Understanding the Associative Law of Multiplication

Oct 13, 2025 by miodeya.com 58 views

Rewrite ${$ (68 - 5) \cdot 2$}$ using the Associative Law of Multiplication

The Associative Law of Multiplication is a fundamental concept in mathematics that allows us to rearrange the order of numbers when multiplying them together. In this article, we will explore how to rewrite the expression ${$ (68 - 5) \cdot 2$}$ using the Associative Law of Multiplication.

Understanding the Associative Law of Multiplication

The Associative Law of Multiplication states that when we multiply three numbers together, we can change the order in which we multiply them without changing the result. This law can be expressed mathematically as:

a * (b * c) = (a * b) * c

This means that we can multiply the numbers in any order, and the result will be the same.

Rewriting the Expression

To rewrite the expression ${$ (68 - 5) \cdot 2$}$ using the Associative Law of Multiplication, we need to apply the law to the expression. Let's break it down step by step:

First, we need to evaluate the expression inside the parentheses: ${ $68 - 5\$}$ . This simplifies to ${ $63\$}$ .
Now, we can rewrite the original expression as: ${ $63 \cdot 2\$}$ .
To apply the Associative Law of Multiplication, we need to multiply the numbers in a different order. Let's multiply 63 and 2 first, and then multiply the result by 5.

Step 1: Multiply 63 and 2

63 * 2 = 126

Step 2: Multiply the result by 5

126 * 5 = 630

Therefore, the rewritten expression using the Associative Law of Multiplication is: ${$ (68 \cdot 2) \cdot 5$}$.

Comparing the Options

Now, let's compare the rewritten expression with the options provided:

A. ${$ (68 \cdot 2) \cdot 5$}$ B. ${ $68 \cdot (5 \cdot 2)\$}$ C. ${$ (5 \cdot 68) \cdot 2$}$ D. ${ $2 \cdot (68 \cdot 5)\$}$

The correct answer is A. ${$ (68 \cdot 2) \cdot 5$}$, which is the rewritten expression using the Associative Law of Multiplication.

Conclusion

In this article, we explored how to rewrite the expression ${$ (68 - 5) \cdot 2$}$ using the Associative Law of Multiplication. We applied the law to the expression and simplified it to ${$ (68 \cdot 2) \cdot 5$}$. This demonstrates the power of the Associative Law of Multiplication in rearranging the order of numbers when multiplying them together.

Frequently Asked Questions

Q: What is the Associative Law of Multiplication? A: The Associative Law of Multiplication is a fundamental concept in mathematics that allows us to rearrange the order of numbers when multiplying them together.
Q: How do I apply the Associative Law of Multiplication? A: To apply the Associative Law of Multiplication, you need to multiply the numbers in a different order, while keeping the result the same.
Q: What is the correct answer to the rewritten expression? A: The correct answer is A. ${$ (68 \cdot 2) \cdot 5$}$.

Additional Resources

For more information on the Associative Law of Multiplication, visit the Khan Academy website.
To practice applying the Associative Law of Multiplication, try the following problems:
- ${$ (24 - 3) \cdot 4$}$
- ${$ (15 \cdot 2) \cdot 3$}$
- ${$ (8 \cdot 5) \cdot 2$}$

By applying the Associative Law of Multiplication, you can simplify complex expressions and make them easier to work with.
Q&A: Associative Law of Multiplication

In our previous article, we explored how to rewrite the expression ${$ (68 - 5) \cdot 2$}$ using the Associative Law of Multiplication. In this article, we will answer some frequently asked questions about the Associative Law of Multiplication.

Q: What is the Associative Law of Multiplication?

A: The Associative Law of Multiplication is a fundamental concept in mathematics that allows us to rearrange the order of numbers when multiplying them together. It states that when we multiply three numbers together, we can change the order in which we multiply them without changing the result.

Q: How do I apply the Associative Law of Multiplication?

A: To apply the Associative Law of Multiplication, you need to multiply the numbers in a different order, while keeping the result the same. For example, if you have the expression ${$ (a \cdot b) \cdot c$}$, you can rewrite it as ${$ a \cdot (b \cdot c)$}$.

Q: What are some examples of the Associative Law of Multiplication?

A: Here are some examples:

${$ (2 \cdot 3) \cdot 4$}$ = ${ $2 \cdot (3 \cdot 4)\$}$ = ${ $2 \cdot 12\$}$ = 24
${$ (5 \cdot 2) \cdot 3$}$ = ${ $5 \cdot (2 \cdot 3)\$}$ = ${ $5 \cdot 6\$}$ = 30
${$ (8 \cdot 9) \cdot 2$}$ = ${ $8 \cdot (9 \cdot 2)\$}$ = ${ $8 \cdot 18\$}$ = 144

Q: Can I apply the Associative Law of Multiplication to expressions with more than three numbers?

A: Yes, you can apply the Associative Law of Multiplication to expressions with more than three numbers. For example:

${$ (2 \cdot 3) \cdot (4 \cdot 5)$}$ = ${ $2 \cdot (3 \cdot (4 \cdot 5))\$}$ = ${ $2 \cdot (3 \cdot 20)\$}$ = ${ $2 \cdot 60\$}$ = 120
${$ (6 \cdot 7) \cdot (8 \cdot 9)$}$ = ${ $6 \cdot (7 \cdot (8 \cdot 9))\$}$ = ${ $6 \cdot (7 \cdot 72)\$}$ = ${ $6 \cdot 504\$}$ = 3024

Q: What are some common mistakes to avoid when applying the Associative Law of Multiplication?

A: Here are some common mistakes to avoid:

Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when applying the Associative Law of Multiplication.
Not simplifying the expression: Make sure to simplify the expression after applying the Associative Law of Multiplication.
Not checking the result: Make sure to check the result to ensure that it is correct.

Q: How can I practice applying the Associative Law of Multiplication?

A: Here are some ways to practice applying the Associative Law of Multiplication:

Try solving problems on your own: Try solving problems on your own to practice applying the Associative Law of Multiplication.
Use online resources: Use online resources such as Khan Academy or Mathway to practice applying the Associative Law of Multiplication.
Work with a tutor: Work with a tutor to practice applying the Associative Law of Multiplication.

Conclusion

In this article, we answered some frequently asked questions about the Associative Law of Multiplication. We hope that this article has helped you to better understand the Associative Law of Multiplication and how to apply it. Remember to practice applying the Associative Law of Multiplication to become more confident and proficient in mathematics.

Frequently Asked Questions

Q: What is the Associative Law of Multiplication? A: The Associative Law of Multiplication is a fundamental concept in mathematics that allows us to rearrange the order of numbers when multiplying them together.
Q: How do I apply the Associative Law of Multiplication? A: To apply the Associative Law of Multiplication, you need to multiply the numbers in a different order, while keeping the result the same.
Q: What are some examples of the Associative Law of Multiplication? A: Here are some examples:
- ${$ (2 \cdot 3) \cdot 4$}$ = ${ $2 \cdot (3 \cdot 4)\$}$ = ${ $2 \cdot 12\$}$ = 24
- ${$ (5 \cdot 2) \cdot 3$}$ = ${ $5 \cdot (2 \cdot 3)\$}$ = ${ $5 \cdot 6\$}$ = 30
- ${$ (8 \cdot 9) \cdot 2$}$ = ${ $8 \cdot (9 \cdot 2)\$}$ = ${ $8 \cdot 18\$}$ = 144

Additional Resources

For more information on the Associative Law of Multiplication, visit the Khan Academy website.
To practice applying the Associative Law of Multiplication, try the following problems:
- ${$ (24 - 3) \cdot 4$}$
- ${$ (15 \cdot 2) \cdot 3$}$
- ${$ (8 \cdot 5) \cdot 2$}$