Question

The associative property is applicable to:-

• A. Addition and subtraction
• B. Multiplication and division
• C. addition and multiplication
• D. subtraction and division​

Answer 1

The correct option is C

addition and multiplication

Correct option: (c) addition and multiplication

This property states that when three or more numbers are added (or multiplied), the sum (or the product) is the same regardless of the grouping of the addends (or the multiplicands). We cannot apply the associative property to subtraction or division. The associative property is helpful while adding or multiplying multiple numbers.

Associative Property

Associative, as the name implies, means grouping. The origin of the term associative is from the word “associate”. Basic mathematical operations which can be performed using associative property are addition and multiplication. This is normally applicable to more than two numbers.

For, numbers $x,y,z$

Associative property of addition states that:

$(x+y)+z=x+(y+z)$

Associative property of multiplication states that,

$x\times \left(y\times z\right)=\left(x\times y\right)\times z$

Example:

Consider the number $6,8,9$

$\Rightarrow (6+8)+9=14+9=23$

Now, let’s regroup the terms

$\Rightarrow 6+(8+9)=6+17=23$

Yes, it can be seen that the sum in both cases are the same. This is the associative property of addition.

Also,

$6\times \left(8\times 9\right)=432$ and $\left(6\times 8\right)\times 9=432$

Yes, it can be seen that the sum in both cases are the same. This is the associative property of multiplication.

But,

$6-\left(8-9\right)=6-\left(-1\right)=6+1=7$ and$\left(6-8\right)-9=-2-9=-11$

So, it can be seen that associative property is not applicable for subtraction.

Also $6÷\left(8÷9\right)\ne \left(6÷8\right)÷9$

So, it can be seen that associative property is not applicable for division.

Hence, option C is correct.