Simplify: $\[ 4 \frac{6}{7} - 2 \frac{5}{7} \\]

Introduction

Understanding Mixed Numbers In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that have both a whole and a part. When dealing with mixed numbers, it's essential to understand how to perform operations such as addition, subtraction, multiplication, and division. In this article, we will focus on simplifying the expression ${ 4 \frac{6}{7} - 2 \frac{5}{7} }$.

What are Mixed Numbers?

Mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that have both a whole and a part. For example, $4 \frac{6}{7}$ can be read as "four and six-sevenths." Mixed numbers can be written in different forms, but the most common form is the combination of a whole number and a fraction.

Understanding the Expression

The given expression is ${ 4 \frac{6}{7} - 2 \frac{5}{7} }$. To simplify this expression, we need to first understand the concept of subtracting mixed numbers. When subtracting mixed numbers, we need to subtract the whole numbers and then subtract the fractions.

Subtracting Mixed Numbers

When subtracting mixed numbers, we need to follow the order of operations (PEMDAS):

1. Subtract the whole numbers.
2. Subtract the fractions.

Let's break down the given expression:

$${ 4 \frac{6}{7} - 2 \frac{5}{7} }$$

Step 1: Subtract the Whole Numbers

The whole numbers in the expression are 4 and 2. To subtract the whole numbers, we need to subtract 2 from 4.

$${ 4 - 2 = 2 }$$

Step 2: Subtract the Fractions

The fractions in the expression are $\frac{6}{7}$ and $\frac{5}{7}$. To subtract the fractions, we need to subtract the numerators (6 and 5) and keep the same denominator (7).

$${ \frac{6}{7} - \frac{5}{7} = \frac{1}{7} }$$

Combining the Results

Now that we have subtracted the whole numbers and the fractions, we can combine the results.

$${ 2 \frac{1}{7} }$$

Conclusion

In this article, we simplified the expression ${ 4 \frac{6}{7} - 2 \frac{5}{7} }$. We broke down the expression into smaller parts, subtracted the whole numbers and the fractions, and then combined the results. The final simplified expression is ${ 2 \frac{1}{7} }$. This example demonstrates the importance of understanding mixed numbers and how to perform operations with them.

Frequently Asked Questions

• What is a mixed number? A mixed number is a combination of a whole number and a fraction.
• How do I subtract mixed numbers? To subtract mixed numbers, you need to subtract the whole numbers and then subtract the fractions.
• What is the final simplified expression? The final simplified expression is ${ 2 \frac{1}{7} }$.

Additional Resources

• Mathematics Glossary: A comprehensive glossary of mathematical terms and concepts.
• Mathematics Tutorials: A collection of tutorials and examples on various mathematical topics.
• Mathematics Practice Problems: A set of practice problems to help you improve your mathematical skills.

Final Thoughts

Simplifying expressions with mixed numbers requires a clear understanding of the concept of mixed numbers and how to perform operations with them. By following the steps outlined in this article, you can simplify expressions with mixed numbers and improve your mathematical skills.

Introduction

In our previous article, we simplified the expression ${ 4 \frac{6}{7} - 2 \frac{5}{7} }$. We broke down the expression into smaller parts, subtracted the whole numbers and the fractions, and then combined the results. In this article, we will answer some frequently asked questions related to the topic.

Q&A

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, $4 \frac{6}{7}$ can be read as "four and six-sevenths."

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, you need to subtract the whole numbers and then subtract the fractions. For example, to subtract $4 \frac{6}{7}$ and $2 \frac{5}{7}$, you need to subtract the whole numbers (4 and 2) and then subtract the fractions ($\frac{6}{7}$ and $\frac{5}{7}$).

Q: What is the final simplified expression?

A: The final simplified expression is ${ 2 \frac{1}{7} }$.

Q: Can I add mixed numbers?

A: Yes, you can add mixed numbers. To add mixed numbers, you need to add the whole numbers and then add the fractions. For example, to add $4 \frac{6}{7}$ and $2 \frac{5}{7}$, you need to add the whole numbers (4 and 2) and then add the fractions ($\frac{6}{7}$ and $\frac{5}{7}$).

Q: Can I multiply mixed numbers?

A: Yes, you can multiply mixed numbers. To multiply mixed numbers, you need to multiply the whole numbers and then multiply the fractions. For example, to multiply $4 \frac{6}{7}$ and $2 \frac{5}{7}$, you need to multiply the whole numbers (4 and 2) and then multiply the fractions ($\frac{6}{7}$ and $\frac{5}{7}$).

Q: Can I divide mixed numbers?

A: Yes, you can divide mixed numbers. To divide mixed numbers, you need to divide the whole numbers and then divide the fractions. For example, to divide $4 \frac{6}{7}$ by $2 \frac{5}{7}$, you need to divide the whole numbers (4 and 2) and then divide the fractions ($\frac{6}{7}$ and $\frac{5}{7}$).

Conclusion

In this article, we answered some frequently asked questions related to the topic of simplifying expressions with mixed numbers. We covered topics such as subtracting mixed numbers, adding mixed numbers, multiplying mixed numbers, and dividing mixed numbers. By following the steps outlined in this article, you can simplify expressions with mixed numbers and improve your mathematical skills.

Frequently Asked Questions

• What is a mixed number? A mixed number is a combination of a whole number and a fraction.
• How do I subtract mixed numbers? To subtract mixed numbers, you need to subtract the whole numbers and then subtract the fractions.
• What is the final simplified expression? The final simplified expression is ${ 2 \frac{1}{7} }$.
• Can I add mixed numbers? Yes, you can add mixed numbers.
• Can I multiply mixed numbers? Yes, you can multiply mixed numbers.
• Can I divide mixed numbers? Yes, you can divide mixed numbers.

Additional Resources

• Mathematics Glossary: A comprehensive glossary of mathematical terms and concepts.
• Mathematics Tutorials: A collection of tutorials and examples on various mathematical topics.
• Mathematics Practice Problems: A set of practice problems to help you improve your mathematical skills.

Final Thoughts

Simplifying expressions with mixed numbers requires a clear understanding of the concept of mixed numbers and how to perform operations with them. By following the steps outlined in this article, you can simplify expressions with mixed numbers and improve your mathematical skills.