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ADDING AND SUBTRACTING INTEGERSMrs. Landon
GOAL: ADD INTEGERS WITH THE SAME SIGN
How do you add integers with the same sign?
When in real life do you use integers?
Integer: Any whole number that is positive, negative, or zero
LESSON 1.1 ADDING AND SUBTRACTING INTEGERS
Integer: Any whole number that is positive, negative, or zero
Non-integers consist of fractions that can be written as terminating or repeating decimals. A terminating decimal comes to a complete stop. A repeating decimal continues the same digit
or block of digits forever.
Rational Number: any number that can be written as ratio in the form of a / b where a and b are both integers and b is NOT zero.
In order to be a rational number, the decimal form of the number either terminates or has a repeating pattern. (Define: terminates and repeats)
LET’S EXPLORE
With your partner go through page 7 and answer the few questions you are presented with.
Raise your hand when you are finished.
Then complete page 8!
ADDING INTEGERS WITH LIKE SIGNS
STEP 1: Find the absolute value of each number Absolute value: a distance of the number from
zero on the number line. Written as ||
Practice |8|=
|-8| =
|-2| =
|4| =
STEP 1: Find the absolute value of each number Absolute value: a distance of the number from
zero on the number line. Written as ||
STEP 2: Find the sum of the absolute values 7 + 6 = 13 -7 + (-6) = -13
STEP 3: Use the sign of the integers to write the sum. 5 + 4 = 9 -5 + (-4) = -9
COMMUTATIVE PROPERTY OF ADDITION
Does this property apply when adding two negative integers?
Definition of Commutative Property of Addition: The Commutative Property of Addition states that changing the order of addends does not change the sum, i.e. if a and b are two real numbers, then a + b = b + a.
So does -5 + (-4) = -4 + -5 ?
CRITICAL THINKING
Choose any two negative integers.
Is the sum of the integers less than or greater than the value of either of the integers?
Will this be true no matter which two negative integers?
USING A NUMBER LINE
-2 + -1 =
1 + 4 =
YOUR TURN
1. -8 + (-6) =
2. 102 + 18 =
3. -42 + (-16) =
4. -8 + (-8) =
5. 12 + 19 =
YOUR TURN
Page 9 # 7-14
1-2 GOAL: ADDING INTEGERS WITH DIFFERENT SIGNS
How do you add integers with different signs?
Example: At the school fundraiser for the band, your class raised $300, but you spent $28 on supplies to raise the money.
How can you express the actual amount you earned as the SUM of two integers with DIFFERENT signs?
ADDING ON A NUMBER LINE
Example: 4 + (-3)
Start at 4. Move 3 units to the left (in the negative
direction)
4 + (-3) = _________
Let’s Try
-4 + 2 Start at -4 Move to the right 2 spaces
-4 + 2 = _______
Page 13 practice
MODELING SUMS OF INTEGERS WITH DIFFERENT SIGNS Each yellow represents a positive integer and each red
represents a negative integer.
4 + (-1) Start with 4 positive counters
Add 1 negative counter
Form zero pairs (add a negative and a positive to get a zero)
What is left when you remove the zero pairs is the sum.
3 positive counters are left so 4 + (-1) = 3
Page 14 practice
NUMERICAL
Step 1: Find the absolute value of each addend.
Step 2: Subtract the lesser absolute value from the greater absolute value.
Step 3:Use the sign of the integer with the greater absolute value for the sum
Practice – 11 + 6
ADDING INTEGERS
Adding Integers Example
Same signs Add the absolute value of the integers. Use the common sign for the sum
3 + 5 =8
-2 + (-7) = -9
Different signs Subtract the lesser absolute value from the greater absolute value. Use the sign of the integer with the greater absolute value for the sum
-3 + 5 = 2
-10 + 1 = -9
A number and its opposite
The sum is 0. The opposite of any numbers is called its additive inverse
4 + (-4) = 0
-11 + 11 = 0
CHOOSE YOUR METHOD
1. - 37 + 37 =
2. 12 + (-4) =
3. 10 + (-15) =
4. -23 + 4 =
5. -4 + (-6) =
ANSWER
1. - 37 + 37 = 0
2. 12 + (-4) = 8
3. 10 + (-15) = -5
4. -23 + 4 = -19
5. -4 + (-6) = -10
YOUR TURN
Page 15 # 3-10
Individual practice page 16 ODD 1, 3, 5, 7, 9, 11, 13 (CHECK)
Homework: EVENS
1.3 SUBTRACTING INTEGERS
Goal: How do you subtract integers?
Consider the following: you have $10 but you want to buy something that costs $15, so you borrow $5 and have a $5 debt. You can write this as 10-15 = -5. How would you subtract a great number from a lesser number?
MODELING SUBTRACTION
You can use counters to find the difference of two integers
Model -3 – (-2)
Start with 3 negative counters to represent -3
Take two negative counters away to represent subtracting -2
What is left? 1 negative counter
So -3 – (-2) = -1
YOUR TURN
-5 – (-3) Start with 5 negative counters to represent -5
Take three negative counters away to represent subtracting -3
What is left? 2 negative counter
So -5 – (-3)= -2
SUBTRACT USING MODEL METHOD
Model 6- (-3) =
Start with 6 positive counters to represent 6
You need to take away 3 negative counters, so add 3 zero pairs.
What is left? 9 positive counters
So 6 – (-3) = 9
YOUR TURN: 4 – (-2) =
Model 4 – (-2) =
Start with 4 positive counters to represent 4
You need to take away 2 negative counters, so add 2 zero pairs.
What is left? 6 positive counters
So 4 – (-2) = 6
YOUR TURN
1. -2 – (-4) = -2 – (-4) = 2
2. -5 – (-4) = -5 – (-4) = -1
3. 6 – (-4) = 6 – (-4) = 10
4. 7 – (-2) = 7 – (-2) = 9
SUBTRACTING ON A NUMBER LINE
To model the difference of 5-3 , you start at 5 and move 3 units to the left.
NOTICE: 5 - 3 = 5 + (-3) . Subtracting 3 is the same as adding its opposite, -3
You can use the fact that subtracting a number is the same as adding its opposite to find the difference of two integers.
NUMBER LINE: -1 – 5
Rewrite subtraction as addition of the opposite -1 – 5 = -1 + (-5)
Practice 1. -4 – 6 =
-4 + (-6)
2. -6 – 2 = -6 + (-2)
3. -7 – (-3) = -7 + 3 =
4. -6 – (-2) = -6 + 2 =
TO GRAPH ON A NUMBER LINE
Example: -1 – 4 Rewrite subtraction as addition of the opposite -1
+ 4
Start at -1 and move 4 units to the left.
The difference is 3
PRACTICE
-5 – (-2) Rewrite subtraction as addition of the opposite - 5 – (-2) = -5 + 2
Start at _____ and move _____ units to the _________.
The difference is _________
YOUR TURN
Complete page 19, 20 and the top of page 21 to practice modeling integer subtraction and subtracting on a number line
SUBTRACTING INTEGERS BY ADDING THE OPPOSITES
Step 1: Write the subtraction expression Step 2: find the difference by adding the opposite.
The temperature on Monday was -5 °Celsius. By Tuesday the temperature rose to -2 °Celsius. Find the change in temperature.
Final temperature – Monday’s temperature = change in the temperature.
-2 °C – (-5 ° C) = the change
-2 + 5 = 3 ° C
Complete page 21 and the top of page 22
GET IT CHECKED
Complete page 22