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2. Confidential2 1.)(-30) + (-16) = 2.)52 + (-12) = 3.)(-22) + 45 = 4.)9 + (-60) =

3. Confidential3 Let's review what we learned in the last lesson.

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7. 7 TODAY we will be studying 2 methods to learn how to subtract integers. METHOD 1 - Zero Pairs Remember that the red chips are NEGATIVE. The grey chips are POSITIVE. + + + - -- - -

8. Confidential8 Let's subtract 6 - 2 = We begin with 6 POSITIVE (grey) chips. + + + + + + next page

9. Confidential9 Let's subtract 6 - 2 = + + + + + + Then we take away (or Subtract) 2 POSITIVE chips. next page

10. Confidential10 + + + + We are left with 4 POSITIVE (Grey) chips. So..... 6 - 2 = 4 Let's subtract 6 - 2 =

11. Confidential11 Now, let's subtract (-5) - (-4) = We begin with 5 NEGATIVE (or red) chips. -- - - - next page

12. Confidential12 Now, let's subtract (-5) - (-4) = - - - - - Then, we take away (or Subtract) 4 NEGATIVE chips. next page

13. Confidential13 Now, let's subtract (-5) - (-4) = - And we are left with 1 NEGATIVE (red) chip. Therefore, (-5) - (-4) = -1 Do you have any questions so far?

14. Confidential14 SOMETIMES we need to add Zero Pairs in order to subtract or take away chips. For example, let's subtract 5 - (-3) = We begin with 5 POSITIVE (grey) chips. + +++ + next page

15. Confidential15 5 - (-3) = We begin with 5 POSITIVE (grey) chips. + + + + Now, we need to take away (or Subtract) 3 NEGATIVE (red) chips but we don't have any!! So we must ADD 3 Zero Pairs............... - - - + + + next page + +

16. Confidential16 + + + + + -- - ++ + Now, we can take away (or Subtract) the 3 NEGATIVE (red) chips. And we are left with 8 POSITIVE (grey) chips. Therefore, 5 - (-3) = 8 5 - (-3) =

17. Confidential17 You try this one… (-4) - 1 = Use your pen to draw the red and grey circles.

18. Confidential18 Try 4 - (-2) = Use your pen to draw the red and grey circles.

19. Confidential19 METHOD 2 - Rule for Subtracting Integers When we subtract an integer, we add its opposite. For example, (-10) - 7 = (-10) + (-7) = (-17) we add its opposite

20. Mauna Loa The base of the Hawaiian volcano Mauna Loa is about 13,000 meters below sea level. Its summit is 4170 meters above sea level. In Example 3, you will use integer subtraction to find the difference between the elevations of the base and summit. In the Real World 4170 m 13,000 m

21. So, 3 – 5 = –2. To find 3 – 5, move right 3 units then left 5 units. EXAMPLE 1 Modeling Integer Subtraction Find the difference 3 – 5. When you add a positive integer, you move to the right on a number line. When you subtract a positive integer, you move to the left. 3–101254–26 ANSWER The final position is –2. To find 2 – (–4), move right 2 units then right 4 units. Find the difference 2 – (– 4). When you add a negative integer, you move to the left on a number line. So to subtract a negative integer, you move to the right. 3–101254–26 ANSWER The final position is 6. So, 2 – (– 4) = 6.

22. NOTE BOOK To subtract an integer b from an integer a, add the opposite of b to a. Subtracting Integers Words Algebra Numbers Subtracting integers As you saw in Example 1, the direction you move to subtract an integer is the opposite of the direction you would move to add the integer. You can use opposites and rules for adding integers to subtract integers. 4 – 7 = 4 + (–7) 3 – (–2) = 3 + 2 a – b = a + (–b)

23. Find the difference. –2 – (–9) To subtract –9, add its opposite. = –2 + 9 = 7 EXAMPLE 2 Subtracting Integers Find | 9 | – | –2 |. Use the sign of 9.

24. Find the difference. –2 – (–9) To subtract –9, add its opposite. To subtract 7, add its opposite. = –2 + 9 = 7 –5 – 7= –5 + (–7) = –12 EXAMPLE 2 Subtracting Integers Find | 9 | – | –2 |. Use the sign of 9. Find | –5 | + | –7 |. Use the common sign.

25. EXAMPLE 3 Using Integers to Solve Problems 1 Given that the summit of the volcano Mauna Loa is 4, 170 meters above sea level and the base of the volcano is 13, 000 meters below sea level, find the approximate difference between the elevations of Mauna Loa’s summit and base. Use integers to represent the two elevations. Summit: 4170 meters Base: –13,000 meters 2 Subtract the lesser elevation from the greater. 4170 – (–13,000)= 4170 + 13,000 = 17,170 ANSWER The difference between the elevations is 17,170 meters. To subtract –13,000, add its opposite. Simplify.

26. Confidential26 Of course, if we are going to ADD its opposite, we must remember the rules for ADDING INTEGERS. 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. Adding the Same Sign - The sum of 2 positive numbers is POSITIVE. The sum of 2 negative numbers is NEGATIVE. LET'S REVIEW

27. Confidential27 Let's try a few more subtraction problems. Remember the RULE - When we subtract an integer, we add its opposite. 9 - (-6) = 9 + 6 = 15 we add its opposite

28. Confidential28 You try a few. (-4) - (-4) =(-2) - 8 =12 - (-3) =

29. Confidential29 LET’S TAKE A BREAK!

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31. Confidential31 1.)Can you find the missing numbers? -32 + = 65 47 - = 80

32. Confidential32 2.)Anne is 8 years older than Jane and 3 years older than Mary. The sum of their ages is 67. How old is each person?

33. Confidential33 3.)Use these digits (4, 7, 9) to make as many 3 digit numbers as possible. You may only use each digit only one time in each number.

34. Confidential34 Let's see how well you understood the lesson today. Find each difference. 1.)-13 - 13 = 2.)9 - (-8) = 3.)28 - 16 =

35. Confidential35 4.)12 - 15 = 5.)0 - (-47) = 6.)-190 - 82 =

36. Confidential36 7.)(-12) - (-26) = 8.)4 - (-60) = 9.)22 - 38 = 10.)(-109) - 10 =

37. Confidential37 Let's review what we learned today. We looked at 2 different methods for SUBTRACTING integers. METHOD 1 - Using Zero Pairs + -

38. Confidential38 SOMETIMES we need to add Zero Pairs in order to subtract or take away chips. 3 - (-1) = Begin with 3 POSITIVE chips Add 1 ZERO PAIR Now we can take away 1 NEGATIVE chip And you're left with 4 POSITIVE chips 3 - (-1) = 4 + + + + -

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40. Confidential40 Great job today! Remember to practice what you learned!