Adding and subtracting integers “the easy box way”

Written and created by Susan o. Johnsey

 

How you ask?  Create or draw 2 boxes.  One is for the negatives and one for positives. 

 

All numbers have a sign.  IT is always on the left side of the number.

-2+4      There a is negative 2 and a positive 4.

3 -5        There is a positive 3 and a negative 5.  Do you see the sign is on the left always.

 If no sign is written then it is positive.  That is why the 3 is positive.

 

What if there are 2 signs on the left?

- (-6)  or - - 6 are the same number.  they both mean Positive 6.  “Double negatives”, that is a negative sign followed immediately by another negative sign yields one positive.

 

[Note I did not say one negative number followed by another negative number,

     such as -7-8.   That  is not what I am explaining here.]

 

7- (-6)  becomes 7 +6  The “double negatives” disappear and become one positive.  Why is this true?  A little logic will explain that.  Positive and negatives are opposites of each other.  Right? yes.  3 and -3 are opposites.  The opposite of a -6 is a +6.  Another way to think of negatives is to think the word opposite.

 -2 can be called negative 2, minus 2, or opposite of 2.  Thus the OPPOSITE of -6 is a positive 6 can be written as a math expression: -( -6) = +6.

-5 - (-3) becomes -5 +3

Now that we know that, let’s use the positive and negative box to explain adding and subtracting of integers.   Most books teach this in 2 lessons,  first adding and then subtracting.   I do not.  When we are “adding integers” there are times when we actually subtract the numbers!! And when “subtracting integers” there are times when we add the numbers.!!  Confused?  Yes ?  no?  Please read on.  First, lose your “mind set” about this topic from any prior  knowledge you may have.  This is simple.

 

-5 +3 or 3 - 5  means a 5 is placed in the negative box and 3 is placed in the positive box.

Remember, the sign of the number is on its left.  If a number has no sign on its left then it is positive.  In both expressions above the 5 is negative and the 3 is positive.

Now we ask these 2 questions:

1.  which box has more?

2.  how much more does it have?

 

-

 

+

5

 

3

 

For -5 +3 or 3 - 5 the negative box has more and it has 2 more than the positive box.

Our answer is thus negative 2.  -5 +3  is -2.

  We  have more negatives.  The negative box has  2 more than the positive box.

          -5 +3  or   3 - 5 are equal to -2.

 

-2-4 means you have 2 in the negative box and then 4 more are placed into the negative box. 

-

 

+

2, 4

 

 

Which box has more?  The negative box. 

How much more?  Since the positive box has none and the negative box has 6 then obviously the negative box has 6 more.  The answer is -6.  that is, -2 - 4 = -6

 

-4 +4  means  4 is placed in the negative box and 4 is placed in the positive box.

If the amounts in the 2 boxes are equal then your answer is 0, ZERO

 Also  -3+3 =0   can be written  +3-3=0  or 3 - 3 =0.

Remember the sign of a number is on its left.

 

-2 + 4  means you have 2 in the negative box and 4 in the positive box .

  Which box has more? The positive box has 2 more.  The answer is +2.   That’s -2+4 = 2.

 

This is the same problem as +4 - 2.  Be sure you see that.   Just look at the signs.

 

What about when there are double signs?

 

-2 - +3 or

 -2 -(+3)  or

 -2 +(-3)

 I suggest ignoring the extra positives.  I said extra positives.  We can never ignore negatives.  All three of these  become -2 - 3. Cover the extra positive with your pencil.

This problem is the same as -2 - 3.  We have 2 in the negative box and another 3 is placed into the negative box .  The answer is -5.

 

What about double negative signs?

- -4  is an example . Think of this as the opposite of negative 4.  The opposite of negative is, of course, positive.  - -4 is simply +4.  or -(-4) = +4 or 4

 

- -4 +6 becomes +4+6.  Both are in the positive box so our answer is +10 or just 10.

 

-7- -8 becomes -7 +8 .  LOOK at that.  The double negative was on the 8.  The sign of a number is always on its left. -7 +8 = +1.  There is one more in the positive box than in the negative.  

  -7- -8 =  1

-

 

+

7

 

8

 

Here is a link to my video, watch part 2.

 

I know these are not the usual math rules.  But if you are struggling then forget what you know and try these.  They work.  Using the other stuff you sort of know can really get in the way.   Now go back and do this, please:

 

Write all of the above examples with their boxes on a card for reference.

 

There are rules also for multiplying and dividing,  but they are easy.  A positive number  times a negative number is always a negative number.  A negative number times another negative number always equals a positive number.  These  2  rules apply to division also, BUT not adding and subtracting!!! ( Use your box for adding and subtracting.)

 

 

Compute and email you answers.  It is a free service and anonymous.

 

1.  -6+9          2.  -6 -9          3.  -6-(-9)       4.  6- 9            5.  6-(-9)

 

6.  8-(-5)        7.  8- (5)        8.  -5 +8         9.  -5 -8          10.  -5 -(-8)

 

Yes, some answers are repeated.

 

Susan Johnsey <><   2003     

sjohnsey@bellsouth.net                                                                          www.mathinabox.com