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

represents which one of the following properties:

Associative

`place`

Notice that on the left side of the equation the parentheses indicate to add the `b`

and the `c`

before you add the `a`

.

On the right side of the equation, we first add `a`

and `b`

before adding `c`

.

The order of the variables has not changed but the groupings (what's inside the parentheses) have.

The groups have changed, and another word for a group is *association*.The above equation demonstrates the Associative Property of addition.

represents which one of the following properties:`A`+(`B`+`C`)=(`A`+`B`)+`C`

Associative

`place`

On the left side of the equation, the parentheses indicate to add the `B` and the `C` before you add the `A`. On the right side of the equation, we first add the `A` and the `B` before adding the `C`.

Notice that the order of the numbers inside the parentheses has not changed but the groupings (what's inside the parentheses) have.

Evaluating the left side:

`A`+(`B`+`C`)=`ASSOCIATIVE_RESULT`

Evaluating the right side, the result is the same:

`(`

`A`+`B`)+`C`=`ASSOCIATIVE_RESULT`

The groups have changed, and another word for a group is *association*. The equation demonstrates the Associative Property.

Which one of the equations on the right represents the Associative Property of addition?

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

`value`

The Associative Property should not be confused with the Commutative Property, in which the sequence or order of numbers is changed.

In contrast to the Commutative Property, the Associative Property justifies rearranging our parentheses. For example, adding `(4+2)+3`

is equivalent to adding `4+(2+3)`

and represents the Associative Property.

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

demonstrates the Associative Property.

`a+b=b+a`

represents which one of the following properties:

Commutative

`value`

As this equation implies, changing the order of `a`

and `b`

will not change the end result.

This property should not be confused with the Associative Property, in which groupings (what's inside the parentheses) are changed.

This equation demonstrates the Commutative Property. The following sentence may help you to remember this property: The *commuting* distance is the same in either direction, from school to home or home to school.

represents which one of the following properties:`A`+`B`=`B`+`A`

Commutative

`value`

This property should not be confused with the Associative Property, in which the order of operations is changed.

As this equation implies, changing the order of `A` and `B` doesn't change the end result.

Evaluating the left side:

`A`+`B`=`COMMUTATIVE_RESULT`

Evaluating the right side, the result is the same:

`B`+`A`=`COMMUTATIVE_RESULT`

This equation demonstrates the Commutative Property. The following sentence may help you to remember this property: The *commuting* distance is the same in either direction, from school to home or home to school.

Which one of the equations on the right represents the Commutative Property of addition?

`a+b=b+a`

`value`

According to the Commutative Property, the order of the numbers doesn't matter.

The Commutative Property should not be confused with the Associative Property, in which you change the groupings (what is contained inside the parentheses).

The following sentence may help you to remember the Commutative Property: "The *commuting* distance is the same in either direction, from school to home or home to school."

`a+b=b+a`

demonstrates the Commutative Property.

`a+b(c+d)=a+bc+bd`

represents which one of the following properties:

Distributive

`value`

On the left side of the equation, `b`

is multiplied by the sum of `c`

and `d`

.

On the right side of the equation, we first multiply `b`

by `c`

and `d`

individually and then add their products.

We say that multiplication *distributes* `b`

over addition of `c`

and `d`

, and this equation demonstrates the Distributive Property.

represents which one of the following properties:`A`+`B`(`C`+`D`)=`A`+(`B`)(`C`)+(`B`)(`D`)

Distributive

`value`

On the left side of the equation,

is multiplied by the sum of `B`

and `C`

. On the right side of the equation, we first multiply `D`

by `B`

and `C`

individually and then add their products.`D`

Evaluating the left side:

`A`+`B`(`C`+`D`)=`DISTRIBUTIVE_RESULT`

Evaluating the right side, the result is the same:

`A`+(`B`)(`C`)+(`B`)(`D`)=`DISTRIBUTIVE_RESULT`

We say that multiplication *distributes*

over addition of `B`

and `C`

and so this is called the Distributive Property.`D`

Which one of the equations on the right represents the Distributive Property of addition?

`a+b(c+d)=a+bc+bd`

`value`

In the correct answer, on the left side the equation `b`

is multiplied by the sum of `c`

and `d`

.

On the right side of this equation, we first multiply `b`

by `c`

and `d`

individually and then add their products.

In this equation, `b`

gets *distributed* to `c`

and `d`

, and so we call this the Distributive Property.

`a+b(c+d)=a+bc+bd`

represents the Distributive Property.