An integer is a whole number .It can be positive, negative, or zero. The integers are natural numbers including 0 together with the negatives of the non-zero natural numbers .The the real numbers that can be written as without a fractional or decimal component.
Properties:
Existence of an identity property m + 0 = m m x 1 = m
Existence of inverse property m + (-m)=0
The ordering of integers with the algebraic operations
if a < b and c < d, then a + c < b + d
if a < b and 0 < c, then ac < bc.
Positive and Negative Integers
Positive integer are all the whole numbers greater than zero example: 1, 2, 3, 4, 5,... . Negative integer are all the opposites of these whole numbers examples : -1, -2, -3, -4, -5, … . We don’t consider zero to be a positive or negative number.
For example:
-5 is the opposite of 5, -22 is the opposite of 22, and 8 is the opposite of -8
The Number Line
It is a line labeled with the integers are increasing order from left to right, that extends in both directions.
Examples:
9 > 5, 6 > -10, - 2 > -5, and 0 > -9
|6| = 6
|-122| = 122
|0| = 0
|-1234| = 1234
|-10234| = 10234
Adding Integers
Adding Integers
Adding integers of the same sign, we add their absolute values, and it give the result the same sign.
Example:
2 + 5 = 7
(-7) + (-2) = -(7 + 2) = -9
(-80) + (-34) = -(80 + 34) = -114
Adding integers of the opposite signs, take their absolute values, subtract smaller value from larger value , and result the sign of the integer is the larger absolute value.
8 + (-3) =5
Subtracting Integers
Subtracting an integer is the same as opposite of adding.
7 - 4 = 7 + (-4) = 3
12 - (-5) = 12 + (5) = 17
-8 - 7 = -8 + (-7) = -15
-22 - (-40) = -22 + (40) = 18
Multiplying Integers
A pair of integers if both numbers are the same sign, their product is positive. If the numbers are opposite signs, their product is negative. If one or both of the integers is 0, the product is 0.
-4) × (-5) = |-4| × |-5| = 4 × 5 = 20
(-7) × 6 = -42.
Properties:
Existence of an identity property m + 0 = m m x 1 = m
Existence of inverse property m + (-m)=0
The ordering of integers with the algebraic operations
if a < b and c < d, then a + c < b + d
if a < b and 0 < c, then ac < bc.
Positive and Negative Integers
Positive integer are all the whole numbers greater than zero example: 1, 2, 3, 4, 5,... . Negative integer are all the opposites of these whole numbers examples : -1, -2, -3, -4, -5, … . We don’t consider zero to be a positive or negative number.
For example:
-5 is the opposite of 5, -22 is the opposite of 22, and 8 is the opposite of -8
The Number Line
It is a line labeled with the integers are increasing order from left to right, that extends in both directions.
Examples:
9 > 5, 6 > -10, - 2 > -5, and 0 > -9
|6| = 6
|-122| = 122
|0| = 0
|-1234| = 1234
|-10234| = 10234
Adding Integers
Adding Integers
Adding integers of the same sign, we add their absolute values, and it give the result the same sign.
Example:
2 + 5 = 7
(-7) + (-2) = -(7 + 2) = -9
(-80) + (-34) = -(80 + 34) = -114
Adding integers of the opposite signs, take their absolute values, subtract smaller value from larger value , and result the sign of the integer is the larger absolute value.
8 + (-3) =5
Subtracting Integers
Subtracting an integer is the same as opposite of adding.
7 - 4 = 7 + (-4) = 3
12 - (-5) = 12 + (5) = 17
-8 - 7 = -8 + (-7) = -15
-22 - (-40) = -22 + (40) = 18
Multiplying Integers
A pair of integers if both numbers are the same sign, their product is positive. If the numbers are opposite signs, their product is negative. If one or both of the integers is 0, the product is 0.
-4) × (-5) = |-4| × |-5| = 4 × 5 = 20
(-7) × 6 = -42.
No comments:
Post a Comment