What Is 1 1 10 + 1 1 5 1 \frac{1}{10} + 1 \frac{1}{5} 1 10 1 ​ + 1 5 1 ​ ?A. 2 3 10 2 \frac{3}{10} 2 10 3 ​ B. 2 2 15 2 \frac{2}{15} 2 15 2 ​ C. 2 1 50 2 \frac{1}{50} 2 50 1 ​ D. 1 3 10 1 \frac{3}{10} 1 10 3 ​

What is $1 \frac{1}{10} + 1 \frac{1}{5}$?

Understanding the Problem

To solve this problem, we need to add two mixed numbers: $1 \frac{1}{10}$ and $1 \frac{1}{5}$. Mixed numbers are a combination of a whole number and a fraction. In this case, we have two mixed numbers with different denominators, which makes it a bit more challenging to add them together.

Converting Mixed Numbers to Improper Fractions

Before we can add these mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. We then write the result as a fraction with the denominator remaining the same.

For the first mixed number, $1 \frac{1}{10}$, we multiply the whole number by the denominator (10) and add the numerator (1). This gives us $1 \times 10 + 1 = 11$. So, the improper fraction for $1 \frac{1}{10}$ is $\frac{11}{10}$.

For the second mixed number, $1 \frac{1}{5}$, we multiply the whole number by the denominator (5) and add the numerator (1). This gives us $1 \times 5 + 1 = 6$. So, the improper fraction for $1 \frac{1}{5}$ is $\frac{6}{5}$.

Finding a Common Denominator

Now that we have both mixed numbers converted to improper fractions, we need to find a common denominator to add them together. The least common multiple (LCM) of 10 and 5 is 10. Since 10 is already a factor of 10, we can use it as the common denominator.

Adding the Improper Fractions

Now that we have a common denominator, we can add the two improper fractions together. We add the numerators (11 and 12) and keep the common denominator (10). This gives us $\frac{11 + 12}{10} = \frac{23}{10}$.

Converting the Result Back to a Mixed Number

To convert the improper fraction $\frac{23}{10}$ back to a mixed number, we divide the numerator (23) by the denominator (10). This gives us a quotient of 2 and a remainder of 3. So, the mixed number equivalent of $\frac{23}{10}$ is $2 \frac{3}{10}$.

Conclusion

In conclusion, the sum of $1 \frac{1}{10} + 1 \frac{1}{5}$ is $2 \frac{3}{10}$. This is the correct answer among the options provided.

Answer

The correct answer is A. $2 \frac{3}{10}$.

Why is this Important?

Understanding how to add mixed numbers is an essential skill in mathematics, particularly in algebra and geometry. It helps us to solve problems involving fractions and mixed numbers, which are commonly used in real-world applications such as cooking, building, and finance.

Real-World Applications

Adding mixed numbers is a crucial skill in various real-world applications, such as:

• Cooking: When a recipe calls for a certain amount of ingredients, we need to add mixed numbers to ensure we have the correct amount.
• Building: When constructing a building, we need to add mixed numbers to calculate the total amount of materials required.
• Finance: When calculating interest rates or investment returns, we need to add mixed numbers to determine the total amount.

Tips and Tricks

Here are some tips and tricks to help you add mixed numbers:

• Always convert mixed numbers to improper fractions before adding them together.
• Find a common denominator to add the improper fractions together.
• Convert the result back to a mixed number to make it easier to understand and work with.

Common Mistakes

Here are some common mistakes to avoid when adding mixed numbers:

• Not converting mixed numbers to improper fractions before adding them together.
• Not finding a common denominator to add the improper fractions together.
• Not converting the result back to a mixed number to make it easier to understand and work with.

Conclusion

In conclusion, adding mixed numbers is a crucial skill in mathematics that requires understanding how to convert mixed numbers to improper fractions, find a common denominator, and convert the result back to a mixed number. By following these steps and avoiding common mistakes, you can become proficient in adding mixed numbers and apply this skill to real-world applications.
Q&A: Adding Mixed Numbers

Q: What is the first step in adding mixed numbers?

A: The first step in adding mixed numbers is to convert them into improper fractions. This involves multiplying the whole number by the denominator and adding the numerator.

Q: Why do we need to find a common denominator when adding mixed numbers?

A: We need to find a common denominator to add the improper fractions together. This ensures that we are adding the same units, which is essential for getting the correct result.

Q: How do we find a common denominator?

A: To find a common denominator, we need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators can divide into evenly.

Q: What is the least common multiple (LCM) of 10 and 5?

A: The least common multiple (LCM) of 10 and 5 is 10.

Q: How do we add the improper fractions together?

A: To add the improper fractions together, we add the numerators and keep the common denominator.

Q: What is the sum of $\frac{11}{10} + \frac{6}{5}$?

A: The sum of $\frac{11}{10} + \frac{6}{5}$ is $\frac{23}{10}$.

Q: How do we convert the improper fraction $\frac{23}{10}$ back to a mixed number?

A: To convert the improper fraction $\frac{23}{10}$ back to a mixed number, we divide the numerator (23) by the denominator (10). This gives us a quotient of 2 and a remainder of 3. So, the mixed number equivalent of $\frac{23}{10}$ is $2 \frac{3}{10}$.

Q: What is the sum of $1 \frac{1}{10} + 1 \frac{1}{5}$?

A: The sum of $1 \frac{1}{10} + 1 \frac{1}{5}$ is $2 \frac{3}{10}$.

Q: Why is it essential to convert mixed numbers to improper fractions before adding them together?

A: It is essential to convert mixed numbers to improper fractions before adding them together because it makes it easier to find a common denominator and add the fractions together.

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 mixed numbers to improper fractions before adding them together, not finding a common denominator to add the improper fractions together, and not converting the result back to a mixed number to make it easier to understand and work with.

Q: How can I practice adding mixed numbers?

A: You can practice adding mixed numbers by using online resources, such as math worksheets and practice problems, or by working with a tutor or teacher who can provide you with additional support and guidance.

Q: What are some real-world applications of adding mixed numbers?

A: Some real-world applications of adding mixed numbers include cooking, building, and finance. In cooking, you may need to add mixed numbers to measure ingredients. In building, you may need to add mixed numbers to calculate the total amount of materials required. In finance, you may need to add mixed numbers to calculate interest rates or investment returns.

Q: How can I apply the concept of adding mixed numbers to my everyday life?

A: You can apply the concept of adding mixed numbers to your everyday life by using it to solve problems in cooking, building, and finance. You can also use it to calculate tips, discounts, and other real-world applications.