Question

8. For numbers 8a-8c, tell whether each expression was rewritten using the Commutative Property or the Associative Property. Choose the correct property of addition. Associative Property 8a. + (2 + 4) = 5 + (4 + 2 Commutative Property Associative Property 8b. 1 히 6 Commutative Property Associative Property 8c. ( 13 + 35) + + (33 + 1 Commutative Property

Answer 1

(a)

`\begin{gathered} (5)/(7)+((2)/(9)+(4)/(7))=(5)/(7)+((4)/(7)+(2)/(9)) \\ \text{This expression was re-written using the Commutative property} \end{gathered}`

(b)

`\begin{gathered} ((1)/(8)+(5)/(6))+(1)/(6)=(1)/(8)+((5)/(6)+(1)/(6)) \\ \text{This expression was re-written using the associative property} \end{gathered}`

(c)

`\begin{gathered} (1(2)/(5)+3(1)/(3))+(4)/(5)=(3(1)/(3)+1(2)/(5))+(4)/(5) \\ \text{This expression was re-written using the Commutative property} \end{gathered}`

The Commutative property of addition (and multiplication) states that the numbers we are dealing with in math can have their positions changed, without making any difference to the final answer.

In number 8(a), the fractions in parenthesis swapped places but this wouold not affect the answer.

The Associative property of addition (and multiplication) states that when two or more numbers are added (or multiplied) the results remain the same regardless of the change in grouping of the parenthesis.

In number 8(b), the first and second expression were grouped into parenthesis. But when the second and third expression were regrouped into the parenthesis, the answer would remain the same.