Subtracting negative numbers

WingZero30

WingZero30

WingZero30

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Hi guys

I am doing a project involving several numerical calculations and I have to explain reasons behind their rules. One such is why subtracting negative numbers results in addition? I have looked online but haven't got concrete evidence.

e.g 3- (-4) = 3+4 = 7

Now I am currently thinking of it like this:

-4 -3 -2 -1 0 1 2 3 4 5 6

Start at 3 and imagine travelling to -4. You will have taken 7 steps. So the answer will always be positive. So I am thinking in terms of difference between 2 numbers. However the problem is this explaination doesn't hold well for other combinations.

e.g 3 -1 = 2

Start at 3 and travel to -1. However this would result in 4 steps which is wrong. So how do I explain it ?:(
 
logic behind subtracting a negative number becomes addition I believe is pretty much the same as how in boolean, false that is false can be concluded as true.

I'm not sure what you're asking though...
 
Using a number line, if that's how you want to explain it, when you subtract a negative you just move the opposite direction on the line.

So 3 - 1, you move one step down, leaves you at 2.

For 3 - -4, you move four steps 'up' the line, leaving you at 7.

I'm not sure if that really helps you or not :confused:

Thinking of subtracting a negative makes it addition instead is probably confusing matters though, whilst a handy rule to get kids to understand it, it kinda confuses things when you need to explain it as you do.
 
Are you sure the rule would apply to just ordinary subtraction?
Because I see that the method words when you do 3 - (-1)
 
Kenai said:
Using a number line, if that's how you want to explain it, when you subtract a negative you just move the opposite direction on the line.

So 3 - 1, you move one step down, leaves you at 2.

For 3 - -4, you move four steps 'up' the line, leaving you at 7.

I'm not sure if that really helps you or not :confused:

Thinking of subtracting a negative makes it addition instead is probably confusing matters though, whilst a handy rule to get kids to understand it, it kinda confuses things when you need to explain it as you do.
Click to expand...

Yeah I was thinking about this aswell. With 3-1 you turn your face to left and move 1 step to reach 2.

With 3- -4 you turn left and then turn around again to face right and move 4 steps arriving at 7. I guess this is the best I can think of.

Lol I have done maths up to engineering level and have never been once taught about thius rule :p
 
WingZero30 said:
Hi guys

I am doing a project involving several numerical calculations and I have to explain reasons behind their rules. One such is why subtracting negative numbers results in addition? I have looked online but haven't got concrete evidence.

e.g 3- (-4) = 3+4 = 7

Now I am currently thinking of it like this:

-4 -3 -2 -1 0 1 2 3 4 5 6

Start at 3 and imagine travelling to -4. You will have taken 7 steps. So the answer will always be positive. So I am thinking in terms of difference between 2 numbers. However the problem is this explaination doesn't hold well for other combinations.

e.g 3 -1 = 2

Start at 3 and travel to -1. However this would result in 4 steps which is wrong. So how do I explain it ?:(
Click to expand...

Surely you problem is in the last example you don't have an operator as written?

So you either have

(3) - (1) = 2 .... no negative number, no issue

(3) - (-1) = 4 .... 4 steps between 3 and -1 as you expected.

As orignally written you actually have, if the second number is -1

(3)(-1) = -3

where ab == (a) * (b)
 
The way my math's teacher in year 9 explained it (back in 2001, never forgotten it, brilliant teacher), imagine the sum as a bowl of water, the temperature is the answer.

Negative numbers are ice cubes, so if you minus a negative number, the temperature increases. If you add negative numbers, the temperature goes down.

So, 3 - (-4) means the temperature is 3, you're taking away ice cubes, so temperature will rise, thus, answer is 7.
 
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WingZero30 said:
Yeah I was thinking about this aswell. With 3-1 you turn your face to left and move 1 step to reach 2.

With 3- -4 you turn left and then turn around again to face right and move 4 steps arriving at 7. I guess this is the best I can think of.

Lol I have done maths up to engineering level and have never been once taught about thius rule :p
Click to expand...

You are massively overcomplicating this, what is all this turning to the left, turning around, then to the right, then left leg in, left leg out?

Do we do the hokey cokey and all turn round at the end? :confused:
 
Kenai said:
You are massively overcomplicating this, what is all this turning to the left, turning around, then to the right, then left leg in, left leg out?

Do we do the hokey cokey and all turn round at the end? :confused:
Click to expand...

multiply by the number you first thought of, and then to the power of your inside leg measurement :D
 
Subtracting a negative gives you two '-' signs. Two '-' signs = 1 '+' sign. Easy.
Though I'm not sure what you're asking.
 
Kenai said:
You are massively overcomplicating this, what is all this turning to the left, turning around, then to the right, then left leg in, left leg out?

Do we do the hokey cokey and all turn round at the end? :confused:
Click to expand...

I meant when facing the number line. So when subtracting you turn left. When adding you turn right on the number line.
 
Number lines suck for teaching, use a real world example like a bowl of water and it sticks in your head. At least it has for me for 9 years.
 
Ahleckz said:
Subtracting a negative gives you two '-' signs. Two '-' signs = 1 '+' sign. Easy.
Though I'm not sure what you're asking.
Click to expand...

What I am trying to find is an explanatory rule that works for all the combinations.

So for 3-1=2: Start at 3 and move one step to the left to give 2 (+ve )

-3-4 = -7: Start at -3 move 4 steps to left to give -7 (-ve)

2+5 = 7: Start at 2 and move 5 steps to the right to give 7(+ve)

1- -5 = 6 : Start at 1 and then ...:confused: to give 6 (+ve) Why is it positive answer :confused:. This is what I am trying to convey.
 
WingZero30 said:
What I am trying to find is an explanatory rule that works for all the combinations.

So for 3-1=2: Start at 3 and move one step to the left to give 2 (+ve )

-3-4 = -7: Start at -3 move 4 steps to left to give -7 (-ve)

2+5 = 7: Start at 2 and move 5 steps to the right to give 7(+ve)

1- -5 = 6 : Start at 1 and then ...:confused: to give 6 (+ve) Why is it positive answer :confused:. This is what I am trying to convey.
Click to expand...

Have you just ignored my ice bowl explanation? :mad:
 
The_Sophisticate said:
Number lines suck for teaching, use a real world example like a bowl of water and it sticks in your head. At least it has for me for 9 years.
Click to expand...

Thanks sophisticate. That explaination does make sense. I am just trying to find a mathematical explaination which it seems is baffling everyone:D. If I can't then I will stick with real life examples. But would love to find out who formed the rule of - - = + :p
 
just put the lines together, in a power rangers style megazord formation, 1 spins round vertical and crosses the other and combines with a big flash :p
 
memyselfandi said:
Surely you problem is in the last example you don't have an operator as written?

So you either have

(3) - (1) = 2 .... no negative number, no issue

(3) - (-1) = 4 .... 4 steps between 3 and -1 as you expected.

As orignally written you actually have, if the second number is -1

(3)(-1) = -3

where ab == (a) * (b)
Click to expand...

Thanks memy. This also seems good explaination
 
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