1.1 Adding and Subtracting Integers Objective: Add and subtract integers.
Adding Integers Ppt
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![Page 1: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/1.jpg)
Do Now
Complete the Do Now questions 1-5.
Herzog
Lesson 14a
Math Procedures
Monday October 5, 2009
![Page 2: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/2.jpg)
WELCOME TO …
Ms. Herzog’s
IntegersLesson!
![Page 3: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/3.jpg)
What is an integer???
Any whole number. It can be positive or negative.
ANSWER
Adding Integers!
Examples:
2, -5, 245, 0, 9, -1,399
![Page 4: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/4.jpg)
How do we add positive and negative integers?
Think in terms of number chips
Example: We can think of 4 as four positive chips
+4
![Page 5: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/5.jpg)
How do we add positive and negative integers?
Think in terms of number chips
Another example: We can think of -3 as three negative chips
-3
![Page 6: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/6.jpg)
How do we add positive and negative integers?
Think in terms of number chips
Another example: We can think of -8 as eight negative chips
-8
![Page 7: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/7.jpg)
How do we add positive and negative integers?
Think in terms of number chips
Another example: We can think of 6 as six positive chips
+6
![Page 8: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/8.jpg)
Let’s do an example!
Use number chips!
4 + 7
ANSWER+4
+7 11
![Page 9: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/9.jpg)
Let’s do an example!
Use number chips!
-2 + 5
ANSWER
+5 3-2
One negative chip and one positive chip cancel!
![Page 10: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/10.jpg)
Let’s do an example!
Use number chips!
3 + (-5)
ANSWER+3
-2One negative chip and one positive chip cancel!
-5
![Page 11: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/11.jpg)
Let’s do an example!
Use number chips!
-8 + 5
ANSWER
-3One negative chip and one positive chip cancel!
-8+5
![Page 12: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/12.jpg)
Let’s do an example!
Use number chips!
-3 + (-5)
ANSWER
-8There are no chips to cancel!
-5-3
![Page 13: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/13.jpg)
-3 + (-8)
-11ANSWER
-3
-8
Number Chips!
![Page 14: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/14.jpg)
4 + (-5)
-1ANSWERNumber Chips!
+4-5
![Page 15: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/15.jpg)
-3 + 9
6ANSWERNumber Chips!
-3+9
![Page 16: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/16.jpg)
Classwork 14A
• Work on problems 1-10 from the handout
Monday October 5, 2009
![Page 17: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/17.jpg)
Homework: Adding Integers Handout 1-15
HomeworkMath Procedures Herzog
Lesson 14a
![Page 18: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/18.jpg)
Do Now
Complete questions 1-5.
Herzog
Lesson 14b
Math Procedures
Tuesday October 6, 2009
![Page 19: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/19.jpg)
Let’s Continue…
Ms. Herzog’s
IntegersLesson!
![Page 20: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/20.jpg)
•So the chip method works fine for adding and subtracting smaller numbers. (e.g. -4 + 7 = 3)
•What if we need to add larger numbers? (e.g. 65 + (-34))
•Writing out 99 chips would not make sense!
![Page 21: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/21.jpg)
One way to solve these problems:
1. If the numbers you are adding have different signs,
2. Subtract the smaller number from the larger number, then
3. Determine which number is larger
4. The sign (positive or negative) of the answer will be the sign of the larger number
![Page 22: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/22.jpg)
Do the numbers have the same sign?
Yes
Add the numbers together
No
Subtract the smaller number from the larger
number
Is the positive or negative number
larger?
Answer = What sign?
+ is largerFinal answer is
positive
- is larger
Final answer is negative
![Page 23: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/23.jpg)
If the
Beginning Signs are…
Then the
Calculation we do is…
The End Sign of our answer is…
Same AddAdd Same
Different SubtractSubtract The sign of the
Larger number
![Page 24: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/24.jpg)
28 + 631. We are adding and the numbers have the same signs
2. Add:
28 + 63 = 91
ANSWER:
91
![Page 25: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/25.jpg)
(-12) + 341. We are adding and the numbers have different signs
2. Subtract:
34 – 12 = 22
3. 34 is larger than 12
4. Since 34 is larger, and positive, the answer will be positive
ANSWER:
22
![Page 26: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/26.jpg)
24 + (-42)1. We are adding and the numbers have different signs
2. Subtract:
42 – 24 = 18
3. 42 is larger than 24
4. Since 42 is larger, and negative, the answer will be negative
ANSWER:
-18
![Page 27: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/27.jpg)
-64 + 391. We are adding and the numbers have different signs
2. Subtract:
64 – 39 = 25
3. 64 is larger than 39
4. Since 64 is larger, and negative, the answer will be negative
ANSWER:
-25
![Page 28: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/28.jpg)
83 + (-46)1. We are adding and the numbers have different signs
2. Subtract:
83 – 46 = 37
3. 83 is larger than 46
4. Since 83 is larger, and positive, the answer will be positive
ANSWER:
37
![Page 29: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/29.jpg)
57 + (-74)1. We are adding and the numbers have different signs
2. Subtract:
74 – 57 = 17
3. 74 is larger than 57
4. Since 74 is larger, and negative, the answer will be negative
ANSWER:
-17
![Page 30: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/30.jpg)
-132 + 2311. We are adding and the numbers have different signs
2. Subtract:
231 – 132 = 99
3. 231 is larger than 132
4. Since 231 is larger, and positive, the answer will be positive
ANSWER:
99
![Page 31: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/31.jpg)
Classwork 14B
1. 15 + (-7)2. -7 + 153. -10 + (-18)4. -34 + 175. 73 + (-25)6. -45 + (-44)7. 55 + (-75)
8. 99 + (21)9. 82 + (-19)10.(-35) + 1711. 22 + (-111)12. 64 + (-73)13. 254 + (153)14. (-432) + (321)
![Page 32: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/32.jpg)
Homework: Adding Integers Handout 1-15
HomeworkMath Procedures Herzog
Lesson 14b
Tuesday October 6, 2009
![Page 33: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/33.jpg)
![Page 34: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/34.jpg)
Subtracting
IntegersLesson!
![Page 35: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/35.jpg)
Subtracting Integers
Let’s start with signs
What is the sign on:
17
Positive
![Page 36: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/36.jpg)
Subtracting Integers
Let’s start with signs
What is the sign on:
-68
Negative
![Page 37: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/37.jpg)
Subtracting Integers
Let’s start with signs
What is the sign on:
5
Positive
![Page 38: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/38.jpg)
Subtracting Integers
Let’s start with signs
What is the sign on:
-22
Negative
![Page 39: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/39.jpg)
Subtracting Integers
Now let’s work on opposites
What is the opposite of:
12-12
![Page 40: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/40.jpg)
Subtracting Integers
Now let’s work on opposites
What is the opposite of:
-4545
![Page 41: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/41.jpg)
Subtracting Integers
Now let’s work on opposites
What is the opposite of:
-99
![Page 42: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/42.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of 11
9 - 11
9 + (-11)
Evaluate using integer addition 9 + (-11)
= -2
![Page 43: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/43.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of 8
-6 - 8
-6 + (-8)
Evaluate using integer addition -6 + (-8) =
-14
![Page 44: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/44.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of -9
-9 – (-9)
-9 + (9)
Evaluate using integer addition -9 + (9) = 0
![Page 45: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/45.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of -1
5 – (-1)
5 + (1)
Evaluate using integer addition 5 + (1) = 6
![Page 46: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/46.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of 10
-4 – (10)
-4 + (-10)
Evaluate using integer addition -4 + (-10)
= -14
![Page 47: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/47.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of -8
2 – -8
2 + 8
Evaluate using integer addition 2 + 8 = 10
![Page 48: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/48.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of -5
-3 – (-5)
-3 + 5
Evaluate using integer addition -3 + 5 = 2
![Page 49: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/49.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of 21
12 – 21
12 + (-21)
Evaluate using integer addition 12 + (-21)
= -9
![Page 50: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/50.jpg)
Subtracting IntegersTo subtract
integers:
Add the opposite of 5
and 2
-3 – 5 – 2
-3 + (-5) + (-2)
Evaluate using integer addition = 10
![Page 51: Adding Integers Ppt](https://reader033.fdocuments.net/reader033/viewer/2022061206/5482f6615806b510058b4754/html5/thumbnails/51.jpg)
Classwork
1. 18 – (-48)
2. 0 – (-14)
3. 19 – (-10)
4. -20 – 32
5. -1 – (-31)
6. -22 – (-9)
7. 39 – (-13)
8. 2 – (-31)
9. 0 - 14
10.42 – 2711.-43 – 1912.3 – (-18)13. -9 – (-39)14.3 – (-24)15. -47 – 4816.-45 – (-33)17. 2 – (-8)18. -14 – (-50)