Today, I asked my Grade-6 students to solve the following problem –
-15 + 20 = ?

Though I have only given them a brief idea of integers in Grade-5, i expected that they would be able to solve this question with the help of a number line.
Well to my surprise,I got 4 different answers to this question and they were : – 20, 5, -35 and 35.

I, therefore, decided to change course and gave the students five important rules that they needed to learn if they were to be good in the world of numbers.
Rule-1: a + b = b + a
Rule-2: a – b is not = b – a
Rule-3: a X b = b X a
Rule-4: a/b is not = b/a
Rule-5: a X 0 = 0, a X 1 = a, a + 0 = a and a – 0 = a

Now, i asked the students to solve the problem again, but still some students weren’t able to solve the problem, so i decided to take help of mathematical induction.Here is what I did –
I said,
In the question -15 + 20 = ?
If we take a = -15 and b = 20, then
-15 + 20 can also be written as 20 + (-15) — Using Rule No.1

Next I told them that now there are 2 possibilities of opening the bracket in case we need to find out the value of 20 + (-15),
Option-1: -15 + 20 = 20 + (-15) = 20 – 15 OR
Option-2: -15 + 20 = 20 + (-15) = 20 + 15

Now, let us assume that option-2 is correct, in which case, we can write,

-15 + 20 = 20 + (-15) = 20 + 15
-15 + 20 = 20 + 15

But we know that,
20 + 15 = 15 + 20 — Using Rule No.1

Therefore, we can replace 20 + 15 with 15 + 20
-15 + 20 = 15 + 20
Now, let us subtract 20 on both sides, we get,
-15 = 15
But, we know that this is not possible, therefore option-2 is wrong and hence Option-1 is correct.

This means that,
-15 + 20 = 20 + (-15) = 20 – 15 = 5 (Answer)

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