The upside of negativity Subtracting Negative Integers! Video # 8 about integers
Negative numbers. Negative numbers are the opposite of positive numbers
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 = = 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 = = 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 – – 5 –
Review with these problems… be sure you’re doing the right operation. 8 – 5-50 – – 5 –
Review with these problems… be sure you’re doing the right operation. 8 – 5 = = = 1 = = – 10= -1 1 + –6= = =-101 5 – 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
I get to add
(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 = = =
You have to change two things – the subtraction to addition, and the number from negative to positive. 6 – 2 = 4-6 – 2 = -8 = = -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) (-3) 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)= = -9 =6-3 - (-3)= 0 4 – (-4)= = 0 5 - (-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)= (-34343) = 0 = 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) = 0
= -5 – 5 = = 5 – 5 = 5 – (-5) = -5 – (-5) = 100 – 1 = – 99 = 100 – (-99) = 75 – 74 = - 74 –(-1) = =
= 0 -5 – 5 = -10 = 10 5 – 5 = 0 5 – (-5) =10 -5 – (-5) = 0 100 – 1 = 99 – 99 = -199 100 – (-99) = 199 75 – 74 = 1 - 74 –(-1) =- 73 = 0
= -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.
/worksheets/numbers/int0601integers_02.ht m is a nice practice sheet – you can click for the answers. /worksheets/numbers/int0601integers_02.ht m aaamath.com has practice under “addition” and “subtraction” – scroll down to find “integers.” aaamath.com