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ABSOLUTE VALUE

ABSOLUTE VALUE. For each value, write it opposite, then its absolute value. Watch this:. http://virtualnerd.com/middle-math/integers-coordinate-plane/integers-absolute-value/calculate-absolue-value. opposite absolute value. -3 +3 3 4 -4 4 15 -15 15

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ABSOLUTE VALUE

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  1. ABSOLUTE VALUE For each value, write it opposite, then its absolute value. Watch this: http://virtualnerd.com/middle-math/integers-coordinate-plane/integers-absolute-value/calculate-absolue-value oppositeabsolute value • -3 +3 3 • 4 -4 4 • 15 -15 15 • -7 +7 7 • 0 0 0 • - • -1 +1 1 • - • 0.6 -0.6 0.6 • -2.5 +2.5 2.5

  2. ABSOLUTE VALUE 1. |17| 3. –|45| 2. |–29| 4. –|–247| –247 –45 17 29 –45 –247 5. –|35 + 76| 6. –|41 – 19| *7. –| – 2– 1| *8. –|–(–7)| –| 101 | –| 22 | –| – 3| –| 7 | – 101 – 22 – 3 –7 –101 –22 –3

  3. Integer Addition - With Counters –3 + 9 • Draw 3 negative counters ... • .. then 9 positive counters • Cancel opposites. +6 • What’s left? 2 + –7 • Draw 2 positive counters ... • . then 7 negative counters • Cancel opposites. –5 • What’s left? • –6 + –4 • Draw 6 negative counters ... • . then 4 negative counters • No opposites, so ... –10 • What’s left?

  4. Integer Addition - Number Line 1. –3+ 9 2. 2 +–7 3. –6+–4 Start at 0 Start at 0 Start at 0 The first integer, -3, is the first move. The first integer, 2, is the first move. The first integer, -6, is the first move. The second integer, 9, is the second move. The second integer,–7, is the second move. The second integer,–4, is the second move. Where did you end up? Where did you end up? Where did you end up? -3+ 9= 6 2+–7= -5 = -10 -6+–4

  5. Integer Addition - The Rules –3 + 9 + 6 2 + –7 – 5 –6 + –4 – 10 • What’s the sign on the bigger absolute value? • ** POSITIVE so the answer is POSITIVE ** • 2. Now, signs are DIFFERENT, so ... • 3. SUBTRACT the absolute values. • 4. Write down that number. • What’s the sign on the bigger absolute value? • ** NEGATIVE so the answer is NEGATIVE ** • 2. Now, signs are DIFFERENT, so ... • 3. SUBTRACT the absolute values. • 4. Write down that number. • What’s the sign on the bigger absolute value? • ** NEGATIVE so the answer is NEGATIVE ** • 2. Signs are SAME, so ... • 3. ADD the absolute values. • 4. Write down that number. 9 – 3 --- 6 7 – 2 --- 5 6 + 4 --- 10

  6. Integer Addition - Practice –2 –16 –6 –12 –6 4 4 0 –10 –2 –8 –1 –10 –5 1 –7 –2 5 –8 –4 –7 –9 5 –11 –10 –17 –6 –16 –2 –3 –3 –2

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

  8. Integer Subtraction - Using Counters For high school and college level math, it’s easier to think of subtraction as adding the opposite sign. I want to take away 14 positives! I want to take away 5 positives! I want to take away 7 negatives! SUBTRACTION11– 14–8 –5–4 – (–7) is the same as or or or ADDING THE OPPOSITE 11 +(–14) –8+(–5) –4+ (+7) –4– (–7) 11– 14 –8– 5 or or or –4 + (+7) 11 +(–14) –8 + (–5) or –4 + 7 +3 or 3 –3 –13

  9. Integer Subtraction – Adding the Opposite So, to change subtraction to addition… you add the opposite. KEEP  CHANGE  CHANGE To do that, remember: Please rewrite each subtraction problem as an addition problem. A. 7 – 9 B. –4 – 1 C. 3 – (–5) D. –6 – (–8) –6 (+8) + 3 (+5) + –4 7 (–1) + (–9) + E. 9 – (–4) F. 1 – 7 G. –3 – 8 H. –5 – (–2) 9 + (+4) –3 + (–8) –5 + (+2) 1 + (–7) I . –1 – (–9) J. 3 – 4 K. 5 – (–6) L. –8 – 7 5 + (+6) 3 + (–4) –1 + (+9) –8 + (–7)

  10. Integer Subtraction - The Rules 11–14 • a. CHANGE the subtraction to addition, then... • b. CHANGE the sign of the 2nd integer [ “–14” --> “+(–14)” ] • c. IGNORE the original problem. • 2. What’s the sign on the bigger absolute value? • ** NEGATIVE (–14) so the answer is NEGATIVE** • Now, signs are DIFFERENT, SUBTRACT the absolute values. • 4. Write down that number. • a. CHANGE the subtraction to addition, then... • b. CHANGE the sign of the 2nd integer [ “–5” --> “+(–5)” ] • c. IGNORE the original problem. • 2. What’s the sign on the bigger absolute value? • ** NEGATIVE (–8) so the answer is NEGATIVE** • Now, signs are SAME, so ADD the absolute values. • 4. Write down that number. • a. CHANGE the subtraction to addition, then... • b. CHANGE the sign of the 2nd integer [ “– (–7)” --> “+ (+7)” --> +7] • c. IGNORE the original problem. • 2. What’s the sign on the bigger absolute value? • ** POSITIVE (+7) so the answer is POSITIVE ** • Now, signs are DIFFERENT, SUBTRACT the absolute values. • 4. Write down that number. 11 + –14 14 – 11 --- 3 –3 – 8 – 5 – 8+–5 8 + 5 --- 13 –13 – 4 – (–7) 7 – 4 --- 3 – 4+ +7 +3

  11. Integer Subtraction - Practice 11 13 1 5 0 17 3 0 –1 2 –8 4 2 –2 –5 –2 –4 3 –8 13 0 –11 12 13 –1 6 3 3 –1 4 –2 –1

  12. More 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)

  13. Mixed Addition & Subtraction - Practice –15 –16 1 1 –1 –13 0 –15 –13 2 3 6 –1 –1 2 0 –4 –10 1 0 –7 –9 5 –11 –10 –17 –6 –16 –2 –3 –3 –2

  14. Integer Multiplication - Using Counters –4 • 5 • Draw 4 negative counters ... • ... 5 TIMES –4 • 5 = –20 Integer Division - Using Counters –28 7 • Draw 28 negative counters ... • ... then DIVIDE them into 7 groups –4 –28 7 =

  15. Integer Multiplication - Using Number Line • Draw a dot at zero 1. –6 • 3 • The 1st integer, –6 , tells you the size of the jump. –18 • The 2nd integer,3 , tells you how many TIMES. • So, jump 6 backward 3 TIMES. Integer Division - Using Number Line • Draw a dot at zero –42 3 • The 1st integer, –42 , is the total • The 2nd integer,3 , tells you into how many pieces to DIVIDE it. • So, DIVIDE the –42 into3 pieces. –14 • How big is each piece?

  16. Integer Multiplication - The Rules 1. –7 •8 When you multiply or divide integers, it’s easy: Look at the signs: • If they’re the SAME ... • then, the answer’s POSITIVE Signs are different, so the answer is negative. – 56 • If they’re DIFFERENT • then, the answer’s NEGATIVE Multiply the absolute values. Integer Division - The Rules When you multiply or divide integers, it’s easy: –90 –9 2. Look at the signs: • If they’re the SAME ... Signs are the same, so the answer is positive. • then, the answer’s POSITIVE • If they’re DIFFERENT • then, the answer’s NEGATIVE + 10 Divide the absolute values.

  17. Integer Multiplication and Division - Practice 36 36 36 36 –6 –6 –6 –6 – 4 – 4 – 4 – 4 –32 –32 –32 –32 – 7 – 7 – 7 – 7 16 16 16 16 6 6 6 6 72 72 72 72

  18. More 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.

  19. Integer Arithmetic – Add, Subtract, Multiply, & Divide 4 -10 1 7 -50 -1 -125 -5 4 3 -8 -3 -1 1 -3 -9 -7 96 -4 -3

  20. Order of Operations Simplify 3(4 - 2) - 8 ÷ 22 + 9 3 (4 - 2) - 8 ÷ 22 + 9 1. First, simplify inside parenthesis 3 (2) - 8 22 + 9 2. Next, evaluate the exponent. ÷ 3 (2) - 8 4 + 9 3. Then, multiply or divide. ÷ * Which one first? 6 ─ 2 + 9 Always work from left to right. 4 + 9 4. Finally, add or subtract. 13 Always work from left to right. So, to simplify an expression using order of operations, you should: Multiply or Divide Add or Subtract Simplify Parenthesis Evaluate Exponents

  21. Order of Operations 11 – 32 ÷ 8 • 3 2. – 7 + (– 9)(12) ÷ 2 3. 18 + (–6) ÷ 3 – (–12)(–4) 4. [48 – (12 – 14) • 2] + 8 ÷ (–8) 5. –23 + 7 – (–8 + 2) (–5 + 9)3 + (–2) 11 – 4 • 3 – 7 + (–108)÷ 2 11 – 12 – 7 + (–54) –1 –61 [48 – (–2) • 2] + 8 ÷ (–8) 18 + (–2) – (–12)(–4) [48 – (–4) ] + 8 ÷ (–8) 18 + (–2) – 48 52 + 8 ÷ (–8) 16 – 48 52 + (–1) –32 51 –23 + 7 – (–8 + 2) –10 –1 –23 + 7 – (–6) = ( 4)3 + (–2) –16 –(–6) 10 12 + (–2) denominator (bottom) = 10 numerator (top) = –10

  22. Order of Operations - PRACTICE 1) 2 – 3 ∙ –5 2) 25 ÷ –5 – 4 3) –5 + 2 – 3 4) –2 ∙ 5 + 6 5) 9 ÷ –3 ∙ 2 + 1 6) 5 + 2 ∙ –8 + 2 – 5 7) 4 + 2 ∙ 8 ÷ –4 8) –30 – 12 ∙ –2 9) 5 + 2 ∙ –3 − 4 10) –10 – 2 ∙ 4 – 1 11) 15 – 10 ÷ –2 12) 25 – (–6) ∙ 4 + 9 13) –1(14 + 6) ÷ 5 14) 4 + 50 ÷ 10 ∙ –9 15) –14 – (4 ∙ –2) 16) (3 + –4) ∙ (–5 + 3) 17) –6(4 + –9) 18) 8 ∙ –9 + 36 ÷ –4 (3 ∙ 3)–1 19) –2 + 3 ∙ –5 ÷ 5 20) 24 – 24 ÷ –1 21) 56 ÷ (–3 + –4) ∙ 6 22) –2[(2 + –5) ∙ 11]

  23. Integer Subtraction - Using Number Line 1. 11–14 2. –8 – 5 3. –4 – (–7) Start at 0. Start at 0. Start at 0. The first integer, +11, is the first move. The first integer, –8, is the first move (left). The first integer, –4, is the first move. The subtraction sign means to move to the left... The subtraction sign means move to the left... The subtraction sign also means to move to the left... ... but the negative sign reversesit, so... ...the second integer, +5, means move 5 spaces to the left. ...the second integer, +14, means move 14 to the left. ...move to the right7 spaces. Where did you end up? Where did you end up? Where did you end up? 11–14 = -3 –8 – 5 = –13 = +3 –4 – (–7)

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