ABSOLUTE VALUE For each value, write it opposite, then its absolute value. Watch this: opposite absolute value 1) ) ) ) ) ) ) ) ) )

ABSOLUTE VALUE 1. | 17 | |– 29 | –| 45 | 45 – –|– 247 | 247 – – – – | | –| 101 | – – – |41 – 19 | –| 22 | – –22 7. – | – 2 – 1 | –| – 3 | – 3 3 –3 8. – | –(–7) | –| 7 | –7

Integer Addition - With Counters 1. – positive.. then 9 positive counters Cancel opposites. What’s left? – 7 2 positive Draw 2 positive counters... 7 negative. then 7 negative counters Cancel opposites. What’s left? –5–5–5–5 3. – 6 + – 4 6 negative Draw 6 negative counters... 4 negative. then 4 negative counters No opposites, so... What’s left? – 10 3 negative Draw 3 negative counters....

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

1. – – 7 – 5 – 5 3. – 6 + – 4 – 10 – 10 1.What’s the sign on the bigger absolute value? ** POSITIVE so the answer is POSITIVE ** 2. Now, signs are DIFFERENT, so SUBTRACT the absolute values. 4. Write down that number. 1.What’s the sign on the bigger absolute value? ** NEGATIVE so the answer is NEGATIVE ** 2. Now, signs are DIFFERENT, so SUBTRACT the absolute values. 4. Write down that number. 1.What’s the sign on the bigger absolute value? ** NEGATIVE so the answer is NEGATIVE ** 2. Signs are SAME, so ADD the absolute values. 4. Write down that number. Integer Addition - The Rules 9– –

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

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

Integer Subtraction - Using Counters – (No Notes, Just Watch) 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! SUBTRACTION 11 – 14–8 – 5 –4 – (–7) is the same as or or or ADDING THE OPPOSITE 11 + (–14) –8 + (–5)–4 + (+7) 11 – 14 or 11 + (–14) –3 –8 – 5 or –8 + (–5) –13 –4 – (–7) or –4 + (+7) or – or 3.

1. 11 – 14 Start at 0. The first integer, + 11, is the first move....the second integer, + 14, means move 14 to the left. 11 – 14 = – 8 – 5 – 8 – 5 = –13 3. – 4 – ( – 7) = +3 – 4 – (–7) The subtraction sign means to move to the left... Start at 0. The first integer, – 8, is the first move (left). The subtraction sign also means to move to the left......the second integer, + 5, means move 5 spaces to the left. Start at 0. The first integer, – 4, is the first move. The subtraction sign means move to the left......move to the right 7 spaces. Integer Subtraction - Using Number Line– (No Notes, Just Watch)... but the negative sign reverses it, so.... Where did you end up?

. KEEP  CHANGE  CHANGE the 1 st subtraction to the sign of the the 1 st subtraction to the sign of the integer addition 2 nd integer integer addition 2 nd integer 7 + (–9) –4 + (–1) 3 + (+5) –6 + (+8) 9 + (+4)1 + (–7) –3 + (–8) –5 + (+2) –1 + (+9)3 + (–4) 5 + (+6) –8 + (–7)

– 3 – – 14 1.a.CHANGE the subtraction to addition, then... b.CHANGE the sign of the 2 nd 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** 3. Now, signs are DIFFERENT, SUBTRACT the absolute values. 4.Write down that number. 1.a.CHANGE the subtraction to addition, then... b.CHANGE the sign of the 2 nd 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** 3. Now, signs are SAME, so ADD the absolute values. 4.Write down that number. 1.a.CHANGE the subtraction to addition, then... b.CHANGE the sign of the 2 nd 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 ** 3. Now, signs are DIFFERENT, SUBTRACT the absolute values. 4.Write down that number. Integer Subtraction - The Rules 14 14– – – – 8 – 5 – 8 + – 5 – 8 + – 5 – 13 – – 4 – ( – 7) – –

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. Integer Subtraction - Practice –1 2 –4 0 –1 – –2 3 – –8 –5 – – – –1

More Integer Subtraction - Practice = – 85 = – 54 = – 65 = – 56 = – 59 = – 15 = – 84 = 79 = 4 = – 37 = – 15 = – 84 = 79 = 4 = – 37 = 60 = 93 = 98 = 97 = 36 – 16 – ( – 95) – 5 – ( – 9)

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

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

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

. Integer Multiplication and Division - Practice –6 –4 –4 –32 –7 – –21 –21 7 –6 –6 –9 – 7 – 7 4 –1 –1 –81 –81 –32 –32 –5 6 –6 4 –8 –8 –4 –4 –7 – – –35 –35 –8 – –1 –1

More Integer Multiplication and Division - Practice = – 48 = – 50 = 143 = 168 = – 105 = – 24 = 168 = – 105 = – 24 = – 70 = 70 = – 96 =288 = 24 =– 200 =288 = 24 =– 200 = – 21 = – 11 = 17 = – 5 = – 20 =

.. 1 –13 2 –1 –10 – –15 – –10 – –15 – – 12 – 12 –13 –13 –11 –11 – 16 – 16 –1 –1 –13 –13 –1 –1 –4 –4 – 10 – 10 0 – 1 – 1

Integers Operations

Order of Operations Simplify 3(4 - 2) - 8 ÷ First, simplify inside parenthesis 3(4 - 2)- 8 ÷ (2) Then, multiply or divide. * Which one first? * Which one first? Always work from left to right. Always work from left to right. 6 ─ Finally, add or subtract. 2. Next, evaluate the exponent. 4(2)3 8 So, to simplify an expression using order of operations, you should: Simplify P arenthesis Evaluate E xponents M ultiply or D ivide D ivide A dd or S ubtract Always work from left to right. Always work from left to right ÷ ÷

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

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