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 has a greater absolute value 6-3=3 use the – sign -3 is the answer

Example 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

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 , you’ll have to subtract 9-6 because – takes over +.

Review for Adding Negatives Here come the questions!!

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 has a greater absolute value use the – sign. -8

Example nine has a bigger absolute value use the – sign -12

Exceptions If the question is positive minus negative, use the + sign (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!

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 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 ÷ ÷11=12 negative and negative result positive use the + sign +12(or 12)

Review for Dividing Negatives Questions! -84÷ ÷ -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 x -9 3) -88 ÷ 11 4) -9-6 BONUS: – 5 x ÷ 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%= great 100%=excellent 150%=awesome!!! 1000%= impossible. You lied.

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