Drag Each Label To The Correct Location On The Image.Here Is A Multiplication Sentence:${ 1 \times (3 \times 6) = 18 }$Drag The Numbers And The Parentheses To Create An Equivalent Multiplication Sentence That Illustrates The Associative
The associative property of multiplication is a fundamental concept in mathematics that helps us understand how numbers can be grouped and multiplied in different ways to get the same result. In this article, we will explore the associative property of multiplication and how it can be applied to create equivalent multiplication sentences.
What is the Associative Property of Multiplication?
The associative property of multiplication states that when we multiply three numbers together, the order in which we group them does not change the result. In other words, if we have three numbers a, b, and c, then the following equation holds true:
a × (b × c) = (a × b) × c
This property allows us to regroup the numbers in different ways and still get the same result.
Example: Multiplication Sentence
Let's consider the following multiplication sentence:
1 × (3 × 6) = 18
In this sentence, we have three numbers: 1, 3, and 6. We can use the associative property of multiplication to create an equivalent multiplication sentence that illustrates the associative property.
Drag the Numbers and Parentheses
To create an equivalent multiplication sentence, we need to drag the numbers and parentheses to the correct location on the image. Here is the image with the numbers and parentheses:
| 1 | (3 × 6) |
|---|---|
| 3 | 6 |
Step 1: Drag the Number 1 to the Correct Location
Let's start by dragging the number 1 to the correct location on the image. We can place it next to the parentheses, like this:
| 1 | (3 × 6) | |
|---|---|---|
| 3 | 6 | |
Step 2: Drag the Parentheses to the Correct Location
Next, let's drag the parentheses to the correct location on the image. We can place them around the numbers 3 and 6, like this:
| 1 | (3 × 6) | |
|---|---|---|
| 1 | 3 | 6 |
Step 3: Drag the Number 3 to the Correct Location
Now, let's drag the number 3 to the correct location on the image. We can place it next to the number 1, like this:
| 1 | (3 × 6) | |
|---|---|---|
| 1 | 3 | 6 |
Step 4: Drag the Number 6 to the Correct Location
Finally, let's drag the number 6 to the correct location on the image. We can place it next to the number 3, like this:
| 1 | (3 × 6) | |
|---|---|---|
| 1 | 3 | 6 |
The Correct Answer
After dragging the numbers and parentheses to the correct location on the image, we get the following equivalent multiplication sentence:
1 × 3 × 6 = 18
This sentence illustrates the associative property of multiplication, which states that the order in which we group the numbers does not change the result.
Conclusion
In conclusion, the associative property of multiplication is a fundamental concept in mathematics that helps us understand how numbers can be grouped and multiplied in different ways to get the same result. By dragging the numbers and parentheses to the correct location on the image, we can create equivalent multiplication sentences that illustrate the associative property. This concept is essential for understanding more advanced mathematical concepts, such as algebra and geometry.
Frequently Asked Questions
- Q: What is the associative property of multiplication? A: The associative property of multiplication states that when we multiply three numbers together, the order in which we group them does not change the result.
- Q: How can I apply the associative property of multiplication to create equivalent multiplication sentences? A: You can apply the associative property of multiplication by dragging the numbers and parentheses to the correct location on the image.
- Q: What is the importance of the associative property of multiplication? A: The associative property of multiplication is essential for understanding more advanced mathematical concepts, such as algebra and geometry.
Further Reading
If you want to learn more about the associative property of multiplication, here are some additional resources:
- Khan Academy: Associative Property of Multiplication
- Math Is Fun: Associative Property of Multiplication
- Wikipedia: Associative Property of Multiplication
References
- "Mathematics for the Nonmathematician" by Morris Kline
- "Algebra and Trigonometry" by Michael Sullivan
- "Geometry: Seeing, Doing, Understanding" by Harold R. Jacobs
Q&A: Associative Property of Multiplication =============================================
In this article, we will answer some frequently asked questions about the associative property of multiplication.
Q: What is the associative property of multiplication?
A: The associative property of multiplication states that when we multiply three numbers together, the order in which we group them does not change the result. In other words, if we have three numbers a, b, and c, then the following equation holds true:
a × (b × c) = (a × b) × c
Q: How can I apply the associative property of multiplication to create equivalent multiplication sentences?
A: You can apply the associative property of multiplication by dragging the numbers and parentheses to the correct location on the image. For example, let's consider the following multiplication sentence:
1 × (3 × 6) = 18
To create an equivalent multiplication sentence, we can drag the numbers and parentheses to the correct location on the image, like this:
1 × 3 × 6 = 18
Q: What is the importance of the associative property of multiplication?
A: The associative property of multiplication is essential for understanding more advanced mathematical concepts, such as algebra and geometry. It also helps us to simplify complex multiplication problems and to identify patterns in numbers.
Q: Can I apply the associative property of multiplication to addition?
A: No, the associative property of multiplication only applies to multiplication. However, there is a similar property called the associative property of addition, which states that the order in which we add three numbers together does not change the result.
Q: How can I use the associative property of multiplication to solve real-world problems?
A: The associative property of multiplication can be used to solve a variety of real-world problems, such as calculating the cost of items on a shopping list or determining the area of a room. For example, let's say we want to calculate the cost of 3 boxes of cereal that cost $6 each. We can use the associative property of multiplication to simplify the calculation, like this:
3 × (6 × 1) = (3 × 6) × 1 = 18 × 1 = 18
Q: Can I apply the associative property of multiplication to fractions?
A: Yes, the associative property of multiplication can be applied to fractions. For example, let's say we want to multiply 1/2 by 3/4. We can use the associative property of multiplication to simplify the calculation, like this:
(1/2) × (3/4) = (1 × 3) / (2 × 4) = 3/8
Q: How can I practice the associative property of multiplication?
A: There are many ways to practice the associative property of multiplication, such as:
- Using online math games and activities
- Creating multiplication charts and tables
- Practicing multiplication problems with a partner or tutor
- Using real-world examples to apply the associative property of multiplication
Q: What are some common mistakes to avoid when applying the associative property of multiplication?
A: Some common mistakes to avoid when applying the associative property of multiplication include:
- Not following the order of operations (PEMDAS)
- Not using parentheses correctly
- Not simplifying complex multiplication problems
- Not checking for errors in calculations
Conclusion
In conclusion, the associative property of multiplication is a fundamental concept in mathematics that helps us understand how numbers can be grouped and multiplied in different ways to get the same result. By practicing the associative property of multiplication, we can improve our math skills and apply it to real-world problems.