Hi, please help me review. I'm trying to remember how to add or subtract positive and negative integers.Thanks, C.D.M.
just think of it in terms of counters:
take 3 plus 5:
three counters is + + +
add five more counters you get + + + + + + + +
or 5 minus 2
five counters is + + + + +
if you remove two counters you get + + +
a negative number is reperesented by a minus sign -
so you could also think of adding negative numbers
5 minus 3
five counters is + + + + +
add three negative counters + + + + + - - -
the negative and positive counters cancel out and you get + +
Hi Caroline-
I found a web site that will let you try as many integer problems as you need to. It gives feedback, of course, and allows you to pick, adding, subtracting, multiplying, or dividing.
Some of my students have found it very helpful. Use it until you've 'got it' then try it again another day to see if you still remember how to do these problems.
The website is at FlashCards with Negative Numbers
I have a link to it on the website I wrote the html code for, Multiplication Facts Drill (an on-line program)
Good luck,
Mr. Taylor
PS- Let me know if it helps!
Hi Caroline,
I have a blog entry that you may find useful. It describes the 2 simple steps that we can take to correctly evaluate negative and positive integers.
Mental Flow for Addition and Subtraction.
Also, you may find useful is the simple steps to evaluate positive and negative integers for multiplication and division.
That is a very nice way of thinking about it dented.
I prefer algebra to counters though (before you ask, yes I probably am crazy lol)
In short, if it contains only two (negative) numbers, then use the formula:
$\displaystyle -(n + m) = q$
where:
n = the first number, but reversed so it is positive
m = the second number, with its value reversed similarly to n
q = the final answer
OR
if there is just one negative number, use this:
$\displaystyle m - n = q$
where:
n = the negative number
m = the positive number
q = the final answer
if you want it to be explained further, try taking a look at these worked examples:
- 7 - 9 = q
- n - m = q
n = 7
m = 9
q = unknown
where:
n = the first number, but reversed so it is positive
m = the second number, with its value reversed similarly to n
q = the final answer
- 7 - 9 = 0 - 7 - 9
- n - m = 0 - n - m
0 - n - m
if:
-n = -1 * n = [n * -1]
-m = -1 * m = [m * -1]
therefore:
0 - [ [ n * -1] [ + m * -1] ]
to identify each term, ive removed the inner [] brackets and used {} brackets to show the term and its operator:
0 - [ { + n } { * [-1] } { + m } { * [-1] } ]
these can be rearranged and simplified as follows:
0 - [ { + n } { + m } { * [-1] } { * [-1] } ]
0 - [ n + m * -1 * -1 ]
0 - [ n + m * 1 ]
0 - [ n + m ]
therefore, in the equation -7 - 9 = q , where n = 7 and m = 9;
0 - [ n + m ] = q
0 - [ 7 + 9 ] = q
0 - [ 16 ] = 9
0 - 16 = q
q = 16
thus:
- 7 - 9 = -16
BUT, if there is only one negative number and one positive number in the equation, then it becomes pointless to do anything except rearrange and solve that way because using a modified version of the above formula simply resulted in exactly the same thing.
Just trust me on this point lol.
just do this:
- 7 + 9 = q
- n + m = q
n = 7
m = 9
q = unknown
where:
n = the negative number
m = the positive number
q = the final answer
- 7 + 9 = q
- n + m = q
+ m - n = q
- 7 + 9 = q
+ 9 - 7 = q
+ 2 = q
q = 2
thus:
9 - 7 = 2
Footnote:
Sorry: when I started typing, the idea of this seemed like a good one, but after finishing it, it seems almost pointless and almost off-topic
I mean, I've made something as simple as -7 + 9 into at least three or four screens of text / numbers lol ... sorry
Anyways .. you wouldn't believe how much time / work it took to do this (I almost don't believe it myself after seeing the finished bit) but I've put too much effort into it to not do anything with it, so there it is .. enjoy
I hope my previous post did not scare you lol.
Adding and subtracting negative numbers is much more simple than it looks.
There are many many different ways of teaching this - including one that I've made myself, but the most common one that ive seen is using these two rules:
** If the symbols are the same, then the number will get bigger and you must move your finger to the right on a number line.
For example, -(-3) and +(+3) will make the number bigger.
** If, however, the symbols are the different, then the number will get smaller and you must move your finger to the left on a number line.
For example, -(+3) and +(-3) will make the number smaller.
EXAMPLES:
can you see the patterns?Code:3 + +7 = 10 [ ++ makes the 3 bigger ] 3 < 10 3 + -7 = -4 [ +- makes the 3 smaller ] 3 > -4 3 - +7 = -4 [ +- makes the 3 smaller ] 3 > -4 3 - -7 = 10 [ -- makes the 3 bigger ] 3 < 10 3 + 7 = 10 [notice that ++ is the same as +] 3 - 7 = -4 [notice that +- is the same as -] 3 - 7 = -4 [notice that -+ is the same as -] 3 + 7 = 10 [notice that -+ is the same as +]