Write A Mixed Number To Complete The Equation.$\[ \begin{aligned} 6 \frac{2}{5}+\frac{4}{5} & = 6 \frac{2}{5}+\frac{3}{5}+\frac{1}{5} \\ & = \, ? \, ? \, , \, ? \, ? \end{aligned} \\]

Introduction

Mixed numbers are a combination of a whole number and a fraction. They are used to represent a value that is part of a whole. In this article, we will explore how to write a mixed number to complete the equation ${ \begin{aligned} 6 \frac{2}{5}+\frac{4}{5} & = 6 \frac{2}{5}+\frac{3}{5}+\frac{1}{5} \ & = , ? , ? , , , ? , ? \end{aligned} }$

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a\frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $6\frac{2}{5}$ is a mixed number that represents $6$ and $\frac{2}{5}$.

Adding Mixed Numbers

To add mixed numbers, we need to follow a specific procedure. The procedure involves adding the whole numbers and the fractions separately. Here's a step-by-step guide on how to add mixed numbers:

1. Add the whole numbers: Add the whole numbers in the mixed numbers. In this case, we have $6$ and $6$, so the sum of the whole numbers is $12$.
2. Add the fractions: Add the fractions in the mixed numbers. In this case, we have $\frac{2}{5}$ and $\frac{4}{5}$, so the sum of the fractions is $\frac{6}{5}$.
3. Combine the whole number and the fraction: Combine the sum of the whole numbers and the sum of the fractions. In this case, we have $12$ and $\frac{6}{5}$, so the sum is $12\frac{6}{5}$.

Solving the Equation

Now that we have a good understanding of mixed numbers and how to add them, let's solve the equation ${ \begin{aligned} 6 \frac{2}{5}+\frac{4}{5} & = 6 \frac{2}{5}+\frac{3}{5}+\frac{1}{5} \ & = , ? , ? , , , ? , ? \end{aligned} }$

To solve the equation, we need to add the mixed numbers on the left-hand side of the equation. We can do this by following the procedure outlined above.

1. Add the whole numbers: Add the whole numbers in the mixed numbers. In this case, we have $6$ and $6$, so the sum of the whole numbers is $12$.
2. Add the fractions: Add the fractions in the mixed numbers. In this case, we have $\frac{2}{5}$ and $\frac{4}{5}$, so the sum of the fractions is $\frac{6}{5}$.
3. Combine the whole number and the fraction: Combine the sum of the whole numbers and the sum of the fractions. In this case, we have $12$ and $\frac{6}{5}$, so the sum is $12\frac{6}{5}$.

Now that we have the sum of the mixed numbers on the left-hand side of the equation, we can rewrite the equation as follows:

$$12\frac{6}{5} = 6\frac{2}{5}+\frac{3}{5}+\frac{1}{5}$$

To solve for the missing mixed number, we need to subtract the mixed numbers on the right-hand side of the equation from the sum of the mixed numbers on the left-hand side.

1. Subtract the whole numbers: Subtract the whole numbers in the mixed numbers. In this case, we have $12$ and $6$, so the difference of the whole numbers is $6$.
2. Subtract the fractions: Subtract the fractions in the mixed numbers. In this case, we have $\frac{6}{5}$ and $\frac{2}{5}+\frac{3}{5}$, so the difference of the fractions is $\frac{1}{5}$.
3. Combine the whole number and the fraction: Combine the difference of the whole numbers and the difference of the fractions. In this case, we have $6$ and $\frac{1}{5}$, so the difference is $6\frac{1}{5}$.

Therefore, the missing mixed number is $6\frac{1}{5}$.

Conclusion

In this article, we explored how to write a mixed number to complete the equation ${ \begin{aligned} 6 \frac{2}{5}+\frac{4}{5} & = 6 \frac{2}{5}+\frac{3}{5}+\frac{1}{5} \ & = , ? , ? , , , ? , ? \end{aligned} }$

We learned how to add mixed numbers by following a specific procedure and how to solve the equation by subtracting the mixed numbers on the right-hand side of the equation from the sum of the mixed numbers on the left-hand side.

Final Answer

Introduction

In our previous article, we explored how to write a mixed number to complete the equation ${ \begin{aligned} 6 \frac{2}{5}+\frac{4}{5} & = 6 \frac{2}{5}+\frac{3}{5}+\frac{1}{5} \ & = , ? , ? , , , ? , ? \end{aligned} }$

In this article, we will answer some of the most frequently asked questions about mixed number equations.

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 $a\frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I add mixed numbers?

A: To add mixed numbers, you need to follow a specific procedure. The procedure involves adding the whole numbers and the fractions separately.

1. Add the whole numbers: Add the whole numbers in the mixed numbers.
2. Add the fractions: Add the fractions in the mixed numbers.
3. Combine the whole number and the fraction: Combine the sum of the whole numbers and the sum of the fractions.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you need to follow a specific procedure. The procedure involves subtracting the whole numbers and the fractions separately.

1. Subtract the whole numbers: Subtract the whole numbers in the mixed numbers.
2. Subtract the fractions: Subtract the fractions in the mixed numbers.
3. Combine the whole number and the fraction: Combine the difference of the whole numbers and the difference of the fractions.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

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 add the numerator. Then, you need to write the result as a fraction with the denominator.

For example, to convert $6\frac{2}{5}$ to an improper fraction, you need to multiply $6$ by $5$ and add $2$. The result is $32$, so the improper fraction is $\frac{32}{5}$.

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

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

For example, to convert $\frac{32}{5}$ to a mixed number, you need to divide $32$ by $5$. The result is $6$ with a remainder of $2$, so the mixed number is $6\frac{2}{5}$.

Q: What are some common mistakes to avoid when working with mixed number equations?

A: Some common mistakes to avoid when working with mixed number equations include:

• Not following the order of operations: When working with mixed number equations, it's essential to follow the order of operations (PEMDAS) to ensure that you're performing the calculations correctly.
• Not converting mixed numbers to improper fractions: Converting mixed numbers to improper fractions can make it easier to perform calculations and avoid errors.
• Not checking your work: It's essential to check your work when working with mixed number equations to ensure that you're getting the correct answer.

Conclusion

In this article, we answered some of the most frequently asked questions about mixed number equations. We covered topics such as adding and subtracting mixed numbers, converting mixed numbers to improper fractions, and avoiding common mistakes. By following the procedures outlined in this article, you can become more confident and proficient when working with mixed number equations.

Final Tips

• Practice, practice, practice: The more you practice working with mixed number equations, the more comfortable you'll become with the procedures and the more confident you'll be in your ability to solve problems.
• Use visual aids: Visual aids such as diagrams and charts can help you understand complex concepts and make it easier to perform calculations.
• Seek help when needed: Don't be afraid to ask for help if you're struggling with a problem or concept. There are many resources available, including online tutorials, videos, and study groups.