Transcript Additional and Subtraction of Integers (PowerPoint)

Add and Subtract Integers
Learning Objective: We will add and
subtract positive and negative integers.
Math NS 1.3
What do we already know?
• Positive integers are on the right side of zero.
4
• Negative integers are on the left side of zero.
-4
• This means that they are opposites.
Negative
Positive
-3 + 3 = 0
You know how to plot an expression on the number
line and find the sum.
5 + -2 = 3
Step 1: Plot the first integer on the
number line.
Step 2: Plot the second integer on the
number line beginning where the last
number left off.
-2
5
You know how to plot an expression on the number line
and find the difference.
5 + -2= 3
Step 1: Plot the first integer on the
number line.
Step 2: Plot the second integer on the
number line beginning where the last
number left off.
-2
5
You know how to plot an expression on the number line
and find each sum.
Step 1: Plot the first integer on the
number line.
Step 2: Plot the second integer on the
number line beginning where the last
number left off.
-3 + -1 = - 4
-1
-3
You already learned that
subtracting a negative integer
gives the same solution as adding
its opposite.
Vocabulary
• Define integers: a positive or negative number.
• Define a positive integer: whole numbers to the
left of zero.
• Define a negative integer: whole numbers to the
right of zero.
negative
positive
Vocabulary
Define absolute value: the distance
from zero.
Plot each of the integers below on a
number line and then tell the absolute value of each.
-1 (1)
2 (2) -5
(5)
-1
-5
2
You already learned that
subtracting a negative integer
gives the same solution as adding
its opposite.
To help predict whether the sum of
two integers will be positive or
negative, you can use these rules.
1st Variation
Is the sum of 2 and 7 positive or negative?
Rule: The sum of two positive integers is positive.
2+7= 9
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
2
Solution: The sum of 2 and 7 is positive.
7
2nd Variation
Is the sum of -2 and -7 positive or negative?
Rule: the sum of two negative integers is negative.
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
-2 + -7= -9
-7
-2
Solution: The sum of -2 and -7 is negative.
3rd Variation
Is the sum of -2 and 7 positive or negative?
Rule: the sum of a positive integer and a negative
integer will have the same sign as the integer with
the greater absolute value.
-2 + 7=
5
7
-2
Solution: The sum of -2 and 7 is positive.
Step 1: Change the
expression to an addition
by using the absolute
value.
Step 2: Plot the first
integer on the number
line.
Step 3: Plot the second
integer on the number line
beginning where the last
number left off.
Why is this important?
If the temperature was 10ｰF at lunch time and
dropped to -5ｰF in the evening. What is the
difference between these temperatures?
10 - -5= 15 degrees
Mauricio were at the corner store. Mauricio forgot
his money and needs $10 to pay for his treats. If
Omar let Mauricio borrow $10, Mauricio now has
$10.
- $10 + $10 = 0
Guided Practice - I Do It
Rule: The sum of two positive integers is positive.
1 + 4= 5
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
1
4
Solution: The sum of 1 and 4 is positive.
Guided Practice - We Do It
Rule: The sum of two positive integers is positive.
5 + 3= 8
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
5
Solution: The sum of 5 and 3 is positive.
3
Guided Practice - You Do It
Rule: The sum of two positive integers is positive.
7 + 3= 10
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
7
Solution: The sum of 7 and 3 is positive.
3
Guided Practice - I Do It
Rule: the sum of two negative integers is negative.
-2 + -3= -5
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
-3
-2
Solution: The sum of -2 and -3 is negative.
Guided Practice - We Do It
Rule: the sum of two negative integers is negative.
-1 + -4= -5
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
-4
-1
Solution: The sum of -1 and -4 is negative.
Guided Practice - You Do It
Rule: the sum of two negative integers is negative.
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
-4 + -6= -10
-6
-4
Solution: The sum of -6 and- 4 is negative.
Guided Practice - I Do It
Rule: the sum of a positive integer and a negative integer will
have the same sign as the integer with the greater absolute
value.
4 - -2=
4 + 2= 6
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
4
Solution: The difference of 4 and -2 is positive.
2
Guided Practice - We Do It
Rule: the sum of a positive integer and a negative
integer will have the same sign as the integer with
the greater absolute value.
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
4
Solution: The difference of 4 and -6 is positive.
4 - -6=
4 + 6= 10
6
Guided Practice - You Do It
Rule: the sum of a positive integer and a negative
integer will have the same sign as the integer with
the greater absolute value.
Step 1: Change the expression to an
addition by using the absolute value.
Step 2: Plot the first integer on the
number line.
Step 3: Plot the second integer on the
number line beginning where the last
number left off.
3 - -7=
3 + 7 = 10
3
Solution: The difference of 3 and -7 is positive.
7
Closure
Quic kTime™ and a
dec ompr es sor
are needed to s ee this pic ture.
• What is a whole number to the right of zero?
• It is a positive integer.
• What is a whole number to the left of zero?
• It is a negative integer
• What is the distance from zero?
• It is the absolute value.
Negativ
e
Positiv
e
Closure
Decide if the sum or difference is positive or negative.
Explain how you decided.
Solve the expression.
-10 + -6 =
8 - -6=
Share with your partner one thing that you learned today.
Step 1: Change the expression to an addition by using the
absolute value.
Step 2: Plot the first integer on the number line.
Step 3: Plot the second integer on the number line beginning
where the last number left off.