1. Bell Ringer 58,021.349 What is the place value of the 8?

2. Integer Operations

3. The Incredible Number Line!!!
The number line contains an infinite amount of points.
5, -6, 3.2, 1.115, 9.9 are all on the number line.
We will deal specifically with integers, which are the whole numbers on the number line.

4. What is an Integer?
A number with no fractional part.
Includes the counting numbers {1, 2, 3, ...}, zero {0}, and the negative of the counting numbers {-1, -2, -3, ...}
Examples of integers: -16, -3, 0, 1, 198
Basically integers are all positive and negative whole numbers and zero!

5. Adding Integers
Number Line – Start at the first number and move forwards or backwards.
= ?
Counters -4
Your answer is 1!!! 5

6. Huh?? Subtracting Integers
Number Line – This can get confusing, but the subtraction sign changes the direction you travel in. 3 – (-4) =
Counters – This isn’t much better! 3 -4
How did I get here?
Huh??

7. Adding Integers Rules for adding integers
Adding (when signs are the same)
Keep the sign
Add
Ex = 7
Ex. (-9) + (-4) = -13
Adding (when signs are different)
Keep the sign of the bigger digit
Subtract
Ex = 2
Ex = -3

8. Sample Additions -5 + 9 = -7 + -8 = 6 + (-12) =
1. The signs are different, so I find the difference, which is 4. The 9 is the bigger digit, so my answer is positive.
2. The signs are the same, so I add, which gives me 15. The signs are the same, so I keep the answer negative.
3. The signs are different, so I find the difference, which is 6. The -12 is the bigger digit, so my answer is negative.

9. Subtracting Integers Rules for subtracting integers
ALL subtraction problems:
Change the subtraction sign to an addition sign.
Change the sign of the second number.
Follow addition rules
Ex: 3 – (- 7) = 3 + (+7) = 10

10. Sample Subtraction 6 – 9 = -5 – (-3) =
1. Change the subtraction to addition and change the sign of the second digit. 6 – 9 = 6 + (-9) = Follow addition rules. 6 + (-9) = Change the subtraction to addition and change the sign of the second digit. -5 – (-3) = = Follow addition rules = -2

11. Multiplying and Dividing Integers
Rules for multiplying and dividing integers
Multiply/Divide
If the signs are the SAME…the answer will be POSITIVE
If the signs are DIFFERENT …the answer will be NEGATIVE
Ex • (-7) = 28
Ex. 5 • (-3) = -15
Ex ÷ (-5) = -5
Ex ÷ (-3) = 5

12. Sample Multiplying and Divding
1. The signs are different, so the answer will be negative.
5 • -8 = -40
2. The signs are the same, so the answer will be positive.
-3 • -6 = -18
3. The signs are different, so the answer will be negative.
-25 ÷ 5 = -5
4. The signs are the same, so the answer will be positive.
-6 ÷ -2 = 3
5 • -8 =
-3 • -6 =
-25 ÷ 5 =
-6 ÷ -2 =

13. Samples =
– (-9) =
3. 5 • -9 =
÷ -3 = 1 3
-45 4