Opposite Numbers and Simplifying Notations

Opposite Numbers

And

Simplifying Notations

Opposites:

     An opposite number is just the same number, no matter how big with the opposite sign. When I say opposite sign I mean positive or negative.

EXAMPLE:

(+5) is the opposite of (-5)

(-7) is the opposite of (+7)

(+2189) is the opposite of (-2189)

Visual Representation: 

    Positive two and negative two are both two away from zero. The difference is that negative two is two places two the left of zero, and positive two is two places to the right of zero! Right and Left are both opposites!

Simplifying Notations: 

     When simplifying notations like these

-(-9) + (8)

 or

(+10) + [-(-11)]

or even

(-8) + {-[-(-21)]}

One thing to look out for is the number of negative signs next to each other. When there is an even number of negative signs next to each other, then they all cancel each other out two by two until there is none left and a positive sign takes its place. If there is an odd number of negatives next to each other then they cancel each other out two by two until there is one negative standing.

So...

(+4) + [-(-2)] is the same as (+4) + (+2) because the negatives cancel out!

and... (+6) + {-[-(-3)]} is the same as (+4) + (-3) because two negatives cancel out leaving one left.

 

Story Time:

      Some people use mini stories to help understand negatives and positive. This is one of my favorites.

So negatives are all bullies and they beat everyone they meet. If they come across a positive then the negatives push them to the side and the positives run away. When negatives meet other negatives then they knock each other out two by two. So if there is an even amount of negatives next to each oher then they fight until they all knocked each other out, then a positive comes out of hiding and takes its place. If there is an odd amount of negatives next to each other then they fight and knock each other out two by two until there is one left standing.