Then, around 1 st grade, you learned about zero, and you started calling them whole numbers.

1. These are all the real numbers. If a number doesn’t fall into any of those categories – but you can write it as a fraction, it’s just called a rational number If you can’t write the number as a fraction, it’s an irrational number. Around 4th grade, you start hearing about negative numbers, and you start calling them integers. -2, -1, 0, 1, 2… Then, around 1st grade, you learned about zero, and you started calling them whole numbers. 0, 1, 2, 3, … 4.561… π The first kind of rational number you learned was called a natural number. 1, 2, 3, …

2. CLASSIFYING RATIONAL NUMBERS W , Z , Q Q N , W , Z , Q N , W , Z , Q Q N , W , Z , Q Q Q Q Z , Q N , W , Z , Q Z , Q Q Q Z , Q

3. rational irrational integer whole natural

4. 200 0 -11 -1.08 200 200 200 0 0 0 -11 -11 -11 -1.08 -1.08 -1.08 rational integer irrational whole natural

5. 1 -87 π 1 1 1 -87 -87 -87 π π π rational irrational integer whole natural

6. rational irrational integer whole natural

7. rational irrational integer whole natural

8. ABSOLUTE VALUE For each value, write it opposite, then its absolute value. Watch this: http://vn2.me/AQKD oppositeabsolute value • -3 +3 3 • 4 -4 4 • 15 -15 15 • -7 +7 7 • 0 0 0 • 1 -1 1 • -1 +1 1 • -50 +50 50 • 10 -10 10 • -2.5 +2.5 2.5

9. ABSOLUTE VALUE – │14│ -│7│ 17 –14 – 7 16 - │ 10 │ 16 - 10 6 – 15 + 16 +1 1 8 4 – 19 –15 16 – 5 11 – │2│+ 19 – 2 + 19 17

10. Integer Addition - Number Line 1. –3 + 9 2. 2+–7 3. –6+–4 It’s an addition problem. It’s an addition problem. It’s an addition problem. The first integer, -3, is the location, The first integer, 2, is the location, The first integer, -6, is the location, The second integer, 9, is the movement. The second integer, –7, is the movement. The second integer, –4, is the movement. -3 + 9 = 6 2+ –7 = -5 -6+–4 = -10

11. Integer Addition - The Rules –3 + 9 9 –3 6 +6 5 + –8 8 –5 3 –3 –2 + –6 2 + 6 8 –8 • Signs are DIFFERENT. • SUBTRACT the absolute values. • Write down that number. • The answer is POSITIVE because the bigger • absolute value (9) is positive. • Signs are DIFFERENT. • SUBTRACT the absolute values. • Write down that number. • The answer is NEGATIVEbecause the bigger • absolute value (-8) is negative. • Signs are SAME. • ADDthe absolute values. • Write down that number. • The answer is NEGATIVEbecause both • integers are negative.

12. Integer Addition - Practice = –34 = –15 = –31 = –26 = –28 = 1 = 6 = –7 = 9 = –8 = –7 = 14 = –12 = 25 = –31 = –11 = 6 = 65 =–80= 41

13. Integer Subtraction - Number Line 1. 3 – 9 2. –2––7 3. –6–3 It’s a subtraction problem. It’s a subtraction problem. It’s a subtraction problem. The first integer, +3, is the location, The first integer, –2, is the location, The first integer, –6, is the location, The subtraction sign means move to the left... The subtraction sign means move to the left... The subtraction sign means move to the left... ...the second integer, +9, means move 9 spaces. ...but, the second integer, –7, means reverse direction, then move 7 spaces. ...the second integer, +3, means move 3 spaces. 3 – 9= -6 –2––7 = 5 –6–3 = -9

14. Integer Subtraction - The Rules 4 – 10 4 + –10 10 – 4 6 –6 –7 – 1 – 7 + –1 7 + 1 8 –8 –1 – –3 – 1 + +3 3– 1 2 +2 • Change the subtraction to addition, then... • ...change the sign of the 2nd integer. • Signs are DIFFERENT. • SUBTRACT the absolute values. • Write down that number. • The answer is NEGATIVEbecause the bigger • absolute value (–10) is negative. • Change the subtraction to addition, then... • ...change the sign of the 2nd integer. • Signs are SAME. • ADDthe absolute values. • Write down that number. • The answer is NEGATIVEbecause both • integers are negative. • Change the subtraction to addition, then... • ...change the sign of the 2nd integer. • Signs are DIFFERENT. • SUBTRACT the absolute values. • Write down that number. • The answer is POSITIVEbecause the bigger • absolute value (+3) is positive.

15. Integer Subtraction - Practice = –85 = –54 = –65 = –56 = –59 = – 15 = – 84 = 79 = 4 = –37 = 60 = 93 = 98 = 97 = 36 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. – 16 – ( – 95) – 5 – ( – 9)

16. Integer Multiplication Watch this: http://nlvm.usu.edu/en/nav/frames_asid_322_g_1_t_1.html?from=topic_t_1.html There’s a number smashed next to parenthesis. 1. –7(8) = Why is this multiplication? When you multiply or divide integers, it’s easy: 7 • 8 Step 1: Multiply (or divide) the absolute values. Step 2: Now, look the signs: – 56 • If they match... it’s positive • If they’re different... it’s negative Integer Division Why is this division? Fractions are division. 2. = +10 When you multiply or divide integers, it’s easy: Step 1: Multiply (or divide) the absolute values. or Step 2: Now, look the signs: 10 • If they match... it’s positive • If they’re different... it’s negative

17. Integer Multiplication and Division - Practice 1. 2. 3. 4. = –48 = –50 = 143 = 168 = –105 = – 24 = – 70 = 70 = – 96 =288 = 24 =– 200 = – 21 = – 11 = 17 = – 5 = – 20 = 13 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

18. Integers Operations 4 -10 1 7 -50 -1 -125 -5 4 3 -8 -3 -1 1 -3 -9 -7 96 -4 -3

19. Integers Operations 1. The change in elevation from the top to the bottom of the Grand Canyon is -1.83 km. A tour guide hikes down to the bottom every day for a week, but rides an ATV back up. For the week, what is the total change in elevation that he hiked? 2. Lina started the week with a checking account balance of $496. During the week, she wrote a check in the amount of $58.50, another check in the amount of $147.29, and then made a deposit in the amount of $180.00. What was her checkbook balance after this deposit? -12.81 km $470.21 3. The temperature at 10 P.M. one evening was 7oC. At 4 A.M. the next morning the temperature was - 3oC . What was the change in temperature from 10 P.M to 4 A.M.? 4. Samantha has $688.52 in her checking account. If she makes a withdrawal of $127.78, what will be the new balance? $560.74 -10oC 5. Jared and Natalie were playing basketball. After playing for a long time, Jared was losing by six points. Then he scored ten points in a row, but Natalie scored the next five points. Then they had to stop playing. Who won and by how many points? Natalie won by a point. 6. Gertrude plays bingo every Tuesday. In the last 5 weeks, she has lost $7, lost $4, won $8, lost $9, and won $2. What was her average weekly gain or loss? $-2 or $2 loss