1. MATHEMATICAL REFLECTIONS 1 ADDING AND SUBTRACTING INTEGERS By Rose Eisenmenger

2. ADDING ONE NEGATIVE AND ONE POSITIVE Example: -4 + 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 1)Choose a number to start at on the number line (I choose - 4, but it dosen’t matter).. 2) Move the amount of spaces as the number you didn’t choose to start with. 3) Where you land is your answer! 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”.

3. ADDING ONE POSITIVE AND ONE NEGATIVE Example: 8 + -10 1) Start at the number you choose on the number line (I choose 8). -10 -8 -6 -4 -2 0 2 4 6 8 10 2) To add -10, you won’t 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. Your new equation is… 8 - 10. 3) Where you land is your answer!

4. ADDING TWO NEGATIVES Example: -6 + -5 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 1) Start at the number you choose (I choose -6). 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. 3) Where you land is your answer!

5. PRACTICE TIME! Solve the following 4 problems on a lined piece of paper: 1)-6 + 4 3) -8 + 11 2) -9 + -74) 14 + -2 = -2 = -16 = 3 = 12

6. SUBTRACTING ONE NEGATIVE FROM A POSITIVE Example: 6 - (-7) 1) When subtracting a negative from a positive, it’s 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. Your new problem would be: 6 + 7! 2) Now, most of you could do 6 + 7 without a numberline, and you would have your answer to 6 – (-7).

7. WHY DOES IT WORK TO CHANGE A SUBTRACTION PROBLEM TO AN ADDITION PROBLEM? Because if you change the operation sign to it’s opposite along with the second number to it’s opposite, you will reach the same answer! Although, if you only change the operation sign, then it won’t work. Let’s 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?

8. SUBTRACTING A POSITIVE FROM A NEGATIVE Example: -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. Your new equation is…-8 + -4 2) Next, we start at -8. -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 3) Now, we jump four spaces to the left since negative numbers do the opposite of what the operation tells us.. 4) Where you land is your answer!

9. SUBTRACTING A NEGATIVE FROM A NEGATIVE Example: (-2) – (-6) 1) First, you should switch the equation to an addition equation. New equation: (-2) + 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 2) Next, start at -2.. 3) Then, you will jump 6 spaces to the right. 4) Where you land is your answer!

10. 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 = 14 = -7 =8