Basic Algebra?

Question

I am trying to help my daughter with her homework. I know the rule of a negitive number and a negitive number makes a positive.
OK, I need someone to explain in very simple terms, why is a negitive # +/- another negitive # a positive number? Why is it I can't have a -12 +-10= -22 or even -2?
If at all possible, can someone explain this graphically as I learn better that way.

Answer 1

i'll try to help
on a number line we get higher numbers by going to the right and lower going to the left
when we add we go more to the right of the number we are starting with and when we subtract we go more to the left
however when there is a negative sign by the number it tells us to switch direction (go left for adding and right for subtracting)
in your problem we start to the left of zero at -12 and since we are adding a number (-10) with a negative sign we go 10 spaces to the left and we land on -22
kids ussually have a hard time grasping this so dont get frustrated and just keep explaining it in as many different ways as possible bec. u never know which perspective will help her understand
good luck

Answer 2

Lets take this one step at a time. because you have made a statement and 2 questions.

(#1) I know the rule of a negitive number and a negitive number makes a positive.
This statement implies you are adding two integers together.
if so the statement would be untrue.
When you add a negative to a negative you get a negative. if you take 2 steps backward (a negative) plus 2 steps backward (another negative) you have taken 4 steps backward (still a negative)
the statement would be true if you were multipling 2 negatives. (-2) X (-2) = 4
(#2) OK, I need someone to explain in very simple terms, why is a negitive # +/- another negitive # a positive number?
This is really just a rewording of the first statement as a question and is also untrue.
when you add two negatives you still get a negative
if you add a negative and a positive you get either or depending on the value of each integer.
example (-2) + 2 =0 or (-2 ) + 4 = 2, or (-2) + (-2) = -4
or (-2) - (-2) = 0 etc.
try using a couple of rulers to get the idea. put them together.
the left ruler would be negative and right ruler would be positive
where the two join would be 0. then do some basic math adding and subtracting along the rulers and you can see the movement of positive and negative integers

(#3) Why is it I can't have a -12 +-10= -22 or even -2?
you can, it would be -22, it would only be -2 if you had
(-12) - (-10) = -2

Here are some of the rules from Wikipedia. or you can check the link yourself.
Adding a negative number is the same as subtracting the corresponding positive number: 5 + (-3) = 5 - 3 = 2
Subtracting a positive number from a smaller positive number yields a negative result: 4 - 6 = −2
Subtracting a positive number from any negative number yields a negative result: −3 - 6 = −9
Subtracting a negative is equivalent to adding the corresponding positive: 5 - −2 = 5 + 2 = 7 Also: −8 - −3 = −5
Multiplication of a negative number by a positive number yields a negative result: (−2) × 3 = −6.
Multiplication of two negative numbers yields a positive result: (−4) × (−3) = 12.

good luck helping your daughter without a teachers copy of a math book to guide you

Answer 3

The rule is actually more like a negative number multiplied by or divided by a negative number is a positive number. Addition and subtraction don't have the same rule.

For example: -3 + -2 = -5

For addition and subtraction, a good way to think of this is on a number line. In the case of the above example the problem can be written as: -3 - 2

If you start at -3 on the number line, then decide whether you are adding or subtracting a positive number. (If you're subtracting a negative number it's equivalent to adding a positive. If you're adding a negative, it's equivalent to subtracting a positive.)

Then think of the operation (add/subtract) as the direction. Subtraction moves further negative, addition moves further positive.

Answer 4

The 'rule' actually is: a negative number TIMES a negative number is a positive one.

For adding and subtracting, you add all the + ones, subtract all the - ones and see which you have more of. Your example is correct; -12 + -10 does equal -22. Think of a number line with 0 in the middle, - values to the left and + values to the right. Start with the first #, and move right to add a + number or left to add a - number. Subtracting moves the opposite way. Subtracting a - number actually moves you to the right.

Sorry, no idea how to transmit a graph, but hope this helps

Answer 5

Use a number line to help her.
My teacher use to show us this to help:
+ X + = +
- X - = +
+ X - = -
- X + = -
when adding and subtracting though use the number line.
If you are doing -12+-10=-22,
explain that the +-10 turns into a -ive as a +ive and a -ive equal
-tive meaning the equation is the same as -12-10=-22

Answer 6

Your question is very vaguely put
Ithink that you are asking why -N added to or subtracted from another number is always a positive number.
Answer, it isn't
For ex: -30 - (-22) is -8
so
-22+30=8
because -1 times - 30 gives a positive and so 8 is the answer

Another example -12+-10 = -22
This is the same as -12-10
If we adda positive ten to it we get -2 as you put.
Hope this answers your question

Answer 7

umm yes it has been a long time for you hasnt it :)

-12 + -10 IS -22

well, the easiest way is to form a number line with negative #s to the left of 0 and positive #s to the right of 0


<-------------------------------------------------------------------------------->
-40 -30 -20 -10 0 10 20 30 40

and if you are adding a -# you will then move leftward on the number line, if you add +# you will then move rightward on the number line

or if you want most everyone on the planet has to deal with $$,
so think of negative #s as money you have to pay out or owe and positive #s as money you would receive [like a paycheck]

in math it can help to make things "more concrete" so that you understand it easier

so for say -12 + -10 think of it as u just paid $12 for something at one store then go to another and pay $10 for something else ..you are now out $22 for the day

well have fun,
Tom

Answer 8

-12 + (-10)= -22.. Isn't it?

here's the simplest way: The sign of the total will follow the sign of the bigger number.. This applies to both addition and subtaction.

example:

a) 4 + (-2)= 2, same as "4 - 2"
b) -4 + 2 = -2, same as "2 - 4", you took more than the existing
amount so your answer would be negative.

Answer 9

-10+ -12 = -22
You are correct on this. a negative number plus a negative number will always equal a negative number

a positive number plus a positive number will always equal a positive number.

other than that, all other combinations vary based on the numbers your adding or subtracting.

Answer 10

Graphically would probably be best, but it's hard to do in this format. Work with me here:

Think of a number line. Positive is to the right, negative is to the left - 0 is in the middle. If I want you to put a point at +3, you'll go three units right. If at -4, you'll go four units left. OK so far?

Now - addition means move to the right, subtraction means move to the left. If I have 3 + 5, it means start three units to the right and move five more units to the right. Of course, you end up eight units to the right.

If I have -3 + 5, it means start three units to the left and move five units to the right. You end up two units to the right.

If I have 5 - 3, it means start five units to the right and move three units to the left.

I hope this makes sense, because now life gets interesting.

If I have 3 + (-2), it means start three units to the right and move negative two units to the right. Moving negative two units to the right is the same as moving two units to the left, so I end up one unit to the right. 3 + (-2) is the same as 3 - 2.

If I have -3 - 2, it means start three units to the left and move two units to the left. I'll end up five units to the left.

If I have -3 - (-2), it means start three units to the left and move (-2) units to the left. Moving negative two units to the left is the same as moving two units to the right, so I'll end up one unit to the left. -3 - (-2) is the same as -3 + 2.

So, in your case, -12 + (-10) means start twelve units to the left and move (-10) units to the right. -10 units to the right is the same as 10 units to the left, so I end up 22 units to the left.

I hope this makes sense - it's easier to draw it. Just remember: + means to the right, - means to the left.