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 NegativesHere 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 NegativesOh 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 SignPositive 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 NegativesI find this easier, so I’ll give some

questions.-5 x -9 6 x 3 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 NegativesQuestions!

-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) -5 +72) -2 x -93) -88 ÷ 114) -9-6

BONUS: -9 + -3 – 5 x -5 + -72 ÷ 8= ???? Hint: PEMDAS

Answers

1) 2 (25%)2) 18 (25%)3) -8 (25%)4) -15 (25%)

Bonus: 23 (50%)

Scoring

25% = ok…50%= pretty good…75%= great100%=excellent150%=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