# The upside of negativity Subtracting Negative Integers! Video # 8 about integers.

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The upside of negativity Subtracting Negative Integers! Video # 8 about integers

Negative numbers. Negative numbers are the opposite of positive numbers. +++ - - - +++ - - -

 6 + -2  Is the same as 6 – 2  Which is 4. If this is confusing, review the earlier lesson on adding integers.

 -- change two things to keep balance Change subtraction to adding Change the sign of the next number Here’s your starting point – is it positive or negative?

 8 – 2 =  8 + - 2 = 6  same sign, add and keep different sign, subtract! Keep the sign of the bigger number… then you’ll be exact

 15 – 5 =  5 – 15 =  9 – 8 =  8 – 9 =  20 – 5 =  5 – 20 =

 15 – 5 =  5 – 15 =  9 – 8 =  8 – 9 =  20 – 5 = 15  5 – 20 = -15

-4 – 5 = -4 + -5 = -9 -4 -9 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, you’ve lost 9.

 Review with these problems… be sure you’re doing the right operation. Watch for trick questions! -2 – 2 is – 4….  8 – 5-50 – 2510 - 9  -1 + 6-30 + 209 - 10  1 - 6100 – 5 -100 - 1  5 – 10 -9 + 101 - 100

 Review with these problems… be sure you’re doing the right operation.  8 – 5-50 – 2510 - 9  -1 + 6-30 + 209 - 10  1 + -6100 – 5 -100 - 1  5 – 10 -9 + 101 - 100

 Review with these problems… be sure you’re doing the right operation.  8 – 5 =3-50 + -25=-75 10 + -9= 1  -1 + 6 =5-30 + 20= -10 9 +– 10= -1  1 + –6= -5100 + -5 =95-100 + -1 =-101  5 – 10= -5 -9 + 10 = 11 – 100 = -99

 8 – 1 = 7, right?... But that’s subtracting a positive number.

 8 – 1 = 7… we take it away.  … what is 8 – (-1)?  What’s the opposite of taking away? Adding.  I’m going to change that to adding the opposite… and go the *opposite direction.  8 + (regular, good old fashioned POSITIVE) 1.

 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… that’s like *giving* me a *good* thing… ADDING.

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. 8

(Honestly – the rules don’t change )

 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 =

 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

 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** … you’re back where you started.

 10 – (-1)-10 - -1  3 - -3-3 - (-3)  4 – (-4)-4 - -4  5 - (-5)-4 - (-5) This will matter more when you’re 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. It’s not because of the parentheses, though; it’s because math people decided that if they didn’t write anything, it meant to multiply.

 10 – (-1)= 11-10 - -1 = -9  3 - -3=6-3 - (-3)= 0  4 – (-4)= 8-4 - -4 = 0  5 - (-5)= 10-5 - (-5) = 0

 Here’s 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, you’re back at zero… even if it’s a negative number. So, negative 133 minus negative 133… is 0.  -3 - (-3)= 0 -34343 - (-34343) = 0  -4 - -4 = 0  -5 - (-5) = 0

 Two main rules… if you’re adding,  Same sign, add and keep different sign subtract keep the sign of the bigger number then you’ll be exact.  If you’re subtracting, change two things so you are adding the opposite.  (remember the “trick questions” : -2 -2 = -4 -2 –(-2) = 0

 -5 + 5 =  -5 – 5 =  5 + 5 =  5 – 5 =  5 – (-5) =  -5 – (-5) =  100 – 1 =  - 100 – 99 =  100 – (-99) =  75 – 74 =  - 74 –(-1) =  - 13 + 13 =

 -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

 -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.

 http://www.helpingwithmath.com/printables /worksheets/numbers/int0601integers_02.ht m is a nice practice sheet – you can click for the answers. http://www.helpingwithmath.com/printables /worksheets/numbers/int0601integers_02.ht m  aaamath.com has practice under “addition” and “subtraction” – scroll down to find “integers.” aaamath.com