Transcript Integers - C on T ech Math : : An application

Integers
Lesson 1a: Integers
Integers are whole numbers and their opposites.
Negative integers are numbers less than zero.
Positive integers are numbers greater than zero.
There is a positive integer to complement every
negative integer.
Addition of Integers
Addition of Integers with the same sign:
Add the absolute value. The absolute value is the number of units
a number is from zero. The sum has the same sign as the number
being added.
Examples:
5 + 4 = a The answer is positive because both 4
9 = a and 5 are positive.
-5 + -4 = a
-9 = a
The answer is negative because both -4
and -5 are negative.
Addition of Integers
Addition of Integers with different signs:
Find the difference in absolute values. The sum has the same sign
as the number with the greatest absolute value.
Examples:
9 + -3 = a The integer with the greatest value is 9. 9
6 = a is positive therefore the sum is positive.
4 + -8 = a
-4 = a
The integer with the greatest value is -8. -8
is negative, therefore the sum is negative
Number Lines
A number line can be helpful when learning to add integers.
Example:
Add -5 + 7
Since you’re adding 7 to -5, you want to start at -5 on the number line.
Then you want to draw an arrow going in the positive direction
going 7 spaces.
Then look at the integer your arrow ends up on.
7 spaces
-6
-5
-5
-4
-3
-2
-1
0
1
2
3
So -5 + 7 = 2
4
5
6
Subtraction of Integers
To subtract an integer, add its opposite.
Example:
a = 7 - 10 Subtract +10 by adding (+) its opposite, -10
a = 7 + -10
a = -3
When you add a number’s opposite, the subtraction problem becomes
an addition problem.
y = 8 - 12
y = 8 + -12
y = -4
12 spaces to the left
-6
-5
-4
-4
-3
-2
So
-1
0
1
2
3
8 - 12 = -4
4
5
6
7
8
Exercises
If you are correct you will hear a chime
1. 9 + 6 =
14
15
16
2. -6 + -8 =
-14
14
12
3. -4 + -6 + -8 =
-18
-8
18
4. 8 - -3 =
-11
-5
11
-2
4
-6
5. - 4 - -2 =
Absolute Values of Integers
For any real number a:
Definition of
Absolute Value If a > 0, then |a| = a, and
Example:
|2| = 2
if a < 0, then |a| = opposite of a. |-2| = 2
Click on the correct answer below for each problem.
If you hear a chime, then you chose the correct answer.
1. |-5| =
5
-5
2. |47| =
-47
47
3. -|25| =
-25
25
4. -|-25| =
-25
25
Review
Definition, Rule,
Review:
Definition of
Absolute Value
or Property
For any real number a:
If a > 0, then |a| = a, and
If a < 0, then |a| = opposite of a.
Adding integers To add integers with the same sign, add their
absolute values. Give the sum the same sign
with the Same
as the integers.
Sign
Adding integers
with Different
Signs
To add integers with the different signs,
subtract the lesser absolute value from the
greater absolute value. Give the result the
same sign as the integer with the greater
absolute value.
Example
|2| = 2
|-2| = 2
3+4=7
-3 + (-4) = -7
-7 + 5 = -2
9 + (-3) = 6
Additive
Inverse
Property
For every number a, a + (-a) = 0.
Subtraction
Rule
8 – (-3) = 8 + 3
To subtract a rational number, you can add its
additive inverse. For rational numbers a and b,
= 10
a – b = a + (-b).
-8 + 8 = 0