Understanding the Commutative Law of Multiplication

Oct 13, 2025 by leolavanderia.com.br 117 views

Understanding the Commutative Law of Multiplication

The commutative law of multiplication is a fundamental concept in mathematics that states that the order of the factors in a multiplication problem does not change the result. In other words, when multiplying two or more numbers together, we can rearrange the numbers and still get the same product. This law is often represented as:

a × b = b × a

where a and b are any two numbers.

Applying the Commutative Law to $$2(4)(6)$$

Now, let's apply the commutative law to the expression $$2(4)(6)$$. We can rewrite this expression by rearranging the factors, using the commutative law. Since the commutative law allows us to swap the order of the factors, we can rewrite $$2(4)(6)$$ as:

4(6)(2)

This is because we can swap the order of the factors 2 and 4, and still get the same product.

Evaluating the Expression $$4(6)(2)$$

Now, let's evaluate the expression $$4(6)(2)$$. To do this, we can follow the order of operations (PEMDAS):

Multiply 4 and 6: 4 × 6 = 24
Multiply 24 and 2: 24 × 2 = 48

Therefore, $$4(6)(2) = 48$$.

Comparing the Original Expression with the Rewritten Expression

Now, let's compare the original expression $$2(4)(6)$$ with the rewritten expression $$4(6)(2)$$. We can see that both expressions have the same product, which is 48.

Evaluating the Other Options

Let's evaluate the other options:

Option B: $$2(4)(6)=8(6)$$

To evaluate this expression, we can follow the order of operations (PEMDAS):

Multiply 8 and 6: 8 × 6 = 48

Therefore, $$8(6) = 48$$.

Option C: $$2(4)(6)=1(3)(16)$$

To evaluate this expression, we can follow the order of operations (PEMDAS):

Multiply 1 and 3: 1 × 3 = 3
Multiply 3 and 16: 3 × 16 = 48

Therefore, $$1(3)(16) = 48$$.

Option D: $$2(4)(6)=48$$

This option is already evaluated in the previous sections, and we know that $$2(4)(6) = 48$$.

Conclusion

In conclusion, we have rewritten the expression $$2(4)(6)$$ in a different way, using the commutative law of multiplication. We have also evaluated the rewritten expression and compared it with the original expression. We have also evaluated the other options and found that they are all equal to 48.

Final Answer

The final answer is: $\boxed{48}$

Understanding the Commutative Law of Multiplication

a × b = b × a

where a and b are any two numbers.

Q&A: Rewrite $$2(4)(6)$$ in a Different Way, Using the Commutative Law of Multiplication

Q: What is the commutative law of multiplication?

A: The commutative law of multiplication is a fundamental concept in mathematics that states that the order of the factors in a multiplication problem does not change the result.

Q: How can we apply the commutative law to $$2(4)(6)$$?

A: We can rewrite $$2(4)(6)$$ as $$4(6)(2)$$ by rearranging the factors, using the commutative law.

Q: Why is the commutative law important in mathematics?

A: The commutative law is important in mathematics because it allows us to simplify complex multiplication problems by rearranging the factors.

Q: Can we use the commutative law to rewrite any multiplication problem?

A: Yes, we can use the commutative law to rewrite any multiplication problem by rearranging the factors.

Q: How do we evaluate the expression $$4(6)(2)$$?

A: To evaluate the expression $$4(6)(2)$$, we can follow the order of operations (PEMDAS):

Multiply 4 and 6: 4 × 6 = 24
Multiply 24 and 2: 24 × 2 = 48

Q: What is the final answer to the expression $$2(4)(6)$$?

A: The final answer to the expression $$2(4)(6)$$ is 48.

Q: Can we use the commutative law to rewrite the expression $$2(4)(6)$$ in other ways?

A: Yes, we can use the commutative law to rewrite the expression $$2(4)(6)$$ in other ways, such as $$8(6)$$ or $$1(3)(16)$$.

Q: How do we evaluate the expression $$8(6)$$?

A: To evaluate the expression $$8(6)$$, we can follow the order of operations (PEMDAS):

Multiply 8 and 6: 8 × 6 = 48

Q: How do we evaluate the expression $$1(3)(16)$$?

A: To evaluate the expression $$1(3)(16)$$, we can follow the order of operations (PEMDAS):

Multiply 1 and 3: 1 × 3 = 3
Multiply 3 and 16: 3 × 16 = 48

Q: What is the final answer to the expression $$1(3)(16)$$?

A: The final answer to the expression $$1(3)(16)$$ is 48.

Conclusion

Final Answer

The final answer is: $\boxed{48}$