0

I reckon this is a kid question, but I was solving a simple problem today and I got stucked in a basic topic: Arithimetic using integer numbers:

My question is: Can someone explain in a logical example or in a logical way why subtracting a negative number gives us a positive one?

For example: 3 - (-2) = 5 OR 1/2 - (-1/3) = 5/6

Thanks in advance

Matheus Minguini
  • 159
  • 1
    As my old school teacher loved to say: If you love to love, that's good. If you love to hate, that's bad. If you hate to love, that's bad, and if you hate to hate, that's good. In the same way, adding a positive number increases something, adding a negative number decreases something, subtracting a positive number decreases something, and subtracting a negative number increases something. – TomGrubb Nov 15 '17 at 20:44
  • 1
    You will need to clarify what you mean by "in a logical way." To a trained mathematician, we will tell you to remember that the subtraction $a-b$ is defined as $a$ plus the additive inverse of $b$, that is to say $a-b = a+(-b)$. We then remember that the additive inverse of $-2$ is equal to $2$ since $(-2)+(-(-2))=0=(-2)+2$. As a result, we have $3-(-2)=3+(-(-2))=3+2=5$ – JMoravitz Nov 15 '17 at 20:47
  • To me, that is a perfectly logical explanation, but you may be looking for a more intuitive explanation instead, to which you might prefer thinking of adding and subtracting as "moving to the right or to the left" by various amounts respectively. If we move to the left of $3$ by an amount of negative two, that is the same as moving to the right of three by an amount of two. – JMoravitz Nov 15 '17 at 20:49
  • Draw the number line and mark on -3 and 2. What meaning would you give to $2-(-3)$? – Paul Nov 15 '17 at 20:49
  • It doesn't. $-3-(-1) =-2$ – Karl Nov 15 '17 at 21:15
  • Thanks guys for all the support! I really appreciate – Matheus Minguini Nov 16 '17 at 00:44

1 Answers1

1

This is more of a didactic question, thus a didactic answer.

Money

Intuitive way of thinking about numbers can be the concept of money.

  • Positive value means you have that amount of money.
  • Negative value means you owe that amount of money.

Adding positive number means I give you money. Subtracting positive number means you give me money. Adding negative number means paid a debt, subtracting negative number means a debt has been forgiven.

Distance

Another concepts used for explaining negative numbers can be made on a road.

  • Addition of positive means going forward.
  • Addition of negative means going backwards.
  • Subtraction of positive means turning around and going forward.
  • Subtraction of negative means turning around and going backwards.
Lukáš Mrazík
  • 97