randRangeUnique( 2, 10, 4 ) [ $._("Associative"), $._("Commutative"), $._("Distributive") ] shuffle( [ "a+b=b+a", "a+b(c+d)=a+bc+bd", "a+(b+c)=(a+b)+c" ] ) A+B+C A+B A+B*C+B*D

a+(b+c)=(a+b)+c represents which one of the following properties:

PROPERTIES[0]

  • 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.

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

PROPERTIES[0]

  • 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:

PROPERTIES[1]

  • 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.

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

PROPERTIES[1]

  • 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.

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).

a+b=b+a demonstrates the commutative property.

a+b(c+d)=a+bc+bd represents which one of the following properties:

PROPERTIES[2]

  • 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.

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

PROPERTIES[2]

  • 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.

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 B over addition of C and D and so this is called the distributive property.

Which one of the equations on the right represents the distributive property of addition over multiplication?

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.