Transcript Adding, Subtracting, Multiplying, and Dividing Negatives

ADDING, SUBTRACTING,
MULTIPLYING, AND DIVIDING
NEGATIVES
Frank Wang
Wut???
What are negatives? Simply, they are numbers under
0! A good example is this: 1 below 0 is 0-1, but
that is actually possible. You must go into the
negatives, so the answer is -1. Think of it with a 0 in
front of it. 0-1=-1.
0 is the ground level here,
underneath are the
negatives.
When?
When do we use negatives? Money. “ I’m 4 bucks in
the hole” means I have to pay $4.00. In other
words, I have -$4.00.
Absolute Value
One thing you will need to know for adding and
subtracting negatives is absolute value. It’s simple.
Technically, the absolute value is how far the
number is from 0. You can just take the number, hide
the sign, and that would be the absolute value.
Part One:
Adding Negatives
This can get tricky. The numbers, I’m sure you can do,
but the symbol changing is harder. If the signs are
the same, just add them normally and use that sign.
If they are different, start by finding out which
number has the greater absolute value. Remember
that sign. Then, cover up the signs and pretend they
are not there. Switch the sign to subtraction.
Subtract normally. Then, use that sign that you had
to find out in the beginning.
Example
-6 + 3=
6 has a greater absolute value
6-3=3
use the – sign
-3 is the answer
Example 2
-1+5
5 has a greater absolute value
1-5= -4
use the + sign
+4 (or 4) is the answer.
Quick Trick
When you change the sign, you can change the
numbers around for convenience. So, you can do5-1
instead of 1-5. You’ll get the same answer because
of the sign changing.
Another Technique
The other technique is thinking of it literally, on a
number line, or whatever. Say we had the first
example. -6+3=??? Negative 6 plus 3. You would
take the negative 6 and add on three. Negative 3.
Here is why:
Addition always goes to the right.
1 2 3
Another Technique (continued)
If you use the second equation, -1 +5, you would get
four. Think about it, draw a number line. You’ll still
get 4. Also, If your question is like 9 + -6, you’ll
have to subtract 9-6 because – takes over +.
Review for Adding Negatives
Here come the questions!!
-8 + 4
5 + -2
-9 + -8
Answers
1)
-4
2)
3
3)
-17
Part Two:
Subtracting Negatives
To subtract, if the two numbers have the same sign,
subtract normally. If the positives go below 0, start
going into the negatives, and vice versa with the
negatives. If the numbers have different signs, do
the same thing as addition. Find the number with the
greatest absolute value. Remember the sign. Cover
the signs. Change the subtraction sign to an addition
sign. Add. Use the sign that you remembered. Your
answer is there.
Example
-5-3
5 has a greater absolute value
5+3
8
use the – sign.
-8
Example 2
-9-3
nine has a bigger absolute value
9+3
12
use the – sign
-12
Exceptions
If the question is positive minus negative, use the +
sign. 8- -9(positive minus negative)=17. That’s also
sign-switching. This is very complicated. If you get it,
very good! You can also use the technique with
addition.
Review for Subtracting Negatives
Oh look! Review questions!
-9-7
-9-4
6- -9
Answers
1)
-16
2)
-13
3)
15
Part Three
Multiplying Negatives
This is a lot easier, if you know your multiplication
facts. All you have to do next is remember sign
changing. To do it, cover the signs, multiply, then use
a certain sign you will figure out in this table.
First Sign
Positive Negative
+
Second Sign
-
Example
-9 x 4
9 x 4= 36
Negative & Positive result negative
use the – sign
-36
Example 2
6 x -5
6 x 5= 30
Positive and negative result negative
use the – sign
-30
Review on Multiplying Negatives
I find this easier, so I’ll give some questions.
-5 x -9
6x3
8 x -6
Answers
1)
45
2)
18
3)
-48
Part Four
Dividing Negatives
Same thing as multiplication, just divide.
Example
-27÷3
27÷3=9
negative and positive result negative
use the – sign
-9
Example 2
-132÷-11
132÷11=12
negative and negative result positive
use the + sign
+12(or 12)
Review for Dividing Negatives
Questions!
-84÷ 7
-35 ÷ -7
77÷-11
Answers
1) -12
2) 5
3) -7
Final Test
Take this quick test… but think of it as a progress
check… because it is. No pressure!
Go!!!
1)
2)
3)
4)
-5 +7
-2 x -9
-88 ÷ 11
-9-6
BONUS: -9 + -3 – 5 x -5 + -72 ÷ 8= ????
Hint: PEMDAS
Answers
2
18
-8
-15
(25%)
(25%)
(25%)
(25%)
Bonus: 23
(50%)
1)
2)
3)
4)
Scoring
25% = ok…
50%= pretty good…
75%= great
100%=excellent
150%=awesome!!!
1000%= impossible. You lied.
Credits
PowerPoint made by Frank Wang
Methods by THE WORLD
Typing by Frank Wang
Wording by Frank Wang
Contributors: YOU!!!!!!!!!!!!
Almost Everything else by Frank Wang