Integers:

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Integers

• The upside of negativity
• Subtracting Negative Integers!

Video 8 about integers
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- - -

• Negative numbers.
• Negative numbers are the opposite of positive
  numbers.

- - -

- - -

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6 2 8
When adding integers Same sign, add and keep
-6 -2 -8
4
Different sign, subtract ?

• 6 -2
• Is the same as 6 2
• Which is 4.

If this is confusing, review the earlier lesson
on adding integers.
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Subtraction is adding the opposite.

• -- change two things to keep balance

Heres your starting point is it positive or
negative?
Change subtraction to adding
Change the sign of the next number
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Two Marks Bam! Bam!

• 8 2
• 8 2
• 8 - 2 6
• same sign, add and keepdifferent sign, subtract!
• Keep the sign of the bigger number then
  youll be exact ?

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A little more practice at making two changes

• 15 5
• 5 15
• 9 8
• 8 9
• 20 5
• 5 20

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The answers

• 15 5
• 5 15
• 9 8
• 8 9
• 20 5 15
• 5 20 -15

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If we start with a negative number same process.
What it means is more important than what it
looks like If you have already lost 4 (pounds,
pickles, whatever!) and you lose five more,
youve lost 9.
-4
-9
-4 5 -4 -5 -9
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And mixin em up

• Review with these problems be sure youre doing
  the right operation. Watch for trick questions!
  -2 2 is 4.
• 8 5 -50 25 10 - 9
• -1 6 -30 20 9 - 10
• 1 - 6 100 5 -100 - 1
• 5 10 -9 10 1 - 100

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Check your operations ?

• Review with these problems be sure youre doing
  the right operation.
• 8 5 -50 25 10 - 9
• -1 6 -30 20 9 - 10
• 1 -6 100 5 -100 - 1
• 5 10 -9 10 1 - 100

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And the answers

• Review with these problems be sure youre doing
  the right operation.
• 8 5 3 -50 -25-75 10 -9 1
• -1 6 5 -30 20 -10 9 10 -1
• 1 6 -5 100 -5 95 -100 -1 -101
• 5 10 -5 -9 10 1 1 100 -99

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Okay, now for the real fun!
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What if I subtract a negative number?

• 8 1 7, right?... But thats subtracting a
  positive number.

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What if I subtract a negative number?

• 8 1 7 we take it away.
• what is 8 (-1)?
• Whats the opposite of taking away? Adding.
• Im going to change that to adding the opposite
  and go the opposite direction.
• 8 (regular, good old fashioned POSITIVE) 1.

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8 (-1) 9

• The soap opera version?
• Subtraction is taking away, right?
• A negative thing is bad, right?
• If I take away a bad thing like that nasty
  smelling thing in my refrigerator thats like
  giving me a good thing ADDING.

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Make it visual
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The difference between 8 and 3 is 5, and 8-3 is
5. The difference between 8 and negative one is
9. 8 is nine more than negative one.
-1
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Make it visuala little differently ) two
marks and a smile ?
10 (- 6) 16
I get to add ? ?
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We are still changing subtraction to adding the
opposite

• (Honestly the rules dont change ?)

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Youll still always make two lines.

• You have to change two things the subtraction
  to addition, and the number from negative to
  positive.
• 6 2 -6 2
• 6 - -2 -6 - -2

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Lines and answers

• You have to change two things the subtraction
  to addition, and the number from negative to
  positive.
• 6 2 4 -6 2 -8
• 6 - -2 8 -6 - -2 -4

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Try a few.

• Remember
• ALWAYS ALWAYS ALWAYS
• Change two things. Adding is not the same as
  subtracting Forward is not the same as
  backwards.
• But if you turn around again youre back
  where you started.

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Parentheses are sometimes added for easier
reading.

• 10 (-1) -10 - -1
• 3 - -3 -3 - (-3)
• 4 (-4) -4 - -4
• 5 - (-5) -4 - (-5)

This will matter more when youre learning
multiplication Parentheses are used to wrap a
number or expression to show things that belong
together. It can be confusing if two numbers
are written like this (3) (4) , that means to
multiply them. Its not because of the
parentheses, though its because math people
decided that if they didnt write anything, it
meant to multiply.
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• 10 (-1) 11 -10 - -1 -9
• 3 - -3 6 -3 - (-3) 0
• 4 (-4) 8 -4 - -4 0
• 5 - (-5) 10 -5 - (-5) 0

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• Heres another example where what it means is
  more important than what it looks like. 8 8 is
  zero 139 139 is zero anytime you take away
  exactly the same thing you started with, youre
  back at zero even if its a negative number.
  So, negative 133 minus negative 133 is 0.
• -3 - (-3) 0 -34343 - (-34343) 0
• -4 - -4 0
• -5 - (-5) 0

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Lets mix these up

• Two main rules if youre adding,
• Same sign, add and keep different sign
  subtractkeep the sign of the bigger numberthen
  youll be exact.
• If youre subtracting, change two things so you
  are adding the opposite.
• (remember the trick questions -2 -2 -4-2
  (-2) 0

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Remember, what they mean is more important than
what they look like.

• -5 5
• -5 5
• 5 5
• 5 5
• 5 (-5)
• -5 (-5)

• 100 1
• - 100 99
• 100 (-99)
• 75 74
• - 74 (-1)
• - 13 13

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Your answers

• -5 5 0
• -5 5 -10
• 5 5 10
• 5 5 0
• 5 (-5) 10
• -5 (-5) 0

• 100 1 99
• - 100 99 -199
• 100 (-99) 199
• 75 74 1
• - 74 (-1) - 73
• - 13 13 0

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Try this ?

• -5 5
• -5 5
• 5 5
• 5 5
• 5 (-5)
• -5 (-5)

• You make up six problems using that as a model,
  and explain why the first and last ones add up to
  zero.

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• http//www.helpingwithmath.com/printables/workshee
  ts/numbers/int0601integers_02.htm is a nice
  practice sheet you can click for the answers.
• aaamath.com has practice under addition and
  subtraction scroll down to find integers.