Dan Is Using Tiles To Add { -8 + 6$}$. He Begins With The Tiles Shown Below.What Is The Sum Of { -8 + 6$}$?A. { -14$}$ B. { -2$}$ C. ${ 2\$} D. ${ 14\$}

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When it comes to adding numbers, we often think of it as combining quantities. However, when dealing with negative numbers, the concept of addition can become a bit more complex. In this article, we will explore the concept of adding negative numbers using tiles, and we will use the example of Dan adding {-8 + 6} to illustrate this concept.

What are Negative Numbers?

Before we dive into the concept of adding negative numbers, let's first understand what negative numbers are. A negative number is a number that is less than zero. It is denoted by a minus sign (-) and is used to represent a quantity that is opposite in direction or magnitude to a positive quantity. For example, -3 is a negative number that is opposite in direction to the positive number 3.

Using Tiles to Represent Negative Numbers

In the example given, Dan is using tiles to add {-8 + 6$}$. To represent negative numbers using tiles, we can use a simple yet effective method. We can use a red tile to represent a negative number and a blue tile to represent a positive number. The number of tiles we use will represent the magnitude of the number, and the color of the tile will indicate whether the number is positive or negative.

Representing {-8$}$ Using Tiles

To represent {-8$}$ using tiles, we can use 8 red tiles. Each red tile represents a negative unit, and the total number of tiles represents the magnitude of the number. So, in this case, we have 8 negative units, which is represented by 8 red tiles.

Representing ${6\$} Using Tiles

To represent ${6\$} using tiles, we can use 6 blue tiles. Each blue tile represents a positive unit, and the total number of tiles represents the magnitude of the number. So, in this case, we have 6 positive units, which is represented by 6 blue tiles.

Adding {-8 + 6$}$ Using Tiles

Now that we have represented both {-8$}$ and ${6\$} using tiles, we can add them together. To do this, we can combine the red tiles and blue tiles, making sure to keep track of the total number of tiles.

When we combine the 8 red tiles and the 6 blue tiles, we get a total of 2 blue tiles. This is because the 8 negative units represented by the red tiles are cancelled out by the 6 positive units represented by the blue tiles, leaving us with 2 positive units.

The Sum of {-8 + 6$}$

So, what is the sum of {-8 + 6$}$? Based on our tile representation, we can see that the sum is 2. This is because the 8 negative units represented by the red tiles are cancelled out by the 6 positive units represented by the blue tiles, leaving us with 2 positive units.

Conclusion

In conclusion, adding negative numbers using tiles can be a fun and interactive way to understand the concept of addition with negative numbers. By using a simple yet effective method of representing negative numbers using red tiles and positive numbers using blue tiles, we can visualize the concept of addition and see how negative numbers can be cancelled out by positive numbers.

Answer

So, what is the answer to the question? Based on our tile representation, we can see that the sum of {-8 + 6$}$ is 2. This is represented by the 2 blue tiles that we are left with after combining the 8 red tiles and the 6 blue tiles.

Final Answer

In our previous article, we explored the concept of adding negative numbers using tiles. We used the example of Dan adding {-8 + 6$}$ to illustrate this concept. In this article, we will answer some frequently asked questions about addition with negative numbers.

Q: What is the difference between adding positive and negative numbers?

A: When adding positive numbers, we are combining quantities that are in the same direction. For example, 3 + 4 = 7. However, when adding negative numbers, we are combining quantities that are in opposite directions. For example, -3 + 4 = 1.

Q: How do I know when to add or subtract when working with negative numbers?

A: When working with negative numbers, you need to remember that a negative number is opposite in direction to a positive number. When adding two negative numbers, you are combining quantities that are in the same direction, so you add them. When adding a negative number and a positive number, you are combining quantities that are in opposite directions, so you subtract the smaller number from the larger number.

Q: Can you give me an example of how to add two negative numbers?

A: Let's say we want to add -5 and -3. To do this, we can use the tile representation we discussed earlier. We can use 5 red tiles to represent -5 and 3 red tiles to represent -3. When we combine these tiles, we get a total of 8 red tiles, which represents -8.

Q: Can you give me an example of how to add a negative number and a positive number?

A: Let's say we want to add -2 and 4. To do this, we can use the tile representation we discussed earlier. We can use 2 red tiles to represent -2 and 4 blue tiles to represent 4. When we combine these tiles, we get a total of 2 blue tiles, which represents 2.

Q: What is the rule for adding negative numbers?

A: The rule for adding negative numbers is that when you add two negative numbers, you add their magnitudes and keep the same sign. For example, -5 + (-3) = -8. When you add a negative number and a positive number, you subtract the smaller number from the larger number and keep the same sign. For example, -5 + 3 = -2.

Q: Can you give me some examples of adding negative numbers?

A: Here are some examples of adding negative numbers:

  • -3 + (-4) = -7
  • -2 + (-5) = -7
  • -1 + (-6) = -7
  • 3 + (-4) = -1
  • 2 + (-5) = -3
  • 1 + (-6) = -5

Q: What is the difference between adding and subtracting negative numbers?

A: When adding negative numbers, you are combining quantities that are in the same direction. When subtracting negative numbers, you are finding the difference between two quantities that are in opposite directions. For example, -3 - (-4) = 1, but -3 + (-4) = -7.

Q: Can you give me some examples of subtracting negative numbers?

A: Here are some examples of subtracting negative numbers:

  • -3 - (-4) = 1
  • -2 - (-5) = 3
  • -1 - (-6) = 5
  • 3 - (-4) = 7
  • 2 - (-5) = 7
  • 1 - (-6) = 7

Conclusion

In conclusion, adding negative numbers can be a bit tricky, but with practice and patience, you can master this concept. Remember to use the tile representation to help you visualize the concept of addition with negative numbers. With this article, you should now have a better understanding of how to add negative numbers and be able to answer some frequently asked questions about this topic.