Intro To Integers

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Intro To Integers
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Integers
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-1.24
-3.4
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90
Integers
-21
4
1/2
0
-50
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Integers

• Integers are whole numbers that describe opposite
  ideas in mathematics.
• Integers can either be negative(-), positive()
  or zero.
• The integer zero is neutral. It is neither
  positive nor negative, but is an integer.
• Integers can be represented on a number line,
  which can help us understand the valve of the
  integer.

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Positive Integers

• Are to the right of zero
• Are valued greater than zero.
• Express ideas of up, a gain or a profit.
• The sign for a positive integer is (), however
  the sign is not always needed.
• Meaning 3 is the same value as 3.

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Negative Integers

• Are to the left of zero
• Are valued less than zero.
• Express ideas of down or a lose.
• The sign for a negative integer is (-). This sign
  is always needed.

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Zero is neither positive or negative
Positive integers are valued more than zero, and
are always to the right of zero.
Negative integers are valued less than zero, and
are always to the left of zero.
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End of Part One
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Representing Integers
- 1
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- 4
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3
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- 3
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2
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2
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2
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2
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Representing Integers

• - 4 using 6 counters
• 2 using 6 counters
• 0 using 6 counters
• - 3 using 6 counters

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Opposite Integers
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The net worth of opposite integers is zero.
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0
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0
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0
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Opposite Integers

• Opposite integers always have a net worth of 0.
  This is called the ZERO PRINCIPAL.
• Opposite integer have the same absolute value,
  meaning the distance from the points on a number
  line to zero is the same.
• This can be referred to as the integers magnitude.

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Movement on a Number LineMagnitude and Direction

• Every integer represents a magnitude and a
  direction.
• The integer 3 describes a movement of 3 units in
  a positive direction.(right)
• The sign () tells you the direction.
• The number (3) indicates how far to move or the
  MAGNIUDE( a move- ment of 3 units)

• 3

Direction
Magnitude
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Comparing Integers
Which integer has a higher value? -4 or -8
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Comparing Integers

• Use your number line to help you compare each set
  of number.
• (i.e. for the numbers 3 ,and - 2 . 3 gt
  -2 -2 lt 3)
• - 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15
• e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14

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Putting Things Together

• What is the greatest valued negative integer?

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(3,5)
(4,-2)
(-1,-3)
(-2,1)
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(4,5)
(-8,3)
(-5.-1)
(-6,3)
(0,-7)
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Comparing Integers

• Use your number line to help you compare each set
  of numbers. Copy the question and write two
  sentences for each pair of numbers.
• (i.e. for the numbers 3 ,and - 2 . 3 gt
  -2 -2 lt 3)
• - 6, 7 b) 12, 3 c)- 5,- 8 d) 11, - 15
• e) - 7, - 4 f) - 3, - 7 g) 7, - 8 h) - 13, -14
• i) 8, 7 j) - 8, - 7 k) 5, -1 l) 0, -2
• m) 0, 3 n) - 5, 0 o) 14, -10 p) - 9, 0
• q) -7, -6 r) -1, 0 s) 4, -4 t) 0, -15

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Comparing Integers Again

• For each of the previous questions (a) to (t),
  write a new mathematical sentence showing how
  much bigger or smaller the first number is than
  the second.
• (i.e. 3, - 2 .. 3 is 5 more than 2)

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Review What We Know
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- 4
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1
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0
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-2
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Direction
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Magnitude
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Comparing Integers

• -5 ___ -8
• 0 ___ -3
• 3 ___ 2

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Quadrant l
(4,-5)
(-8,3)
(-5,-1)
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Intro To Adding Integers
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Outcomes

• A12 represent integers (including zero)
  concretely, pictorially, and symbolically, using
  a variety of models
• B11 add and subtract integers concretely,
  pictorially, and symbolically to solve problem
• B14 solve and pose problems which utilize
  addition of integers
• B2 use mental math strategies for calculations
  involving integers

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Net Result Positive 9
(5) (4) 9 Or (4) (5) 9
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Finding The Sum of Positive Integers

• When finding the sum of positive integers you add
  the magnitudes and keep the positive sign.

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Net Result Negative 10
(-3) (-7) -10 Or (-7) (-3) -10
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Finding The Sum of Negative Integers

• When finding the sum of negative integers you add
  the magnitudes and keep the negative sign.

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Net Result Positive 2
(7) (-5) 2 Or (-5) (7) 2
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Finding The Sum of a Positive and a Negative
Integer

• When finding the sum of a positive and a negative
  integer you subtract the magnitudes and keep the
  sign of the integer with the largest magnitude.

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Net Result Zero
(5) (-5) 0 Or (-5) (5) 0
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Integer Recap
You Have or Youve Earned

• Positive symbol means
• Negative symbol means

You Owe
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• (3) (-7)
• (-5) (-2)
• (-3) (-6) (4)
• (3) (-2) (2)

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• (50) (-100)
• (-25) (10)
• -60 -20
• -20 15
• 30 -5

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Rules For Adding Integers

• Positive Integers
• To add two positive integers you add the
  magnitude and keep the positive sign.
• Negative Integers
• To add two negative integers you add the
  magnitude and keep the negative sign.
• A Negative and a Positive Integer
• To add a positive and a negative integer you
  subtract the magnitudes and keep the sign of the
  integer with the largest magnitude.

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Intro To Subtracting Integers
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(5) (3) 2
(5) (3)

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(-6) (-2) -4
(-6) (-2)

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(3) (5) -2
(3) (5)

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(-2) (-6) 4
(-2) (-6)

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(3) (-2) 5
(3) (-2)

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(1) (4) -3
(1) (4)

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(-5) (3) -8
(-5) (3)

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(-2) (-5) 3
(-2) (-5)

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Try These

• (-8) (-3)
• (4) (-5)
• (-4) (-5)
• (1) (-6)
• (-5) (6)
• (-2) (-3)
• (-20) (-10)
• (30) (-3)
• (-20) (-30)

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Try These

• (-3) (-2)
• (6) (-2)
• (-1) (-4)
• (3) (-2)
• (-5) (2)
• (-2) (-4)
• (-30) (-20)
• (50) (-10)
• (-20) (-30)

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Try These

1. (-5) (2)
2. (6) (-2)
3. (-2) (-6)
4. (7) (-2)
5. (-5) (2)
6. (8) (-4)
7. (-3) (6)
8. (50) (-10)
9. (-20) (-30)

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Try These

1. (-5) (2) -3
2. (6) (-2) 4
3. (-2) (-6) 4
4. (7) (-2) 5
5. (-5) (2) -3
6. (8) (-4) 4
7. (-3) (6) -9
8. (50) (-10) 60
9. (-20) (-30) -50

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Multiplying and Dividing Integers
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Intro To Multiplying and Dividing Integers

• Site www.aplusmath.com
• Go to Flashcards
• Go to Non-Java Flashcards
• Go to Adding, Subtracting, Multiplying and
  Dividing With Negative Numbers
• Click on Multiplying (One by One) Use the site to
  help you complete the chart
• Then, Go To Division (One by One)

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(2) x (4) 8
(2) x (4)

This means you have two sets of four positive
tiles or you have earned two groups of four
dollars.
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(2) x (-4) -8
(2) x (-4)

This means you have two sets of four negative
tiles or you have two bills that you owe,each
bill is for four dollars.
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(-2) x (-4) 8
(-2) x (-4)

This means you dont have two sets of four
negative tiles or you dont owe two bills, each
bill is for four dollars.
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(-2) x (4) -8
(-2) x (4)

This means you dont have two sets of four
positive tiles or you dont have two groups of
four dollars.
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Try These

• (3) x (-2)
• (-2) x (-2)
• (5) x (-2)
• (-3) x (2)
• (3) x (4)
• (3) x (-2)

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Try These

• (-91) x (-101)
• (152) x (-21)
• (-19) x (203)
• (-69) x (-102)
• (-62) x (-11)
• (-128) x (12)

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Try These

• (-91) x (-101)
• (152) x (-21)
• (-19) x (203)
• (-69) x (-102)
• (-62) x (-11)
• (-128) x (12)

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Try These

• (-1) x (1) x (-1)
• (1) x (1) x (-1)
• (-1) x (-1) x (1)
• (-1) x (-1) x (-1)
• (-1) x (-1) x (1) x (-1) x (1)
• (-1) x (1) x (1) x (-1) x (1)

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Short Cuts For Multiplying Several Integer Factors
If there is an even number of negative signs, the
product is positive

• (-1) x (1) x (-1) 1
• (1) x (1) x (-1) -1
• c. (-1) x (-1) x (1) 1
• d. (-1) x (-1) x (-1) -1

If there is an odd number of negative signs, the
product is negative
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Short Cuts For Multiplying Several Integer Factors

• a. (-1) x (1) x (-1) x (1)
• b. (1) x (1) x (-1) x(-1)
• c. (-1) x (1) x (-1) x (-1) x (1)
• d. (-1) x (-1) x (-1) x (-1) x (1) x (-1)
• e. (1) x (1) x (-1) x (-1) x (1) x (-1)
• (-1) x (-1) x (-1) x (-1) x (-1) x (-1)
• (-2) x (-3) x (-2) x (1)
• (-1) x (-3) x (-2) x (-2) x (-3)

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Try These

• (-2) x (2) x (-1)(-3)
• (1) x (4) x (-5)
• (-17) x (-2) x (2)
• (-2) x (-3) x (-6) x 4
• (-2) x (-3) x (-3)

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(2) x (4) 2
(2) x (4)

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Positive and Negative Integers

• For each of the following numbers, write down an
  example of where it could be used and what it
  means in that situation.
• -3 -100m 15
• 3050m -45.83

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Order of Operations With Integers
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Order of Operations With Integers

• 3 x (7) 4 x (-5)
• 15 (5)2 x 2
• (-18) -- 32 9 x 2

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Practice for Problem Solving

• Fiona spends 5 per week on bus fare. How much
  does she spend in 2 weeks?
• Lucy spends 2 per week on snacks. How much does
  she spend in 4 weeks?
• Anton earns 8 each week for baby-sitting. How
  much does he earn in 3 weeks?

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Practice for Problem Solving

• Lional pays 3 per day for bus transportation.
  How much does she pay in a school week?
• Jill has 100 in the bank. She owes 3 of her
  friends 10 dollars each. What is her net worth?