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.

Jaun has to use inverse before using those properties as they does not support subtraction but only addition. Solution:Given that , 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) + 22Juan can use the associative and commutative properties to rewrite the expression again.  We have to explain why he had to use the additive inverse before he could use these properties. Now, Associative property and commutative property true for addition. i) a + (b + c) = (a + b) + c  ---> Associative property of addition ii) a + b = b + a --> commutative property of addition. These properties not true for subtraction. That's the reason Juan used additive inverse before applying these property. Hence, jaun has to use inverse before using those properties as they does not support subtraction but only addition.