Tell how the Commutative and Associative Properties of Addition can help you find the sum mentally. Then find the sum.

Question

ok so I'm confused on this equation 9+6+(−6)  I was wondering if you can help me with it please????

Answer 1

I think what your teacher wants you to see is that you can add in any order.

 

In the example you gave 9 + 6 + (-6)  instead of adding from left to right you could notice that the 6 + (-6) would equal zero and you are just left with the 9 as an answer.

This would be easier than adding 9 + 6 = 15 and then adding (-6) = 9.

 

This can really help with big numbers and adding them in your head.

 

For example if you were asked to add 38 + 57 + 62 + 43  you could notice that 38 + 62 = 100 and 57 + 43 =  100

and 100 + 100 = 200.  All of this can be done without a calculator.

 

The commutative and associative properties allow you to add in any order or in any combination.

Answer 2

Problem:     Evaluate 9+6+(−6) 

 

The rules of precedence have a cute mnemonic:  Please-Excuse-My-Dear-Aunt-Sally  (P-E-M-D-A-S).  These stand for:

    Parentheses

    Exponentiation

    Multiplication and Division

    Addition and Subtraction

 

The rule is that you scan the full expression each time you evaluate an item and perform them in the order specified by P-E-M-D-A-S going from left to right.

 

Scanning left to right, "9 + 6" is associated and added.  That makes 15.  We now have:

        15 + (-6)

 

The parentheses surround a negative number (really, a "unary minus" that implies subtract this value from 0).  We add negative 6 to 15 (which is the same as subtracting 6 from 15) and get the result 9.

 

Now, if we look at the problem again and make it:     9 + ( 6 + (-6) ), we can associate the positive 6 with the negative 6 that's going to produce 0 when we follow the rules mentioned above and get a 9 really quick.  We used the Associative Property of Addition; we did not need to use the Commutative Property of Addition.