Download - Adding Positive and Negative Integers
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Adding Positive and Negative Integers
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WARM-UPWARM-UP
1) Order from least to greatest 7, -3, 0, -1, 3-3, -1, 0, 3, 7
2) Insert
a) -15 > -16
b) 1 < 2
3) Find the sum:748 + 93 = 841
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Let's review what we learned in the last lesson
A variable is a letter that stands for a number
We use variables when we don’t know the number
A variable can be any letter
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A VARIABLE EXPRESSION contains a variable and an operation such as addition, subtraction, multiplication, division.
We can also write VARIABLE EXPRESSIONS such as
s + 9
8 n
16 x h
Review
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Word phrases can be translated into VARIABLE EXPRESSIONS
Word Phrase Variable Expression
2 more than n 2 + n
k times 8 k x 8
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The absolute value of a number is its distance from zero on the number line
The absolute value of 4 is written as
4The absolute value is always positive!
Absolute Value
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OppositesOpposites
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When we add an integer and its opposite, the sum is zero
EXAMPLES: (-5) + 5 = 0
98 + (-98) = 0
Opposites are also called ADDITIVE INVERSES.
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6/1/2 Adding Integers
Today we are going to learn how to add integers.
We will explore 3 different METHODS
METHOD 1 - ZERO PAIRS
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The red chips are NEGATIVE.
The grey chips are POSITIVE
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+
+
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- +
1 red chip 1 grey chip+ = 0
We call 1 red chip and 1 grey chip a
ZERO PAIR
Zero Pair
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We begin with 3 grey chips
And we add 2 more grey chips
FOR A TOTAL OF 5 GREY CHIPS
If we want to add 3 + 2 ++ ++
++ ++
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3 + 2 = 53 + 2 = 5
Lets take an ExampleLets take an Example
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We begin with 2 red chips
And we add 4 more red chips
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FOR A TOTAL OF 6 RED CHIPS.
-2 + (-4) = -6
Do you have any questions so far????
If we want to add -2 + (-4)
Remember Remember red chipsred chips
are negativeare negative
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BUT if we want to add integers with different signs,
we must use
ZERO PAIRS
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These 2 chips form a ZERO PAIR.These 2 chips equal zero.
Adding integers with different signs
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Let's add (-5) + 3
We begin with 5 red chips
And we add 3 grey chips
+ ++
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Lets see with an ExampleLets see with an Example
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Adding (-5) + 3
We begin with 5 red chips
And we add 3 grey chips
We circle the Zero Pairs and remove them!
(Remember a ZERO PAIR equals zero.)
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+ + +
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We begin with 5 red chips
And we add 3 grey chips
We are now left with 2 red chips OR -2
Therefore, (-5) + 3 = -2
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ResultResult
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You try a few. Use your red and black pens to make your chips.
(-3) + 1 = 4 + (-5) =
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+
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-3 + 1 = (-2)
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4+(-5) = (-1)
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METHOD 2 - Number Line
We can use a number line to find the sum of 2 integers.
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
WE ALWAYS START AT ZERO!
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1. Start at zero and move to the right (in a positive direction) 3 spaces.
2. Next, move further to the right 4 spaces.
3. Your answer is 7.
Lets add 3 + 4 by number lineLets add 3 + 4 by number line
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
3 + 4 = 73 + 4 = 7
1.1.2.2.
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Now, let's add (-2) + (-8)
1. Start at zero and move to the left (in a negative direction) 2 spaces.
2. Next, move further to the left 8 spaces.
3. Your answer is -10. (-2) + (-8) = -10
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
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Let's see what happens when we add a positive AND a negative number. (-6) + 8
=
1. Start at zero and move to the left (in a negative direction)
6 spaces.2. Next, move to the RIGHT 8 spaces.
3. Your answer is 2. as (-6) + 8 = 2
DO YOU HAVE ANY QUESTIONS??
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
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You try a couple.....
4 + (-7) = (-3)
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
Start at zero and draw your arrows!
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
(-2) + (-5) = (-7)
Start at zero and draw your arrows!
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Method 3 - Rules for adding integers
Adding the The sum of 2 positive numbers is POSITIVE.
Same sign The sum of 2 negative numbers is NEGATIVE.
Example: 4 + 7 = 11
(-3) + (-6) = (-9)
11 + 8 =
(-9) + (-1) =
1919
-10-10
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Adding Different Signs -
1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.
Example: (-2) + 9 =
1.) 2 9 Absolute Values
2.) 9 - 2
Step
Step Subtract
Step 3.) +7 Sign of the larger number
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Adding Different Signs -
1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.
Step 1.)
Step 2.)
Step 3.)
Try (-11) + 5 =
Absolute Values
Subtract
Sign of the larger number
11 , 5 11 , 5
11 – 5 = 6 11 – 5 = 6
- 6- 6
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1.) The temperature in Minneapolis was 7 degrees F at
noon. By 8 pm, the temperature had dropped15 degrees F. What was the temperature at 8
pm?
7 – 15 = (-8)
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2.) You have $60 in your bank account. You withdraw (or take out) $45 to buy new tires for your bike. You then deposit(or add in) your babysitting money of $18.What is the new balance in your bank account?
60 – 45 + 18 = 33
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Let's see how well we understood the lesson today.
Use a number line to find each sum.
1.) (-7) + 12 = 5
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10
2.) 4 + (-10) = (-6)
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Find each sum. Remember your Addition Rules!
3.) (-7) + (-11) = (-18)
4.) 12 + (-5) = 7
5.) 22 + 7 = 29
6.) (-9) + 5 = (-4)
7.) 3 + (-10) = (-7)
8.) (-8) + 20 = 12
9.) 1 + (-30) = (-29)
10.) (-15) + (-5) = (-20)
11.) Opposites are also called
ADDITIVE INVERSE.
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Let's Review...
We can add integers using ZERO PAIRS.
There are 3 METHODS we can use to Add Integers.
METHOD 1
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To add (-5) + 3 =
Then we are left with 2 red chips. Therefore, (-5) + 3 = -2
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We can also use a number line to find the sum of 2 integers.
METHOD 2
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METHOD 3
Adding the Same Sign –
The sum of 2 positive numbers is POSITIVE. The sum of 2 negative numbers is NEGATIVE.
Rules
Adding Different Signs -
1. Find the absolute value of the 2 numbers.2. Subtract the smaller number from the larger number.3. Take the sign of the larger number for your answer.
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You had a great lesson today!
Be sure to practice what you learned!