Evaluate The Expression:${ 2 \frac{2}{5} + 2 \frac{2}{5} }$

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Introduction

In this article, we will evaluate the expression $2 \frac{2}{5} + 2 \frac{2}{5}$. This expression involves adding two mixed numbers, which can be a bit challenging. However, with the right approach and techniques, we can simplify the expression and find the final result.

Understanding Mixed Numbers

Before we dive into the evaluation, 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 $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator, and $c$ is the denominator.

In the given expression, we have two mixed numbers: $2 \frac{2}{5}$ and $2 \frac{2}{5}$. To evaluate this expression, we need to add these two mixed numbers together.

Adding Mixed Numbers

To add mixed numbers, we need to follow a specific procedure. Here are the steps:

1. Convert the mixed numbers to improper fractions: We need to convert each mixed number to an improper fraction. To do this, we multiply the whole number part by the denominator and add the numerator. Then, we write the result as an improper fraction.

For the first mixed number, $2 \frac{2}{5}$, we have:

$$2 \frac{2}{5} = \frac{(2 \times 5) + 2}{5} = \frac{12}{5}$$

For the second mixed number, $2 \frac{2}{5}$, we have:

$$2 \frac{2}{5} = \frac{(2 \times 5) + 2}{5} = \frac{12}{5}$$

2. Add the improper fractions: Now that we have converted both mixed numbers to improper fractions, we can add them together. Since the denominators are the same, we can simply add the numerators.

$$\frac{12}{5} + \frac{12}{5} = \frac{24}{5}$$

Simplifying the Result

The result we obtained is an improper fraction. However, we can simplify it further by converting it back to a mixed number.

To do this, we divide the numerator by the denominator:

$$\frac{24}{5} = 4 \frac{4}{5}$$

Therefore, the final result is $4 \frac{4}{5}$.

Conclusion

In this article, we evaluated the expression $2 \frac{2}{5} + 2 \frac{2}{5}$. We first converted the mixed numbers to improper fractions, then added them together, and finally simplified the result to a mixed number. The final answer is $4 \frac{4}{5}$.

Frequently Asked Questions

• Q: What is the result of $2 \frac{2}{5} + 2 \frac{2}{5}$? A: The result is $4 \frac{4}{5}$.
• Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.
• Q: How do I add mixed numbers? A: To add mixed numbers, convert them to improper fractions, add the numerators, and then simplify the result.

Related Topics

• Adding fractions with different denominators
• Converting improper fractions to mixed numbers
• Simplifying fractions

References

• [1] "Adding Mixed Numbers" by Math Open Reference
• [2] "Converting Mixed Numbers to Improper Fractions" by Mathway
• [3] "Simplifying Fractions" by Khan Academy
  

Introduction

In our previous article, we evaluated the expression $2 \frac{2}{5} + 2 \frac{2}{5}$. We learned how to convert mixed numbers to improper fractions, add them together, and simplify the result. In this article, we will answer some frequently asked questions related to evaluating expressions with mixed numbers.

Q&A

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, written in the form $a \frac{b}{c}$. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, written in the form $\frac{a}{b}$.

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

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.

For example, to convert $2 \frac{2}{5}$ to an improper fraction, we have:

$$2 \frac{2}{5} = \frac{(2 \times 5) + 2}{5} = \frac{12}{5}$$

Q: How do I add mixed numbers?

A: To add mixed numbers, convert them to improper fractions, add the numerators, and then simplify the result.

For example, to add $2 \frac{2}{5}$ and $2 \frac{2}{5}$, we have:

$$2 \frac{2}{5} + 2 \frac{2}{5} = \frac{12}{5} + \frac{12}{5} = \frac{24}{5}$$

Q: How do I simplify a fraction?

A: To simplify a fraction, divide the numerator by the denominator and write the result as a mixed number or an improper fraction.

For example, to simplify $\frac{24}{5}$, we have:

$$\frac{24}{5} = 4 \frac{4}{5}$$

Q: What is the order of operations when evaluating expressions with mixed numbers?

A: When evaluating expressions with mixed numbers, follow the order of operations:

1. Convert mixed numbers to improper fractions.
2. Add or subtract the numerators.
3. Simplify the result.

Q: Can I use a calculator to evaluate expressions with mixed numbers?

A: Yes, you can use a calculator to evaluate expressions with mixed numbers. However, it's always a good idea to understand the underlying math and be able to do the calculations by hand.

Q: How do I evaluate expressions with multiple mixed numbers?

A: To evaluate expressions with multiple mixed numbers, follow the same steps as before:

1. Convert each mixed number to an improper fraction.
2. Add or subtract the numerators.
3. Simplify the result.

For example, to evaluate $2 \frac{2}{5} + 3 \frac{3}{5}$, we have:

$$2 \frac{2}{5} + 3 \frac{3}{5} = \frac{12}{5} + \frac{18}{5} = \frac{30}{5} = 6$$

Conclusion

In this article, we answered some frequently asked questions related to evaluating expressions with mixed numbers. We covered topics such as converting mixed numbers to improper fractions, adding mixed numbers, simplifying fractions, and evaluating expressions with multiple mixed numbers. We hope this article has been helpful in clarifying any doubts you may have had.

Frequently Asked Questions

• 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, written in the form $a \frac{b}{c}$. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, written in the form $\frac{a}{b}$.
• Q: How do I convert a mixed number to an improper fraction? A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. Then, write the result as an improper fraction.
• Q: How do I add mixed numbers? A: To add mixed numbers, convert them to improper fractions, add the numerators, and then simplify the result.

Related Topics

• Adding fractions with different denominators
• Converting improper fractions to mixed numbers
• Simplifying fractions

References

• [1] "Adding Mixed Numbers" by Math Open Reference
• [2] "Converting Mixed Numbers to Improper Fractions" by Mathway
• [3] "Simplifying Fractions" by Khan Academy