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# Chapter 2

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McDougal Littell Math Course 3
NYS edition

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### Chapter 2

1. 1. Chapter 2 Integers + - * ÷
2. 2. Integers <ul><li>Integers- Negative and Positive whole numbers. INCLUDES 0 </li></ul><ul><li>Write some integers on your paper: </li></ul><ul><li>…-4, -3, -2, -1, 0, 1, 2, 3, 4… </li></ul>
3. 3. Ordering integers <ul><li>Order the following from least to greatest: </li></ul><ul><li>-7, 2, -1, 0, -2 </li></ul><ul><li>-7, -2, -1, 0, 2 </li></ul><ul><li>9, -4, 12, -11, -1 </li></ul><ul><li>-11, -4, -1, 9, 12 </li></ul><ul><li>3) 0, -99, 44, -60, 16 </li></ul><ul><li>-99, -60, 0, 16, 44 </li></ul>
4. 4. Absolute Value <ul><li>Absolute Value- The distance between the number and zero on a number line. </li></ul><ul><li>The absolute value of n looks like: │ n │ </li></ul><ul><li>Find the absolute value of the following: </li></ul><ul><li>│ 6 │ │ -8 │ │ 15 │ </li></ul>
5. 5. Opposite <ul><li>Opposite of a number- same distance from 0. On different sides of 0. Opposite numbers have the same AV. </li></ul><ul><li>Find the opposite: </li></ul><ul><li>-6 </li></ul><ul><li>14 </li></ul><ul><li>-27 </li></ul>
6. 6. Evaluate: <ul><li>- │ 8 │ </li></ul><ul><li>- │ -5 │ </li></ul><ul><li>(-6) </li></ul><ul><li>-(- 4) </li></ul>
7. 7. Do Now 9/30 <ul><li>Write the opposite and Absolute Value: </li></ul><ul><li>18 </li></ul><ul><li>-45 </li></ul><ul><li>-16 </li></ul><ul><li>Evaluate: </li></ul><ul><li>4) -(-2) </li></ul><ul><li>5) - │ -18 │ </li></ul>
8. 8. Adding Integers – Number Line <ul><li>Use your number line to add integers: </li></ul><ul><li>Positive numbers right, Negative numbers left </li></ul><ul><li>3 + (-4) </li></ul><ul><li>-5 + 2 </li></ul><ul><ul><li>Start at zero </li></ul></ul><ul><ul><li>Move 3 units to the right </li></ul></ul><ul><ul><li>Move 4 units to the left </li></ul></ul><ul><ul><li>1) Start at zero </li></ul></ul><ul><ul><li>2) Move 5 units to the left </li></ul></ul><ul><ul><li>3) Move 2 units to the right </li></ul></ul>
9. 9. Adding Integers – Number Line <ul><li>Use your number line to add integers: </li></ul><ul><li>Positive numbers right, Negative numbers left </li></ul><ul><li>3) -6 + -1 </li></ul><ul><li>4) -4 + 2 </li></ul><ul><ul><li>1) Start at zero </li></ul></ul><ul><ul><li>2) Move 6 units to the left </li></ul></ul><ul><ul><li>3) Move 1 unit to the left </li></ul></ul><ul><ul><li>1) Start at zero </li></ul></ul><ul><ul><li>2) Move 4 units left </li></ul></ul><ul><ul><li>3) Move 2 units right </li></ul></ul>
10. 10. Do Now 10/1/09 <ul><li>Add using a number line: </li></ul><ul><li>7 + (-10) </li></ul><ul><li>-2 + ( -3) </li></ul><ul><li>-8 + 5 </li></ul><ul><li>5 + 3 </li></ul>
11. 11. Adding Integers- Walking on a number line <ul><li>-2 + 4 </li></ul><ul><li>7 + (-8) </li></ul><ul><li>-6 + -3 </li></ul><ul><li>5 + (-4) </li></ul><ul><li>-8 + 3 </li></ul><ul><li>-2 + (-7) </li></ul><ul><li>12 + (-8) </li></ul><ul><li>-16 + 9 </li></ul>9) 9 + (-11) 10) -6 + 14 11) 17 + (-7) 12) -14 + - 6 13) 7 + (-4) 14) -8 + 8 15) -12 + (-7) 16) 15 + (-8) 17) 19 + (-11) 18) -16 + 3 19) 7 + (-7) 20) -16 + - 2 21) 15 + (-8) 22) -8 + 3 23) -12 + (-2) 24) 19 + (-7)
12. 12. What are the Adding Integer RULES?! <ul><li>Write a rule for: </li></ul><ul><li>(+) + (+) </li></ul><ul><li>(-) + (- ) </li></ul><ul><li>( - ) + (+) / (+) + (- ) </li></ul>
13. 13. Adding Integers - Integer song: <ul><li>Integer Operations Song </li></ul><ul><li>( Row Row Row Your Boat) </li></ul><ul><li>Same sign - add and keep </li></ul><ul><li>Different sign - subtract </li></ul><ul><li>Keep the sign of the bigger number </li></ul><ul><li>Then you’ll be exact. </li></ul>
14. 14. Adding Integers – Using the Song <ul><li>1) -3 + -4 </li></ul><ul><li>2) -8 + -5 </li></ul><ul><li>7) 33 + -15 </li></ul><ul><li>8) -29 + -64 </li></ul>3) -20 + -30 4) 7 + -8 9) -47 + -20 10) -8 + 75 5) -6 +1 +-3 6) 4 + -7 + -11 11) 7 + -13 + 6 12) -19 + 48 + -5
15. 15. Do Now 10/5 <ul><li>Add: </li></ul><ul><li>-35 + 42 </li></ul><ul><li>-64 + -37 </li></ul>3) 73 + -19 4) -128 + -84
16. 16. Adding Integers – Zero Pairs <ul><li>zero pairs- is a pair of numbers whose sum is zero. </li></ul><ul><li>4 + -7 </li></ul><ul><li>3 + -2 </li></ul><ul><li>-6 + 5 </li></ul><ul><li>-3 + - 4 </li></ul>
17. 17. Subtracting Integers – Add Opposite <ul><li>Subtract Integers- Add the opposite of the second number. </li></ul><ul><li>11 – 12 </li></ul><ul><li>-5 – 3 </li></ul><ul><li>-7 – (-6) </li></ul><ul><li>8 – (-2) </li></ul>
18. 18. Do Now 10/7/09 <ul><li>Subtract – Add the opposites </li></ul><ul><li>-6 – 9 </li></ul><ul><li>72 – 114 </li></ul><ul><li>-18 – (-88) </li></ul><ul><li>25 – (-93) </li></ul>
19. 19. Subtracting Integers –Song <ul><li>Subtract – no, don’t do! </li></ul><ul><li>Just change the second sign </li></ul><ul><li>Now add the numbers like you did </li></ul><ul><li>And then you will be fine </li></ul>
20. 20. Subtracting Integers – Using the song <ul><li>1) -3 – (-4) </li></ul><ul><li>2) -8 – (-5) </li></ul><ul><li>7) 33 – (-15) </li></ul><ul><li>8) -29 - 64 </li></ul>3) 20 – (-30) 4) 7 – (-8) 9) -47 – (-20) 10) -8 - 75 5) -6 - 1 - 3 6) 4 - (-7) – (-11) 11) 7 – (-13) - 6 12) -19 - 48 – (-5)
21. 21. Do Now- 10/8/09 <ul><li>Subtract: </li></ul><ul><li>-8 – (-3) </li></ul><ul><li>- 74 – 19 </li></ul><ul><li>-56 – (-32) </li></ul><ul><li>43 – 93 </li></ul>
22. 22. Adding and Subtracting Integers <ul><li>Be careful, you have to decide which rule to follow (adding or subtracting) </li></ul><ul><li>-54 + 84 </li></ul><ul><li>- 35 – 32 </li></ul><ul><li>49 – 9 </li></ul><ul><li>23 + -84 </li></ul><ul><li>-34 - 63 </li></ul>6) - 5 – 28 7) 19 – 57 8) 38 + -45 9) -79 + -11 10) -42 – 34
23. 23. Do Now 10/14/09 <ul><li>Add or subtract: </li></ul><ul><li>14 + -12 </li></ul><ul><li>48 – 59 </li></ul><ul><li>-71 + - 34 </li></ul><ul><li>-84 - 49 </li></ul>
24. 24. Multiplying and Dividing Integers- <ul><li>Multiply and Divide numbers </li></ul><ul><li>as you normally do. </li></ul><ul><li>-If both signs are positive or negative the answer is positive </li></ul><ul><li>-If one sign is positive and one sign is negative the answer is negative </li></ul>
25. 25. Multiply and Divide <ul><li>-12 ÷ 3 </li></ul><ul><li>-14 * -7 </li></ul><ul><li>-35 ÷ -5 </li></ul><ul><li>6 * -5 </li></ul><ul><li>5) 49 ÷ -7 </li></ul><ul><li>6) -30 ÷ -10 </li></ul><ul><li>7) -7 * 3 </li></ul><ul><li>8) -9 * -2 </li></ul>
26. 26. Do Now 10/15 <ul><li>1) 20 * (-3) </li></ul><ul><li>2) 16 ÷ (-8) </li></ul><ul><li>3) -40 ÷ (-20) </li></ul><ul><li>4) -8 * 5 </li></ul>
27. 27. Multiplying and Dividing with Zeros <ul><li>Zero – 0 </li></ul><ul><li>Multiplying- </li></ul><ul><li>0 * -32 = 0 </li></ul><ul><li>Dividing- </li></ul><ul><li>0 ÷ -4 = 0 = </li></ul><ul><li> -4 </li></ul><ul><li>-4 ÷ 0= -4 = </li></ul><ul><li>0 </li></ul>0 undefined = u
28. 28. Multiplying and Dividing Integers- Song <ul><li>Multiply or Divide - what do I do now? </li></ul><ul><li>Same sign- positive – </li></ul><ul><li>Different sign- negative </li></ul><ul><li>I got it now KERPOW!! </li></ul>
29. 29. Multiplying and Dividing Integers- Song <ul><li>-10 ÷ 5 </li></ul><ul><li>-2 * -7 * 5 </li></ul><ul><li>-90 ÷ -5 </li></ul><ul><li>6 * -3 * -3 </li></ul>5) 49 ÷ -7 6) -110÷ -10 7) -7 * -4 * -2 8) -9 * -12
30. 30. Do Now 10/16 <ul><li>Add/subtract/Multiply and Divide </li></ul><ul><li>5 + -3 </li></ul><ul><li>-3 * 7 </li></ul><ul><li>-28 ÷ -2 </li></ul><ul><li>14 – (-8) </li></ul>
31. 31. Peer Grading of projects <ul><li>Tell what Grade you should get and why on back of rubric. </li></ul><ul><li>Show each other all the rules on your project. (check that each person included all parts of the rules) </li></ul><ul><li>Show each other all the real life examples on your project. (check that there are atleast 3 and that they are different ideas). </li></ul>
32. 32. Do Now: Identify the following properties of Math (use your text if you forgot): <ul><li>1- Identity Property- </li></ul><ul><li>Sum of a number and zero = the number </li></ul><ul><li>Product of a number and 1 = the number </li></ul><ul><li>a + 0 = a </li></ul><ul><li>b * 1 = b </li></ul><ul><li>2- Commutative Property- </li></ul><ul><li>Can add or multiply numbers in any order </li></ul><ul><li>a+b = b +a cd= dc </li></ul><ul><li>3-Associative Property- </li></ul><ul><li>Changing the grouping will not affect the sum or product </li></ul><ul><li>a + (b+c) = (a + b) + c abc= cba </li></ul>
33. 33. <ul><li>Distributive Property- You can multiply a number and a sum by multiplying the number by each part of the sum and then adding these products. The same applies to subtraction. </li></ul>A(B + C) = AB + AC D(E – F) = DE – DF
34. 34. <ul><li>Ex1: -5 (x + 10) </li></ul><ul><li>-5 x + -5 (10) </li></ul><ul><li>= -5x + -50 or </li></ul><ul><li> = -5x – 50 </li></ul>
35. 35. <ul><li>Ex2: 2 (x - 7) </li></ul><ul><li>2 x - 2 (7) </li></ul><ul><li>= 2x - 14 </li></ul>
36. 36. <ul><ul><li>Ex3: 3 [x – 20 + (-5)] </li></ul></ul><ul><ul><ul><li>3 (x) – 3 (20) + 3 (-5) </li></ul></ul></ul><ul><ul><ul><li>3x – 60 + (-15) </li></ul></ul></ul><ul><ul><ul><li> 3x + (-60) + (-15) </li></ul></ul></ul><ul><ul><ul><li>3x + (-75) </li></ul></ul></ul>
37. 37. Simplify using Distributive Property <ul><li>1) -2 (5 + 12) </li></ul><ul><li>2) -4(-7 – 10) </li></ul><ul><li>3) 2(w – 8) </li></ul><ul><li>4) -8(z + 25) </li></ul>
38. 38. Tell Which property each displays: Do Now 10/28 <ul><li>1) 3(2x + 1)= 6x +3 </li></ul><ul><li>2) (2 + 4) + y = 2 + (4 + y) </li></ul><ul><li>4x = x*4 </li></ul><ul><li>6(2*15)= (6*2)15 </li></ul>
39. 39. Like Terms- Identical variable parts raised to the same power <ul><li>For example: 2m and 14m </li></ul><ul><li>3x 4 and 12x 4 </li></ul><ul><li> 12xy 2 z and xy 2 z </li></ul><ul><li>3 and 62 </li></ul><ul><li>Write 3 more examples on your page: </li></ul>
40. 40. Simplify the expression by combining like terms: <ul><li>c + 8c </li></ul><ul><li>3m + -4m </li></ul><ul><li>15y 2 + 9y + 11y 2 </li></ul><ul><li>-5x -7t +2x -9t </li></ul>
41. 41. Like Terms- <ul><li>5x – 2x </li></ul><ul><li>2a + 3a </li></ul><ul><li>7p – 3p + 25 </li></ul><ul><li>10k + 21+ -8k </li></ul><ul><li>13z + 7 - 5z </li></ul>
42. 42. Simplify the expressions: <ul><li>9w (w + -4) </li></ul><ul><li>8(1 +4d) – 3d </li></ul><ul><li>9p – ( 7p + 2) </li></ul><ul><li>11(2g - 4) +12 -18g </li></ul>
43. 43. Solve Equations Involving Distribution <ul><li>3(x – 9) = -39 </li></ul><ul><li>z + 4(6 – z) = 21 </li></ul><ul><li>8 = -7(y + 1) + 2y </li></ul>