What Kind Of Problem Is It?

ABSOLUTE VALUEhttps://www.brainpop.com/math/numbersandoperations/absolutevalue/zoom.weml

For each value, write it opposite, then its absolute value.Watch this:opposite absolute value-3 +3 34 -4 4 15 -15 15-7 +7 70 0 01 -1 1-1 +1 1-50 +50 5010 -10 10-2.5 +2.5 2.51p.6 - Integer ArithmeticABSOLUTE VALUE1. |17| 172. |29| 293. |45| 454. |247| 247 45 2475. |35 + 76| | 101 | 101 1016. |41 19| | 22 | 22 227. | 2 1| | 3 | 3 3 8. | (7)| | 7 | 7Integer Addition - With Counters

3 + 9

.. then 9 positive countersCancel opposites.Whats left? +62 + 7Draw 2 positive counters .... then 7 negative countersCancel opposites.Whats left? 56 + 4Draw 6 negative counters .... then 4 negative countersNo opposites, so ...Whats left? 10 Draw 3 negative counters ...

.Integer Addition - Number Line

1. 3 + 9Start at 0The first integer, -3, is the first move.The second integer, 9, is the second move.-3 + 9 = 62. 2 + 7Start at 0The first integer, 2, is the first move.The second integer,7, is the second move.

2 + 7 = -53. 6 + 4= -10Start at 0The first integer, -6, is the first move.The second integer,4, is the second move.-6 + 4.Where did you end up?Where did you end up?Where did you end up?.3 + 9 + 6

2 + 7 5

6 + 4 10Whats 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.

Whats 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.

Whats 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. Integer Addition - The Rules 9 3--- 6 7 2--- 5 6+ 4--- 10.

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16 425 591736 48 18 56312 01741116226101027102Integer 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.Integer Subtraction - Using Counters (No Notes, Just Watch)For high school and college level math, its 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 11 148 5 4 (7) is the same as or or orADDING THE OPPOSITE 11 + (14) 8 + (5)4 + (+7)11 14or11 + (14)38 5or8 + (5)134 (7)or4 + (+7)or4 + 7+3 or 3.1. 11 14Start at 0.The first integer, +11, is the first move....the second integer, +14, meansmove 14 to the left.11 14 = -32. 8 58 5 = 133. 4 (7)= +34 (7)The subtraction signmeans to move to the left...Start at 0.The first integer, 8, is the first move (left).The subtraction signalso 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 signmeans 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?Where did you end up?Where did you end up?..

KEEP CHANGE CHANGE the 1st subtraction to the sign of the integer addition 2nd integer7 + (9) 4 + (1) 3 + (+5)6 + (+8)9 + (+4)1 + (7) 3 + (8)5 + (+2)1 + (+9)3 + (4) 5 + (+6)8 + (7) 311 14a.CHANGE the subtraction to addition, then...b.CHANGE the sign of the 2nd integer [ 14 --> + (14) ]c.IGNORE the original problem.

2.Whats 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.Whats 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.Whats 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. Integer Subtraction - The Rules 14 11--- 3 8+ 5--- 13 7 4--- 311 + 14 8 5 8 + 5 13 4 (7) 4 + +7+3.

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Integer Subtraction - Practice 11 01 24 011 13 17 22 311 6 4 1 385 8 12 32 5 0 421313 31More Integer Subtraction - Practice

= 85 = 54 = 65 = 56 = 59

= 15 = 84 = 79 = 4 = 37

= 60 = 93 = 98 = 97 = 36 16 ( 95) 5 ( 9)1.

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15..Integer Multiplication - Using CountersDraw 4 negative counters ... 4 5 ... 5 TIMES

4 5 = 20Draw 28 negative counters ... 28 7 428 7 =

... then DIVIDE them into 7 groups Integer Division - Using Counters.

Integer Multiplication - Using Number LineInteger Division - Using Number Line

1.6 3 Draw a dot at zeroThe 1st integer, 6 , tells you the size of the jump.The 2nd integer, 3 , tells you how many TIMES.So, jump 6 backward 3 TIMES.1842 3 Draw a dot at zeroThe 1st integer, 42 , is the total The 2nd integer, 3 , tells you into how many pieces to DIVIDE it.So, DIVIDE the 42 into 3 pieces.14How big is each piece? .Integer Multiplication - The Rules1. 7 8 When you multiply or divide integers, its easy:56 Look at the signs: If theyre the SAME ...Integer Division - The Rules2. +10 then, the answers POSITIVE If theyre DIFFERENT then, the answers NEGATIVE Multiply the absolute values.Signs are different, so the answer is negative.When you multiply or divide integers, its easy: Look at the signs: If theyre the SAME ... then, the answers POSITIVE If theyre DIFFERENT then, the answers NEGATIVE Divide the absolute values.Signs are the same , so the answer is positive.90 9...

Integer Multiplication and Division - Practice 366 432 7 16 6 72 217 69 7 4 1 81 325 66 4 8 4 7 219 263 35 8 12 1

More Integer Multiplication and Division - Practice= 48 = 50 = 143

= 168 = 105 = 24

= 70 = 70 = 96

=288 = 24 = 200

= 21 = 11 = 17

= 5 = 20 = 131.

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Integers Operations 4-50-81-7-10-125-3-396 1 -1 4 -9-4 7 -5 3 -1-3..Order of OperationsSimplify 3(4 - 2) - 8 22 + 9 1. First, simplify inside parenthesis3(4 - 2) - 8 22 + 9 (2) 3 - 8 223. Then, multiply or divide. * Which one first? Always work from left to right.6244. Finally, add or subtract.2. Next, evaluate the exponent. 4(2) 3 8So, to simplify an expression using order of operations, you should:Simplify ParenthesisEvaluate ExponentsMultiplyor DivideAddorSubtract Always work from left to right.13+ 9+ 9+ 9+ 9-Order of Operations, p. 2Order of Operations, p. 2. 11 32 8 32. 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)

Order of Operations11 4 311 12 1 7 + (108) 2 7 + (54) 6118 + (2) (12)(4)18 + (2) 48 16 48 32[48 (2) 2] + 8 (8)[48 (4) ] + 8 (8) 52 + 8 (8) 52 + (1) 51( 4 )3 + (2) 12 + (2) denominator (bottom) = 1023 + 7 (8 + 2)23 + 7 (6) 16 (6) numerator (top) = 1010 101=.

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