Nathan Looked At The Picture Frame Below And Computed The Following Sum: 8 3 4 + ( − 4 8 \frac{3}{4} + (-4 8 4 3 ​ + ( − 4 ]. What Value Did He Find?

Understanding Mixed Numbers

Before we dive into the problem, let's first understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as $8 \frac{3}{4}$. In this case, the whole number is 8 and the fraction is $\frac{3}{4}$.

The Problem

Nathan looked at the picture frame below and computed the following sum: $8 \frac{3}{4} + (-4)$. The problem asks us to find the value of this sum.

Step 1: Understanding the Problem

To solve this problem, we need to understand that we are adding a mixed number to a negative integer. The mixed number is $8 \frac{3}{4}$, and the negative integer is -4.

Step 2: Converting the Mixed Number to an Improper Fraction

To add the mixed number to the negative integer, we need to convert the mixed number to an improper fraction. To do this, we multiply the whole number by the denominator and then add the numerator.

$8 \frac{3}{4} = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}$

Step 3: Adding the Improper Fraction to the Negative Integer

Now that we have the mixed number in the form of an improper fraction, we can add it to the negative integer.

$\frac{35}{4} + (-4) = \frac{35}{4} - \frac{16}{4} = \frac{19}{4}$

Step 4: Converting the Improper Fraction Back to a Mixed Number

To make the answer more understandable, we can convert the improper fraction back to a mixed number.

$\frac{19}{4} = 4 \frac{3}{4}$

Conclusion

In conclusion, Nathan found that the value of the sum $8 \frac{3}{4} + (-4)$ is $4 \frac{3}{4}$.

Why is this Important?

Understanding how to add mixed numbers is an important skill in mathematics. It is used in a variety of real-world applications, such as cooking, building, and finance. For example, if you are cooking a recipe that requires you to add 2 cups of flour and 3/4 cup of sugar, you need to be able to add mixed numbers to get the total amount of ingredients.

Real-World Applications

Adding mixed numbers is used in a variety of real-world applications, such as:

• Cooking: When cooking a recipe, you may need to add mixed numbers to get the total amount of ingredients.
• Building: When building a structure, you may need to add mixed numbers to get the total amount of materials needed.
• Finance: When calculating interest rates or investments, you may need to add mixed numbers to get the total amount.

Common Mistakes

When adding mixed numbers, there are several common mistakes that people make. These include:

• Not converting the mixed number to an improper fraction: This can lead to incorrect answers.
• Not adding the whole numbers correctly: This can lead to incorrect answers.
• Not converting the improper fraction back to a mixed number: This can make the answer difficult to understand.

Tips and Tricks

When adding mixed numbers, here are some tips and tricks to keep in mind:

• Always convert the mixed number to an improper fraction: This will make it easier to add the numbers.
• Add the whole numbers correctly: Make sure to add the whole numbers correctly to get the correct answer.
• Convert the improper fraction back to a mixed number: This will make the answer easier to understand.

Conclusion

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as $8 \frac{3}{4}$.

Q: How do I add mixed numbers?

A: To add mixed numbers, you need to follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Add the improper fractions.
3. Convert the sum back to a mixed number.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $\frac{35}{4}$ is an improper fraction.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator.

For example, to convert $8 \frac{3}{4}$ to an improper fraction, you would multiply 8 by 4 and add 3:

$8 \frac{3}{4} = \frac{(8 \times 4) + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}$

Q: How do I add improper fractions?

A: To add improper fractions, you need to follow these steps:

1. Make sure the denominators are the same.
2. Add the numerators.
3. Keep the denominator the same.

For example, to add $\frac{35}{4}$ and $\frac{16}{4}$, you would add the numerators and keep the denominator the same:

$\frac{35}{4} + \frac{16}{4} = \frac{35 + 16}{4} = \frac{51}{4}$

Q: How do I convert an improper fraction back to a mixed number?

A: To convert an improper fraction back to a mixed number, you need to divide the numerator by the denominator and write the remainder as a fraction.

For example, to convert $\frac{51}{4}$ back to a mixed number, you would divide 51 by 4 and write the remainder as a fraction:

$\frac{51}{4} = 12 \frac{3}{4}$

Q: What are some common mistakes to avoid when adding mixed numbers?

A: Some common mistakes to avoid when adding mixed numbers include:

• Not converting the mixed number to an improper fraction.
• Not adding the whole numbers correctly.
• Not converting the improper fraction back to a mixed number.

Q: How do I use mixed numbers in real-world applications?

A: Mixed numbers are used in a variety of real-world applications, such as:

• Cooking: When cooking a recipe, you may need to add mixed numbers to get the total amount of ingredients.
• Building: When building a structure, you may need to add mixed numbers to get the total amount of materials needed.
• Finance: When calculating interest rates or investments, you may need to add mixed numbers to get the total amount.

Q: What are some tips and tricks for adding mixed numbers?

A: Some tips and tricks for adding mixed numbers include:

• Always convert the mixed number to an improper fraction.
• Add the whole numbers correctly.
• Convert the improper fraction back to a mixed number.

Conclusion

In conclusion, adding mixed numbers is an important skill in mathematics. By understanding how to add mixed numbers, you can make the answer more understandable and avoid common mistakes. Remember to always convert the mixed number to an improper fraction, add the whole numbers correctly, and convert the improper fraction back to a mixed number.