Transcript Powerpoint of Notes

PRE-ALGEBRA
Lesson 1-5 Warm-Up
PRE-ALGEBRA
“Adding Integers” (1-5)
What is the “Identity
Property of Addition”?
Identity Property of Addition: A number plus 0 is equal to the original
number [In other words, the number keeps its identity (doesn’t change)
when 0 is added to it.]
Examples:
5+0=5
n+0=n
What is the “Inverse
Property of Addition”?
Inverse Property of Addition: A number plus its additive inverse (its
opposite = same number with the opposite sign) is equal to zero.
Examples:
17 + (-17) = 0
n + (-n) = 0
How can you use a
number line to add
integers?
To add integers using a number line, start at the first number and move
/ jump the number of units right (+) or left (-) the second number tells you
to.
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Additional Examples
Examples: Use a number line to simplify each expression.
a. 3 + (–5) Start at –3.
Move left 5 units.
3 + (–5) = –2
b. –3 + 5
Start at –3.
Move right 5 units.
–3 + 5 = 2
–3 + (–5) = –8
Start at –3.
c. –3 + (–5)
Move left 5 units.
PRE-ALGEBRA
“Adding Integers” (1-5)
To add integers using a model, create a symbol (like a yellow box) to
represent (stand for) one positive unit and another symbol (like a red
box) to represent one negative unit. Then, model the espression and
cancel out each positive (yellow) and negative (red) pair, since
Example: Use a model to find 2 + (-5).
2 + (-5) = -3.
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Additional Examples
Use models to find (–7) + 3.
(–7) + 3
Model the sum.
–4
Group and remove zero pairs.
Write the integer that the simplified
model represents.
(–7) + 3 = – 4
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Additional Examples
From the surface, a diver goes down 20 feet and then
comes back up 4 feet. Find –20 + 4 to find where the diver is.
Start at 0. To represent –20,
move left 20 units.
To add positive 4, move right 4
units to –16.
–20 + 4 = –16
The diver is 16 feet below the surface.
PRE-ALGEBRA
“Adding Integers” (1-5)
Rule: Adding Numbers With the Same Signs: To add to numbers with
What are the rules for
the same signs, add their absolute values (add them) and use the same
adding integers with the
same and different signs? sign as both the addends (the numbers you’re adding)
Examples:
2+6=8
-2 + (-6) = -8
Rule: Adding Numbers With Different Signs: To add to numbers with
different signs, find the difference of their absolute values (subtract them)
and use the same sign as the addend with the greatest absolute value
(take the sign from the bigger number).
Examples:
-2 + 6 = 4
2 + (-6) = -4
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Additional Examples
Find each sum.
a. –20 + (–15)
–20 + (–15) = –35
Since both integers are negative,
the sum is negative.
b. 13 + (–17)
|–17| – |13| = 17 – 13
=4
13 + (–17) = – 4
Find the difference of the absolute values.
Simplify.
Since –17 has the greater absolute
value, the sum is negative.
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Additional Examples
A player scores 22 points. He then gets a penalty of
30 points. What is the player’s score after the penalty?
22 + (–30)
Write an expression.
|–30| – |22| = 30 – 22
Find the difference of the absolute values.
=8
22 + (–30) = – 8
Simplify.
Since –30 has the greater absolute value,
the sum is negative.
The player’s score is – 8.
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Additional Examples
Find –7 + (– 4) + 13 + (–5).
–7 + (– 4) + 13 + (–5)
–11
+ 13 + (–5)
2 + (–5)
–3
Add from left to right.
The sum of the two negative
integers is negative.
|13| – |11| = 2. Since 13 has the greater
absolute value, the sum is positive.
|5| – |2| = 3. Since –5 has the greater
absolute value, the sum is negative.
–7 + (– 4) + 13 + (–5) = –3
PRE-ALGEBRA
Adding Integers
LESSON 1-5
Lesson Quiz
Find each sum.
1. –37 + (–5)
–42
3. –100 + 5 + (–3)
–98
2. 14 + (–4)
10
4. 33 + ( – 21) + ( – 12)
0
PRE-ALGEBRA