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

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) + 22

Juan 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.

Answer 2

Answer:Juan can add the numbers

Step-by-step explanation:

Answer 3

The associative and commutative properties can be applied only to problems with addition. Juan had to change the subtraction to addition by adding the additive inverse.

Answer 4

Sample response: The associative and commutative properties can be applied only to problems with addition. Juan had to change the subtraction to addition by adding the additive inverse.