Mathematical Reflections 1

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Mathematical Reflections 1

• Adding and subtracting integers

By Rose Eisenmenger
2
Adding one negative and one positive
Why does it work to switch the equation around?
In addition and multiplication, you can switch
the order of the numbers. This is called
Communtive Property, which is a Math Law.
Example -4 6

1. Choose a number to start at on the number line (I
   choose -4, but it dosent matter).

.

-10 -8 -6 -4
-2 0 2 4
6 8 10
2) Move the amount of spaces as the number you
didnt choose to start with.
3) Where you land is your answer!
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Adding One positive and one negative
Your new equation is 8 - 10

• Example 8 -10

1) Start at the number you choose on the number
line (I choose 8).
3) Where you land is your answer!
.
-10 -8 -6 -4
-2 0 2 4
6 8 10
2) To add -10, you wont go 10 spaces to the
right, you will go 10 spaces to the left. You go
to the left because, a negative sign does the
opposite of what the operation says. In this case
the operation is addition, but since there is a
negative sign you switch it to subtraction.
How do I change the operation to subtraction? You
switch the plus sign to a minus sign, and since
you are doing the opposite of what it says, you
take away the negative sign.
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Adding Two Negatives
Example -6 -5
1) Start at the number you choose (I choose -6).
3) Where you land is your answer!
.
-20 -18 -16 -14 -12
-10 -8 -6 -4
-2 0
2) The two negative numbers build onto each other
to go farther from zero. Therefore, if you start
at -6, you go five spaces away from zero (left).
Could I Change This Problem To Subtraction? Yes,
you could! You would change the plus sign to a
minus sign, and take away the negative from the
five. Your new equation would be -6 5.
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Practice Time!

• Solve the following 4 problems on a lined piece
  of paper
• -6 4 3) -8 11
• 2) -9 -7 4) 14 -2

-2
3
-16
12
6
Subtracting one negative from a positive
Your new problem would be 6 7!
Example 6 - (-7)
1) When subtracting a negative from a positive,
its the same as adding two positive numbers. To
switch it to an addition problem, you trade the
plus sign for a minus sign, and change the second
number to a positive number.
2) Now, most of you could do 6 7 without a
numberline, and you would have your answer to 6
(-7).
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Why does it work to change a subtraction problem
to an addition problem?

• Because if you change the operation sign to its
  opposite along with the second number to its
  opposite, you will reach the same answer!
• Although, if you only change the operation sign,
  then it wont work.
• Lets test this out- Is 6 (-4) this same as 6
  4?
• For 6 (-4), we know that instead of going right
  on the number line, we will go to the left.
  Imagine a number line in your head, start at 6
  and jump 4 spaces to your left. The answer is 2,
  right?
• Now if we try 6 4, we know the answer is 2
  also, right?

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Subtracting a positive from a negative

• Example -8 4

Your new equation is
-8 -4
1) You would also switch this equation to
addition by, changing the sign to a plus sign,
and putting a negative sign in front of the 4.
4) Where you land is your answer!
.
-20 -18 -16 -14 -12
-10 -8 -6 -4
-2 0
2) Next, we start at -8.
3) Now, we jump four spaces to the left since
negative numbers do the opposite of what the
operation tells us.
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Subtracting a negative from a negative

• Example (-2) (-6)

New equation (-2) 6
1) First, you should switch the equation to an
addition equation.
2) Next, start at -2.
.
-10 -8 -6 -4
-2 0 2 4 6
8 10
3) Then, you will jump 6 spaces to the right.
4) Where you land is your answer!
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Practice Time!

• Solve the following 4 problems on a lined piece
  of paper
• 1 (-6) (-9) 3 (-4) - 3
• 2 9 (-5) 4 1 (-7)

3
-7
14
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