1. Confidential Adding Positive and Negative Integers

2. Confidential WARM-UP 1) 1)Order from least to greatest 7, -3, 0, -1, 3 -3, -1, 0, 3, 7 2)Insert a) -15 > -16 b) 1 < 2 3)Find the sum: 748 + 93 = 841

3. Confidential Let's review what we learned in the last lesson A variable is a letter that stands for a number We use variables when we don’t know the number A variable can be any letter

4. Confidential A VARIABLE EXPRESSION contains a variable and an operation such as addition, subtraction, multiplication, division. We can also write VARIABLE EXPRESSIONS such as s + 9 8 n 16 x h Review

5. Confidential Word phrases can be translated into VARIABLE EXPRESSIONS Word Phrase Variable Expression 2 more than n 2 + n k times 8 k x 8

6. Confidential The absolute value of a number is its distance from zero on the number line The absolute value of 4 is written as 4 The absolute value is always positive! Absolute Value

7. Confidential Opposites

8. Confidential When we add an integer and its opposite, the sum is zero EXAMPLES: (-5) + 5 = 0 98 + (-98) = 0 Opposites are also called ADDITIVE INVERSES.

9. Confidential 6/1/2 Adding Integers Today we are going to learn how to add integers. We will explore 3 different METHODS METHOD 1 - ZERO PAIRS + The red chips are NEGATIVE. The grey chips are POSITIVE - - - - + +

10. Confidential - + 1 red chip1 grey chip + = 0 We call 1 red chip and 1 grey chip a ZERO PAIR Zero Pair

11. Confidential We begin with 3 grey chips And we add 2 more grey chips FOR A TOTAL OF 5 GREY CHIPS If we want to add 3 + 2 ++ ++ + 3 + 2 = 5 Lets take an Example

12. Confidential We begin with 2 red chips And we add 4 more red chips - - - - - - FOR A TOTAL OF 6 RED CHIPS. -2 + (-4) = -6 Do you have any questions so far???? If we want to add -2 + (-4) Remember red chips are negative are negative

13. Confidential + BUT if we want to add integers with different signs, we must use ZERO PAIRS - These 2 chips form a ZERO PAIR. These 2 chips equal zero. Adding integers with different signs

14. Confidential - Let's add (-5) + 3 We begin with 5 red chips And we add 3 grey chips + ++ - - - - - Lets see with an Example

15. Confidential Adding (-5) + 3 We begin with 5 red chips And we add 3 grey chips We circle the Zero Pairs and remove them! (Remember a ZERO PAIR equals zero.) - - - - - + + +

16. Confidential We begin with 5 red chips And we add 3 grey chips We are now left with 2 red chips OR -2 Therefore, (-5) + 3 = -2 -- Result

17. Confidential You try a few. Use your red and black pens to make your chips. (-3) + 1 =4 + (-5) = - + -- -3 + 1 = (-2) ----- + + + + 4+(-5) = (-1)

18. Confidential METHOD 2 - Number Line We can use a number line to find the sum of 2 integers. 10234567 89 10 -2-3-4-5-6-7-8-9-10 WE ALWAYS START AT ZERO!

19. Confidential 1. Start at zero and move to the right (in a positive direction) 3 spaces. 2. Next, move further to the right 4 spaces. 3. Your answer is 7. Lets add 3 + 4 by number line 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10 3 + 4 = 7 1. 2.

20. Confidential Now, let's add (-2) + (-8) 1. Start at zero and move to the left (in a negative direction) 2 spaces. 2. Next, move further to the left 8 spaces. 3. Your answer is -10. (-2) + (-8) = -10 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10

21. Confidential Let's see what happens when we add a positive AND a negative number. (-6) + 8 = 1. 1.Start at zero and move to the left (in a negative direction) 6 spaces. 2. Next, move to the RIGHT 8 spaces. 3. Your answer is 2. as (-6) + 8 = 2 DO YOU HAVE ANY QUESTIONS?? 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10

22. Confidential You try a couple..... 4 + (-7) = (-3) 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10 Start at zero and draw your arrows! 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10 (-2) + (-5) = (-7) Start at zero and draw your arrows!

23. Confidential Method 3 - Rules for adding integers Adding the The sum of 2 positive numbers is POSITIVE. Same sign The sum of 2 negative numbers is NEGATIVE. Example: 4 + 7 = 11 (-3) + (-6) = (-9) 11 + 8 = (-9) + (-1) = 19 -10

24. Confidential Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Example:(-2) + 9 = 1.)2 9 Absolute Values 2.)9 - 2 Step Subtract Step3.) +7 Sign of the larger number

25. Confidential Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer. Step 1.) Step 2.) Step 3.) Try (-11) + 5 = Absolute Values Subtract Sign of the larger number 11, 5 11 – 5 = 6 - 6

26. Confidential 1.)The temperature in Minneapolis was 7 degrees F at noon. By 8 pm, the temperature had dropped 15 degrees F. What was the temperature at 8 pm? 7 – 15 = (-8)

27. Confidential 2.)You have $60 in your bank account. You withdraw (or take out) $45 to buy new tires for your bike. You then deposit (or add in) your babysitting money of $18.What is the new balance in your bank account? 60 – 45 + 18 = 33

28. Confidential Let's see how well we understood the lesson today. Use a number line to find each sum. 1.)(-7) + 12 = 5 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10 102 34567 89 10 -2 -3-4-5-6-7-8-9 -10 2.)4 + (-10) = (-6)

29. Confidential Find each sum. Remember your Addition Rules! 3.)(-7) + (-11) = (-18) 4.)12 + (-5) = 7 5.)22 + 7 = 29 6.)(-9) + 5 = (-4) 7.)3 + (-10) = (-7) 8.)(-8) + 20 = 12 9.)1 + (-30) = (-29) 10.)(-15) + (-5) = (-20) 11.) Opposites are also called ADDITIVE INVERSE.

30. Confidential Let's Review... We can add integers using ZERO PAIRS. There are 3 METHODS we can use to Add Integers. METHOD 1

31. Confidential To add (-5) + 3 = Then we are left with 2 red chips. Therefore, (-5) + 3 = -2

32. Confidential We can also use a number line to find the sum of 2 integers. METHOD 2.

33. Confidential METHOD 3 Adding the Same Sign – The sum of 2 positive numbers is POSITIVE. The sum of 2 negative numbers is NEGATIVE. Rules Adding Different Signs - 1. Find the absolute value of the 2 numbers. 2. Subtract the smaller number from the larger number. 3. Take the sign of the larger number for your answer.

34. Confidential You had a great lesson today! Be sure to practice what you learned!