Question

Juan used the expression 16 – 9 – 12 + 22 to find his profit for days 2 and 3. He rewrote the expression as 16 + (–9) + (–12) + 22.

Juan can use the associative and commutative properties to rewrite the expression again. Explain why he had to use the additive inverse before he could use these properties.

Answer 1

Answer:

16 + ( -9 ) + ( - 12 ) + 22

= 16 - 9 - 12 + 22

= 17 ( answer )

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Answer 2

Associative and Commutative properties  are applicable for Addition not on subtraction that's why additive inverse  used to have all terms in addition,

Associative and Commutative properties  are applicable for Addition and multiplication

These property are not for Division and subtraction

Commutative property of Addition

a + b = b+a

Associative property of Addition

a + (b + c) = (a + b) + c

a - b = b - a   does not hold true until a = b

Hence Commutative property  can not be applied on subtraction.

Similarly

Associative property can not be applied on subtraction

That's why  additive inverse  used to have all terms in addition,

So that Associative and Commutative properties can be applied

Associative and Commutative properties  are applicable for Addition not on subtraction that's why additive inverse  used to have all terms in addition,

Additional Info:

16 – 9 – 12 + 22 = 17