1. Integers How We add and Subtract LIVE A. Gilleran
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2. What will You Learn LIVE What Integers are
Rules for adding and subtracting Integers
A way to show that a rule is true
What will You Learn
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3. Integers include positive and negative whole numbers
What is an Integer
Integers include positive and negative whole numbers
NEWS
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4. 1 2 3 4 5 6
Positive number – a number greater than zero.
Positive Numbers
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5. 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 Negative Numbers1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
Negative number – a number less than 0
Negative Numbers
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6. What are negative numbers used for?
Negative numbers are used to measure temperature
Used to measure under sea level
Negative numbers used to show debt
Negative Numbers
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7. Temperature A. Gilleran
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8. Sea Level 10 20
-10
-20
-30
-40
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9. Debt
If you owe your friend €20, you would add in -20 to your budget show that you still owe money.
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10. Question 5 6 7 8 9 10 11 12 13
If it was -3 Degrees in the morning, but by lunch it was +6 degrees. How much did the temperature go up?
Clue: If you do not see a negative or positive sign in front of the number, it is positive
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11. Question 5 6 7 8 9 10 11 12 13
If it was -3 Degrees in the morning, but by lunch it was +6 degrees. How much did the temperature go up?
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12. Integer Addition Rules
LIVE
Rule # 1 – Same Signs
If the signs are the same, pretend the signs are not there.
Add the numbers, then put the signs that the number had in front of your answer.
= 15
= -15
Integer Addition Rules
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13. You Try
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14. (+8) (+13) = ? 5 21 -5 +5
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15. (-22) + (-11) = ?
+33
-11
+11
-33
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16. (-12) + (+6) = ? +6 -6
+18
-18
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17. (-16) + (+5) = ? 11 21
-21
-11
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18. -9 + +5 = 9 - 5 = 4 Larger . value Answer = - 4 LIVE
Rule # 2 – Different Signs
If the signs are different, pretend they are not there.
Subtract the smaller from the bigger and put the sign of the bigger number in front of your answer.
= 15
= -15 =
Larger . value
Answer = - 4
9 - 5 = 4
Integer Addition Rules
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19. One Way to Add Integers Is With a Number Line
When the number is positive, count
to the right.
When the number is negative, count
to the left. - + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
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20. One Way to Add Integers Is With a Number Line= -2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -
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21. One Way to Add Integers Is With a Number Line= +2 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -
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22. One Way to Add Integers Is With a Number Line= -4 + 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 -
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23. One Way to Add Integers Is With a Number Line= +4 - 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6 +
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24. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!
Subtracting a negative number is the same as adding a positive. Change the signs and add.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!
Integer Subtraction Rules
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25. You Try
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26. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8
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27. (+12) – (-8) = ? 4 -4 20
-20
Answer Now
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28. (-3) – (-11) = ? 14
-14 8 -8
Answer Now
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29. (+12) - (+8) = ? -4 +4 20
-20
Answer Now
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30. (-3) – (+11) = ? 8 -8 11
+11
Answer Now
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31. How can we check “Subtracting a negative number is the same as adding a positive” is true?
We can use the same method we use to check our answers when we subtract.
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32. Suppose you subtract a – b and it equals c: a – b = c 5 – 2 = 3
To check if your answer is correct, add b and c:
a = b + c
5 = 2 + 3
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33. You Try
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34. a – b = c a = b + c
9 – 5 = 4 9 = 5 + 4
20 – 3 = =
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35. If the method for checking subtraction works, it should
also work for subtracting
negative numbers.
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36. Then let’s check with the negative numbers to see if it’s true…
If a – b = c, and….
2 – (-5) is the same as
2 + (+5), which equals 7,
Then let’s check with the negative numbers to see if it’s true…
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37. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works!
2 – (-5) = =
It works!
a – b = c a = b + c
-11 – (-3) = =
YES!
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38. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7)
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39. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25
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40. Review You have learned a lot about adding and subtracting integers
Let’s Review
Review
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41. Integer Addition Rules
Rule #1 – If the signs are the same, pretend the signs aren’t there.
Add the numbers and then put the sign of the numbers in front of your answer.
9 + 5 = 14
= -14
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42. Integer Addition Rules
If the signs are different pretend the signs aren’t there.
Subtract the smaller from the larger one
Put the sign of the one with the larger value in front of your answer. =
Larger value
Answer = - 4
9 - 5 = 4
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43. Integer Subtraction Rule
Subtracting a negative number is the same as adding a positive.
Change the signs and add.
2 – (-7)
is the same as
2 + (+7)
2 + 7 = 9!
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44. 6 – (-9) = 15 Discuss with a partner ways that you know that this
problem is solved correctly.
6 – (-9) = 15
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