SOLUTION: How can you remember the difference between Distributive, associative, cummutative and remember the difference between factors and terms

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Question 261252: How can you remember the difference between Distributive, associative, cummutative and remember the difference between factors and terms
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Start with the associative property. Associate means to be together. Addition and multiplication are "binary" operations. That means you can only perform either of them on two quantities at a time. The associative property says that it doesn't matter which of several pairs of quantities you associate first, second, etc., it all comes out the same in the end. That is:



and



for all values of a, b, and c.

Next, the commutative property. Commute means to move from one place to the other. You commute from home to school, your parents commute from home to work. The commutative property allows you to move the order of quantities you add or multiply as in:



and



for all values of a and b.

The distributive property. Distribute means to spread around or pass around. The teacher distributes test booklets, the paperboy distributes newspapers, and so on. The distributive property allows you to distribute a factor across a set of terms.



The factor a was distributed across the set of terms b plus c.

A product is the result of multiplying two or more numbers called factors. Consider the number 6. It has two non-trivial factors, namely 2 and 3. Consider the number . It has factors of and . The number has 4 factors: and then three factors of

Terms are numbers that are elements of a sum, that is they are the individual numbers that are added. Note that I do not include subtraction. There is no such thing as subtraction. If you want the difference of two numbers add the opposite. For example, never think of 6 - 2 as "six minus two" Rather, think of it as "six plus the opposite of two", namely 6 + (-2). In this example, 6 and -2 are terms. This is because the operation of subtraction is NOT commutative. Note that:



whereas



has three terms, namely , , and

I also do not define division. Rather, I always multiply by the reciprocal. That is because the operation of division is not commutative.

In general:



However, multiplication by the reciprocal, like any other multiplication IS commutative.




John