Question

The associative property is applicable to
1) addition and subtraction
2) multiplication and division
3) addition and multiplication
4) subtraction and division

Answer 1

Hint: This question is based on fundamental concepts of mathematics, i.e., the associative property. The associative property is a maths rule that says that the way in which factors are grouped in a multiplication problem does not change the product. Same applies for addition.

Complete step-by-step answer:
This question is based on the direct property of maths in which you get the same answer if three or more numbers are operated by some specific mathematical operators regardless of the grouping.
Associative property is applicable to addition. Therefore, three or more numbers can be added in any order and the result would remain same.
For example: if we have to add three numbers: $4,7,11$.
Then, we have, $4 + \left( {7 + 11} \right) = 4 + 18 = 22$ and $\left( {4 + 7} \right) + 11 = 11 + 11 = 22$.;
So, the sum of three numbers remains the same regardless of the order of their addition.
Similarly, associative property is applicable to multiplication. Therefore, three or more numbers can be multiplied in any order and the result would remain same.
For example: if we have to multiply three numbers: $4,7,11$.
Then, we have, $4 \times \left( {7 \times 11} \right) = 4 \times 77 = 308$ and $\left( {4 \times 7} \right) \times 11 = 28 \times 11 = 308$.
So, the product of three numbers remains the same regardless of the order of their multiplication.
But, we cannot apply this property to subtraction and division.
For example:
We have, $4 - \left( {7 - 11} \right) = 4 - \left( { - 4} \right) = 4 + 3 = 8$ and $\left( {4 - 7} \right) - 11 = - 3 - 11 = - 14$. Since both answers are different. Hence, associative property is not applicable for subtraction.
Similarly for division, if we have to solve $4 \div \left( {8 \div 2} \right)$ and $\left( {4 \div 8} \right) \div 2$.
So, we get, $4 \div \left( {8 \div 2} \right) = 4 \div 4 = 1$ and $\left( {4 \div 8} \right) \div 2 = \left( {\dfrac{4}{8}} \right) \div 2 = \left( {\dfrac{1}{2}} \right) \div 2 = \dfrac{1}{4}$.
Therefore, the associative property is applicable for addition and multiplication. Hence,
So, the correct answer is “Option 3”.

Note: The question is based on the fundamental concepts of maths, one who is not well versed with them will find it difficult to solve the question. We must know the BODMAS rule to simplify the expression and solve the mathematical operations in the correct order of sequence.
BODMAS rule is an acronym to help children to remember the order of operations in calculations. Operations are simply the different things that we can do to numbers in maths. It stands for, 'Brackets, Order, Division, Multiplication, Addition, Subtraction.