value of a number is always a positive number (or zero). We specify the absolute value of a numberAbsolute Value of an Integernby writingnin between two vertical bars: |n|.Examples:

|6| = 6

|-12| = 12

1) When adding integers of the same sign, we add their absolute values, and give the result the same sign.Adding IntegersExamples:

2 + 5 = 7

(-7) + (-2) = -(7 + 2) = -9

(-80) + (-34) = -(80 + 34) = -114

2) When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value.

Example:

8 + (-3) = ?

The absolute values of 8 and -3 are 8 and 3. Subtracting the smaller from the larger gives 8 - 3 = 5, and since the larger absolute value was 8, we give the result the same sign as 8, so 8 + (-3) = 5.

Example:

8 + (-17) = ?

The absolute values of 8 and -17 are 8 and 17.

Subtracting the smaller from the larger gives 17 - 8 = 9, and since the larger absolute value was 17, we give the result the same sign as -17, so 8 + (-17) = -9.

Subtracting an integer is the same as adding its opposite.Subtracting IntegersExamples:

In the following examples, we convert the subtracted integer to its opposite, and add the two integers.

7 - 4 = 7 + (-4) = 3

12 - (-5) = 12 + (5) = 17

-8 - 7 = -8 + (-7) = -15

-22 - (-40) = -22 + (40) = 18

Note that the result of subtracting two integers could be positive or negative.

To multiply a pair of integers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opposite signs, their product isMultiplying Integersoppositeof the product of their absolute values (their product is negative). If one or both of the integers is 0, the product is 0.

To divide a pair of integers both integers have the same sign, divide the absolute value of the first integer by the absolute value of the second integer.Dividing IntegersTo divide a pair of integers if both integers have different signs, divide the absolute value of the first integer by the absolute value of the second integer, and give this result a negative sign.

The following video shows more examples of multiplying and dividing negative numbers:And now................. enjoy and practice Mathshttp://classroom.jc-schools.net/basic/math-integ.html