During the Age of Enlightenment, Ludwig Von Prague, a rather mediocre mathematician was searching for a theory that would make him famous. While eating his usual breakfast of bagels and cream cheese, he struck upon the idea that if you added up all the
of the all the bagels, their sum would still be equal to the hole in the first bagel. Thus he created the theory that
nothing plus nothing equals nothing
or more commonly known as the "
Von Prague Bagel Theory
The Zero Property
Chef Henri is very particular about where he gets the ingredients for his recipes. For instance, for eggs, he will only buy from two specific farmers, Monsieur Egblanc and Monsieur Egbrun. One day, he purchases 4 dozen eggs from M. Egblanc and no eggs from M. Egbrun. How many eggs did Chef Henri buy that day?
Of course, the answer to that is 4 dozen eggs because 4 + 0 = 4.
This illustrates the
Additive Identity Property of Zero
is called the
because adding zero to any number doesn't change that number's value. Therefore, the number keeps its identity.
On the particular day on which Chef Henri bought the
4 dozen eggs
from M. Egblanc, he used
4 dozen eg
to fill orders at his restaurant that night. We can represent the eggs he bought as
(positive four) and the eggs he used as
(negative four). If he adds these together, he will find that he has no eggs left.
This is an example of the
Property of Opposites.
are examples of additive inverses or opposites. The additive inverse of
17 is -17
the additive inverse of
-42 is 42
and the additive inverse of
-½ is ½
Adding additive inverses will always produce the sum of zero.
Use the Additive Identity Property of Zero and the Property of Opposites to help Chef Henri with this problem:
The following day Chef Henri buys
eggs from M. Egblanc and
eggs from M. Egbrun. Henri uses
eggs in his recipes that evening.
Write an equation which shows how many eggs Henri has left at the end of the day.
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