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Some great answers were provided here, but I wanted to add something which I think is essential: to emphasize to the student that it is a very good thing to question this! Why am I saying that? Because indeed, for many operations in algebra the associative property does not hold! For example, when talking about division: $8/(4/2) \neq (8/4)/2$. So in fact I would go so far as to say, that a student who questions this may have a latent / undeveloped talent for Math! Because clearly here is an example of a single operation, namely division, where the associative property does not hold. So I would definitely compliment the student for not taking this for granted, and go on to explain that multiplication is one of the special operations where it holds that $a\times(b \times c) = (a\times b)\times c$ and therefore we can drop the parentheses without ambiguity.

A similar example can also explain the commutativity of multiplication: $2 \times 4 = 4 \times 2$ but $2 / 4 \neq 4 / 2$. Actually I realize that this is actually more relevant to the examples given in the question, and in fact it is important to notice the relation between these two properties. It can actually be a fun exercise for a student to prove that given:

1. $(a \times b) \times c = a \times (b \times c)$
2. $a \times b = b \times a$

then also: $ a \times b \times c = c \times b \times a $ (Given only 1. or 2., this doesn't hold!).

Another thing which occasionally helps here is to ask the student the simplest possible question: "What is bothering you about this rule?". I think I've already established, there is something to be bothered about here. But the student, not always having the faculty with words to explain what is bothering him, just feels "silly" and "inadequate" to deal with the problem. In other words, he feels that it is already wrong to be bothered about something so "simple", which is absolutely bananas! The opposite is true.

Some great answers were provided here, but I wanted to add something which I think is essential: to emphasize to the student that it is a very good thing to question this! Why am I saying that? Because indeed, for many operations in algebra the associative property does not hold! For example, when talking about division: $8/(4/2) \neq (8/4)/2$. So in fact I would go so far as to say, that a student who questions this may have a latent / undeveloped talent for Math! Because clearly here is an example of a single operation, namely division, where the associative property does not hold. So I would definitely compliment the student for not taking this for granted, and go on to explain that multiplication is one of the special operations where it holds that $a\times(b \times c) = (a\times b)\times c$ and therefore we can drop the parentheses without ambiguity.

A similar example can also explain the commutativity of multiplication: $2 \times 4 = 4 \times 2$ but $2 / 4 \neq 4 / 2$. Actually I realize that this is actually more relevant to the examples given in the question, and in fact it is important to notice the implication of having these two properties together for a single operation such as multiplication. It can actually be a fun exercise for a student to prove that given:

1. $(a \times b) \times c = a \times (b \times c)$
2. $a \times b = b \times a$

then also: $ a \times b \times c = c \times b \times a $ .

Note that given only 1. or 2., this doesn't hold! This is also a source of (justified) confusion: a lot of students implicitly think that commutativity (swapping rule) implies associativity, but those are totally independent properties.

Another thing which occasionally helps here is to ask the student the simplest possible question: "What is bothering you about this rule?". I think I've already established, there is something to be bothered about here. But the student, not always having the faculty with words to explain what is bothering him, just feels "silly" and "inadequate" to deal with the problem. In other words, he feels that it is already wrong to be bothered about something so "simple", which is absolutely bananas! The opposite is true.

Some great answers were provided here, but I wanted to add something which I think is essential: to emphasize to the student that it is a very good thing to question this! Why am I saying that? Because indeed, for many operations in algebra the associative property does not hold! For example, when talking about division: $8/(4/2) \neq (8/4)/2$. So in fact I would go so far as to say, that a student who questions this may have a latent / undeveloped talent for Math! Because clearly here is an example of a single operation, namely division, where the associative property does not hold. So I would definitely compliment the student for not taking this for granted, and go on to explain that multiplication is one of the special operations where it holds that $a\times(b \times c) = (a\times b)\times c$ and therefore we can drop the parentheses without ambiguity.

(A similar example can also explain the commutativity of multiplication: $2 \times 4 = 4 \times 2$ but $2 / 4 \neq 4 / 2$)

Another thing which occasionally helps here is to ask the student the simplest possible question: "What is bothering you about this rule?". I think I've already established, there is something to be bothered about here. But the student, not always having the faculty with words to explain what is bothering him, just feels "silly" and "inadequate" to deal with the problem. In other words, he feels that it is already wrong to be bothered about something so "simple", which is absolutely bananas! The opposite is true.

Some great answers were provided here, but I wanted to add something which I think is essential: to emphasize to the student that it is a very good thing to question this! Why am I saying that? Because indeed, for many operations in algebra the associative property does not hold! For example, when talking about division: $8/(4/2) \neq (8/4)/2$. So in fact I would go so far as to say, that a student who questions this may have a latent / undeveloped talent for Math! Because clearly here is an example of a single operation, namely division, where the associative property does not hold. So I would definitely compliment the student for not taking this for granted, and go on to explain that multiplication is one of the special operations where it holds that $a\times(b \times c) = (a\times b)\times c$ and therefore we can drop the parentheses without ambiguity.

A similar example can also explain the commutativity of multiplication: $2 \times 4 = 4 \times 2$ but $2 / 4 \neq 4 / 2$. Actually I realize that this is actually more relevant to the examples given in the question, and in fact it is important to notice the relation between these two properties. It can actually be a fun exercise for a student to prove that given:

1. $(a \times b) \times c = a \times (b \times c)$
2. $a \times b = b \times a$

then also: $ a \times b \times c = c \times b \times a $ (Given only 1. or 2., this doesn't hold!).

Another thing which occasionally helps here is to ask the student the simplest possible question: "What is bothering you about this rule?". I think I've already established, there is something to be bothered about here. But the student, not always having the faculty with words to explain what is bothering him, just feels "silly" and "inadequate" to deal with the problem. In other words, he feels that it is already wrong to be bothered about something so "simple", which is absolutely bananas! The opposite is true.

Some great answers were provided here, but I wanted to add something which I think is essential: to emphasize to the student that it is a very good thing to question this! Why am I saying that? Because indeed, for many operations in algebra the associative property does not hold! For example, when talking about division: $8/(4/2) \neq (8/4)/2$. So in fact I would go so far as to say, that a student who questions this may have a latent / undeveloped talent for Math! Because clearly here is an example of a single operation, namely division, where the associative property does not hold. So I would definitely compliment the student for not taking this for granted, and go on to explain that multiplication is one of the special operations where it holds that $a\times(b \times c) = (a\times b)\times c$ and therefore we can drop the parentheses without ambiguity.

(A similar example can also explain the commutativity of multiplication: $2 \times 4 = 4 \times 2$ but $2 / 4 \neq 4 / 2$)

Some great answers were provided here, but I wanted to add something which I think is essential: to emphasize to the student that it is a very good thing to question this! Why am I saying that? Because indeed, for many operations in algebra the associative property does not hold! For example, when talking about division: $8/(4/2) \neq (8/4)/2$. So in fact I would go so far as to say, that a student who questions this may have a latent / undeveloped talent for Math! Because clearly here is an example of a single operation, namely division, where the associative property does not hold. So I would definitely compliment the student for not taking this for granted, and go on to explain that multiplication is one of the special operations where it holds that $a\times(b \times c) = (a\times b)\times c$ and therefore we can drop the parentheses without ambiguity.

(A similar example can also explain the commutativity of multiplication: $2 \times 4 = 4 \times 2$ but $2 / 4 \neq 4 / 2$)

Another thing which occasionally helps here is to ask the student the simplest possible question: "What is bothering you about this rule?". I think I've already established, there is something to be bothered about here. But the student, not always having the faculty with words to explain what is bothering him, just feels "silly" and "inadequate" to deal with the problem. In other words, he feels that it is already wrong to be bothered about something so "simple", which is absolutely bananas! The opposite is true.