Hi Mrs Marcus,

the actual mathematical proof of why a negative integer becomes a positive integer when multiplied by itself is rather complex. 

Imagine you are standing on a road in Jurong East. You measure distance to your left (East) as positive, and distance to your right (West) as negative, so you are standing at zero.

If Chinese Garden is 1km toward the East, it would be +1km. Clementi, which is 1km away towards the West, becomes -1km to the West.

Now imagine a car travelling toward the East at 60km/h; we would say that it can travel +60km in one hour. For a car travelling West at 60km/h, we would say that it can travel -60km.

Now , if the car passes by you on its way to the East, and we want to calculate where it was 1 hour ago, we would use (-1h) x (60km/h) = -60km = 60km West.

Finally, a car that is travelling West passes by you. One hour ago, it was somewhere in the East, correct? 
So our solution would have to show that (-1h) x (-60km/h) = +60km East. Therefore, the negatives have to cancel out the positive, if not we would not be able to explain mathematically how decreases and increases occur.

I hope this helps, and if it does- please like and accept it as an answer 🙂 

-Michelle (DingleTutors)

Examples adapted from: http://mathforum.org/dr.math/faq/faq.negxneg.html

If one says “Do NOT not eat!”, one is actually saying one doesn’t want another to starve; so one is back to saying “Eat!” (positive). Thus, two negatives make a positive.