Integers The upside of negativity Subtracting Negative Integers
Integers: The upside of negativity Subtracting Negative Integers! Video # 8 about integers
-- +++ - Negative numbers. + + + Negative numbers are the opposite of positive numbers. +++ - - ---
When adding integers: Same sign, add and keep 6+2=8 -6 + -2 = -8
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.
Subtraction is “adding the opposite. ” � -- change two things to keep balance Here’s your starting point – is it positive or negative? Change subtraction to adding Change the sign of the next number
Two Marks – Bam! � 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
A little more practice at making two changes: � 15 – 5= � 5 – 15 = � 9 – 8= � 8 – 9 = � 20 – 5= � 5 – 20 =
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, you’ve lost 9. -4 -9 -4 – 5 = -4 + -5 = -9
And mixin’ ‘em up… � Review with these problems… be sure you’re doing the right operation. Watch for trick questions! -2 – 2 is – 4…. � 8 – 5 � -1 +6 � 1 -6 � 5 – 10 -50 – 25 10 - 9 -30 + 20 9 - 10 100 – 5 -100 - 1 -9 + 10 1 - 100
Check your operations � Review with these problems… be sure you’re doing the right operation. � 8 – 5 � -1 +6 � 1 + -6 � 5 – 10 -50 – 25 10 - 9 -30 + 20 9 - 10 100 – 5 -100 - 1 -9 + 10 1 - 100
And the answers… � Review with these problems… be sure you’re doing the right operation. � 8 – 5 =3 -50 + -25=-75 10 + -9= 1 + 6 =5 -30 + 20= -10 9 +– 10= -1 � 1 + – 6= -5 100 + -5 =95 � 5 – 10= -5 -9 + 10 = 1 � -1 -100 + -1 =-101 1 – 100 = -99
Okay, now for the real fun!
What if I subtract a negative number? � 8 – 1 = 7, right? . . . But that’s subtracting a positive number.
What if I subtract a negative 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.
8 – (-1) = 9 � The soap opera version? � Subtraction �A � If is taking away, right? negative thing is bad, right? I take away a bad thing… like that nasty smelling thing in my refrigerator… that’s like *giving* me a *good* thing… ADDING.
Make it visual… 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 -1
Make it visual…a little differently ; ) two marks and a smile 10 – (- 6) = 16 I get to add
We are *still* changing subtraction to adding the opposite… (Honestly – the rules don’t change )
You’ll 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 =
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
Try a few. � Remember � 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.
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 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.
� 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 � -4 - -4 = 0 � -5 - (-5) = 0 -34343 - (-34343) = 0
Let’s mix these up… � 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
Remember, what they mean is more important than what they look like. � -5 +5= � -5 – 5 = � 5 + 5 = � 5 – (-5) = � -5 – (-5) = � 100 – 1= � - 100 – 99 = � 100 – (-99) = � 75 – 74 = � - 74 –(-1) = � - 13 + 13 =
Try this � -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/int 0601 integers_02. ht m is a nice practice sheet – you can click for the answers. � aaamath. com has practice under “addition” and “subtraction” – scroll down to find “integers. ”
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