There are several ways to add integers. One way is to use the
1-tiles from a set of algebra tiles.
Find 3 + 2.
Combine 3 positive tiles with 2 positive tiles on a mat.
There are 5 positive tiles on the mat. Therefore, 3 + 2 = 5.
Find –3 + (–2).
Combine 3 negative tiles with 2 negative tiles.
There are 5 negative tiles on the mat. Therefore, –3 + (–2) = –5.
You can also add integers on a number line. Start at 0.
Positive integers are represented by arrows pointing right. Negative integers are represented by arrows pointing left. Start at 0. Move 3 units to the right.
From there, move another 2 units to the right.
Start at 0. Move 3 units to the left. From there, move
another 2 units to the left.
These and other similar examples suggest the following rule
for adding integers with the same sign.
Example
Find each sum.
1.
4
+ 5
Alternative Solutions :
4 + 5 =
9 Both numbers are positive, so the sum is positive.
2.
–6 + (–2)
Alternative Solutions :
–6 +
(–2) = –8 Both numbers are negative, so the sum is
negative.
What is the result when you add two numbers that differ only
in sign, like 3 and –3?
You can also use tiles. When one positive tile is paired with
one negative tile, the result is a zero pair. You
can remove zero pairs from the mat because removing zero does not change the
value.
The models above show 3 + (–3) = 0. If the sum of two numbers
is 0, the numbers are called opposites or additive inverses.
–3 is the additive inverse, or opposite, of 3. 3 + (–3) = 0
7 is the additive inverse, or opposite, of –7 –7 + 7 = 0
In the following activity, you’ll use tiles to find a rule for adding two integers with different signs.
Example
Find each sum.
3.
5
+ (–3)
Alternative Solutions :
│5│– │3│= 5 – 3 or 2
│5│>│–3│, so the sum is positive.
Therefore,
5 + (–3) = 2.
4.
4
+ (6)
Alternative Solutions :
│–6│–│4│= 6 – 4 or 2
│–6│>│4│, so the sum is negative.
Therefore,
4 + (–6) = –2.
Example
Banking Link
5. Talisa
opened a checking account with a deposit of $25. During the next two weeks, she
wrote checks for $20 and $15 and made a deposit of $30. Find the balance in her
account.
Alternative Solutions :
Explore You know
that Talisa made deposits of $25 and $30.
She wrote
checks for $20 and $15. You want to find
the
balance in her account.
Plan Deposits
are represented by positive integers
(+25
and +30). Checks are represented by negative
integers
(–20 and –15). Write an addition sentence
and
solve.
Solve Let x
represent the balance in her account.
x = 25 + (–20) + (–15) + 30
x = 5 + (–15) + 30 25 + (–20) = 5
x = –10 + 30 5 + (–15) = –10
x = 10 –10
+ 30 = 20
The
balance in Talisa’s account is $20.
Examine Addition of
integers is commutative. So, you can check
The solution
by adding the integers in a different order.
One way
is to group all of the positive numbers and all
of the
negative numbers.
x = 25 + 30 + (–20) + (–15)
x = 55 + (–35) 25 + 30 = 55; –20 + (–15) = –35
x = 20
You can use the rules for adding integers to simplify
expressions.
Example
6.
Simplify
5x + (–3x).
Alternative Solutions :
5x + (–3x) = [5 + (–3)]x Use the Distributive Property.
= 2x 5
+ (–3) = 2
Sumber
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