Why do subtraction and division not need to exist
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Why do subtraction and division not need to exist

[From: ] [author: ] [Date: 12-01-02] [Hit: ]
While this may seem like semantics, this is actually a major flaw in most mathematics curricula.The same type of argument holds for division where you are multiplying the inverse.Think about it.Addition is commutative as is multiplication.However if you think of subtraction or division,......
I have report I have to do on this subject and I have no idea what the answer is, please help.

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Subtraction is really the opposite of addition, or adding the opposite.

for example, a-b is really a + (-b) or a with b in the negative direction added to it.

While this may seem like semantics, this is actually a major flaw in most mathematics curricula.

The same type of argument holds for division where you are multiplying the inverse.

Think about it. Addition is commutative as is multiplication. However if you think of subtraction or division, you need to nullify the commutative rules. This inconsistancy causes many new students to have issues with mathematics.
Is this a relatively simple thing to teach, yes. But most people are brought up as children subtracting rather than adding negatives.

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we can think of subtraction as additon. for example, 5 - 3 = 5 + (- 3). division is can be multiplication as shown with this example 5/6 = 1/6 * 5.

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subtraction is really addition of an additive inverse and

division is multiplication be a multiplicative inverse..

the only operations defined on the reals are addition and multiplication !

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because any subtraction equation written a - b can also be written a + -b

and any division equation written a/b can also be written as a * 1/b
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