[Math] How should we calculate difference between two numbers

algebra-precalculusarithmetic

if we are told to find the difference between 3 and 5,

then we usually subtract 3 from 5 ,5-3=2
and thus, we say that the difference is 2.
but why can't we subtract 5 from 3 ,3-5= -2 to get the
difference -2??
which result is right?
is the difference ( 2) or (-2)?

Also tell me how can we calculate the difference if we are told to calculate difference between two numbers,-5 and 2 on the number line.

Best Answer

Traditionally, the “difference" between two numbers refers to the distance on a number line between the points corresponding to each of the two numbers, a.k.a. the absolute value. Analogously, if you asked “What is the distance from Toronto to Vancouver?” or "What is the distance from Vancouver to Toronto?", you would expect the same answer: the [positive] distance separating the two cities, regardless of the direction of travel.

On the other hand, if asked “What is the result when you subtract 3 from 5?”, you should give a different answer (2) than if you were asked “What is the result if you subtract 5 from 3?” (-2).

As for calculating on the number line:

  1. If the two numbers are on the same side of $0$ (e.g., $-2$ and $-6$), the difference is the result when you subtract the smaller absolute value from the larger absolute value (e.g., $\lvert -6 \rvert - \lvert -2 \rvert = 6-2 = 4$);
  2. If the two numbers are on opposite sides of $0$ (e.g., $-5$ and $2$), then you add the absolute values (e.g., $\lvert -5 \rvert + \lvert 2 \rvert = 5+2 = 7$), or alternatively subtract the negative number from the positive one which effects a sign change (e.g., $2-(-5)=2+5=7$).
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