1. Subtracting Integers 10.1

2. Subtracting Integers CCS: 6.NS.2: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

3. Subtracting Integers  OBJECTIVES:  Students will be able to:  Use Algebra tiles to subtract Integers  Use a Number line to subtract integers  Use the standard algorithm to subtract integers  Solve real world problems with Integers.

4. SUBTRACTING INTEGERS  We often think of subtraction as a “take away” operation.  Which diagram could be used to compute + 3 - + 5 = ? +3+3 +3+3

5. SUBTRACTING INTEGERS We can’t take away 5 yellow tiles from this diagram. There is not enough tiles to take away!! This diagram also represents +3, and we can take away +5. When we take 5 yellow tiles away, we have 2 red tiles left.

6. SUBTRACTING INTEGERS Use your red and yellow tiles to model each subtraction problem. - 2 - - 4 = ? - 2 - - 4 = ? ANSWER

7. SUBTRACTING INTEGERS This representation of - 2 doesn’t have enough tiles to take away - 4. Now if you add 2 more reds tiles and 2 more yellow tiles (adding zero) you would have a total of 4 red tiles and the tiles still represent - 2. Now you can take away 4 red tiles. - 2 - - 4 = + 2 2 yellow tiles are left, so the answer is…

8. SUBTRACTING INTEGERS Work this problem. Work this problem. + 3 - - 5 = ? ANSWER

9. SUBTRACTING INTEGERS Add enough red and yellow pairs so you can take away 5 red tiles. Take away 5 red tiles, you have 8 yellow tiles left. + 3 - - 5 = + 8

10. SUBTRACTING INTEGERS Work this problem. Work this problem. - 3 - + 2 = ? ANSWER

11. SUBTRACTING INTEGERS Add two pairs of red and yellow tiles so you can take away 2 yellow tiles. Take away 2 yellow tiles, you have 5 red tiles left. - 3 - + 2 = - 5

12. SUBTRACTING INTEGERS 2 - (-8) Step 1: Draw your number line and zero Step 2: Locate the beginning integer. 2

13. Sample 3 continued 2 - (-8) Step 3: Determine your direction. Step 4: Count out your moves 2 = turn left Step 5: The Answer. Where do you end up? 10 = turn right

14. Sample 4 -2 - (-5) Step 1: Draw your number line and zero Step 2: Locate the beginning integer. -2

15. Sample 4 continued -2 - (-5) Step 3: Determine your direction. Step 4: Count out your moves -2 = turn left Step 5: The Answer. Where do you end up? 3 = turn right

16. One Rule for Adding & Subtracting Integers “Always go right on the number line unless you get turned around by a subtraction or negative sign."

17. SUBTRACTING INTEGERS  Standard Algorithm: RULE: Subtract Integers by adding the opposite First…change the subtraction sign to an addition sign Second…change the second number to its opposite Third…follow the rules for adding integers.

18. 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!

19. Here are some more examples. 12 – (-8) 12 + (+8) 12 + 8 = 20 -3 – (-11) -3 + (+11) -3 + 11 = 8

20. (+12) – (-8) = ? a)4 b)-4 c)20 d)-20

21. (-3) – (-11) = ? a)14 b)-14 c)8 d)-8

22. (+12) - (+8) = ? 1.-4 2.+4 3.20 4.-20

23. (-3) – (+11) = ? 1.8 2.-8 3.11 4.+11

24. How do we know that “ 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.

25. 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

26. Here are some examples: a – b = ca = b + c 9 – 5 = 49 = 5 + 4 a – b = ca = b + c 20 – 3 = 1720 = 3 + 17

27. If the method for checking subtraction works, it should also work for subtracting negative numbers.

28. 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…

29. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! a – b = ca = b + c -11 – (-3) = -8-11 = -3 + -8 YES!

30. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Continued on next slide Check: 17 = -12 + 29

31. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5 Check: -7 = -2 + -5

32. Subtraction With Integers Video  Video on Subtracting Integers Video on Subtracting Integers

33. Classwork: Try these online Games to help you subtract integers fluently: Spider Match, Walk the Plank & Math Racing Spider MatchWalk the PlankMath Racing Homework: p.505, 2-48 Even