COMMUTATIVE PROPERTY DISTRIBUTIVE PROPERTY ASSOCIATIVE PROPERTY

Commutative Property :

If two quantities are added or multiplied, even changing the order that we add or multiply, in both ways we will get the same answer. This is known as commutative property.

a + b = b + a

ab = ba

Arithmetic operator

Addition

Subtraction

Multiplication

Division

True/False

True

False

True

False

Associative Property :

Sum of three quantities or product of three quantities even changing the order of addition and multiplication. The answer will not change.

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

a x (b x c) = (a x b) x c

Distributive Property :

The distributive property multiplies the value outside the brackets with each of the terms in the brackets.

a x (b + c) = ab + ac

a x (b - c) = ab - ac

Problem 1 :

6 x (22 + 9) = 6 x 22 + 6 x 9

This is an example of __________________ property.

Solution :

6 x (22 + 9) = 6 x 22 + 6 x 9

6 is distributed with 22 as well 9. 

This is an example of distributive property.

Problem 2 :

2 x (6 + 4) = 2 x 6 + 2 x 4

This is an example of _________________ property.

Solution :

Here 2 is multiplied with 6 and 4. So, this is an example of distributive property.

Problem 3 :

14 + 13 = 13 + 14

This is an example of __________________ property.

Solution :

13 and 14 are added, even we change the order of adding these quantities the answer will never change. So, this is an example of commutative property.

Problem 4 :

The _____________ property means the numbers can be swapped.

Solution :

2 + 3 and 3 + 2, in both ways we will get the same answer. Even we change the order of adding or multiplying these two quantities, the answer will never be affected. So, this is called commutative property.

Problem 5 :

The rule that refers to grouping is _____________ property.

Solution :

Associative property is the rule of grouping. 

Problem 6 :

The _____________ property says that, changing the GROUPING of numbers that are either being added or multiplied does NOT change the value of it.

Solution :

Grouping involves associative property. In this property, even we change the order of grouping that will change the answer.

Problem 7 :

(12 x 5) x 3 = 12 x (5 x 3)

This is an example of __________________ property.

Solution :

Here we see three quantities are involved and it says the order that we multiply can change, it will not affect the answer. So, it is associative property.

Problem 8 :

The _____________ property multiplies the value outside the brackets with each of the terms in the brackets.

Solution :

Consider a(b + c)

Here a should be multiplied by b and c separately, then add the results. 

It is distributive property.

Problem 9 :

(6 x 9) x 2 = 6 x (9 x 2)

This is an example of __________________ property.

Solution :

Here three quantities are involved, changing the order of multiplication will never change the answer. So, it is associative property.

Problem 10 :

In the _____________ property, the parenthesis (or brackets) can be moved.

Solution :

Considering associative property :

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

a x (b x c) = (a x b) x c

brackets is not removed in associative property.

Considering distributive property :

a x (b + c) = ab + ac

So, in distributive property, the brackets can be removed.

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