Solve:${ 1 \frac{3}{10} + 2 \frac{5}{8} }$

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Introduction

When dealing with mixed numbers, it's essential to understand how to add them together. A mixed number is a combination of a whole number and a fraction. In this case, we have two mixed numbers: $1 \frac{3}{10}$ and $2 \frac{5}{8}$. Our goal is to find the sum of these two mixed numbers.

Understanding Mixed Numbers

Before we dive into the addition process, let's take a closer look at what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It's written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

For example, $1 \frac{3}{10}$ can be broken down into two parts: the whole number part (1) and the fraction part ($\frac{3}{10}$). Similarly, $2 \frac{5}{8}$ can be broken down into two parts: the whole number part (2) and the fraction part ($\frac{5}{8}$).

Adding Mixed Numbers

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

1. Convert the mixed numbers to improper fractions: We need to convert both mixed numbers to improper fractions. 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 $1 \frac{3}{10}$, we multiply 1 by 10 to get 10, and then add 3 to get 13. So, $1 \frac{3}{10}$ becomes $\frac{13}{10}$.

For $2 \frac{5}{8}$, we multiply 2 by 8 to get 16, and then add 5 to get 21. So, $2 \frac{5}{8}$ becomes $\frac{21}{8}$.

2. Find a common denominator: Now that we have both mixed numbers in improper fraction form, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.

In this case, the denominators are 10 and 8. The LCM of 10 and 8 is 40.

3. Add the fractions: Now that we have a common denominator, we can add the fractions. We multiply the numerator of each fraction by the denominator of the other fraction, and then add the results.

$\frac{13}{10} + \frac{21}{8} = \frac{13 \times 4}{10 \times 4} + \frac{21 \times 5}{8 \times 5} = \frac{52}{40} + \frac{105}{40}$

4. Add the numerators: Now that we have the fractions with a common denominator, we can add the numerators.

$\frac{52}{40} + \frac{105}{40} = \frac{52 + 105}{40} = \frac{157}{40}$

Converting the Result to a Mixed Number

Now that we have the result in improper fraction form, we can convert it to a mixed number. To do this, we divide the numerator by the denominator and write the result as a mixed number.

$\frac{157}{40} = 3 \frac{37}{40}$

Conclusion

In this article, we learned how to add mixed numbers. We started by understanding what mixed numbers are and how to convert them to improper fractions. Then, we followed a step-by-step process to add the mixed numbers. Finally, we converted the result to a mixed number. With this knowledge, you can now add mixed numbers with confidence.

Frequently Asked Questions

• What is a mixed number? A mixed number is a combination of a whole number and a fraction.
• How do I add mixed numbers? To add mixed numbers, you need to convert them to improper fractions, find a common denominator, add the fractions, and then convert the result to a mixed number.
• What is an improper fraction? An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Example Problems

• Add $2 \frac{1}{4} + 3 \frac{2}{3}$ To add these mixed numbers, we need to convert them to improper fractions. $2 \frac{1}{4}$ becomes $\frac{9}{4}$, and $3 \frac{2}{3}$ becomes $\frac{11}{3}$. Then, we find a common denominator, which is 12. We multiply the numerator of each fraction by the denominator of the other fraction, and then add the results. Finally, we convert the result to a mixed number.
• Add $1 \frac{3}{5} + 2 \frac{4}{7}$ To add these mixed numbers, we need to convert them to improper fractions. $1 \frac{3}{5}$ becomes $\frac{8}{5}$, and $2 \frac{4}{7}$ becomes $\frac{18}{7}$. Then, we find a common denominator, which is 35. We multiply the numerator of each fraction by the denominator of the other fraction, and then add the results. Finally, we convert the result to a mixed number.

Tips and Tricks

• Make sure to convert the mixed numbers to improper fractions before adding them.
• Find a common denominator before adding the fractions.
• Add the numerators after finding a common denominator.
• Convert the result to a mixed number after adding the fractions.

Resources

• Mathway: A math problem solver that can help you with adding mixed numbers.
• Khan Academy: A website that provides video lessons and practice exercises on adding mixed numbers.
• Math Open Reference: A website that provides interactive math lessons and examples on adding mixed numbers.
  

Introduction

Adding mixed numbers can be a challenging task, but with the right approach, it can be made easier. In this article, we will answer some of the most frequently asked questions about adding mixed numbers.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It's written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

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. Find a common denominator.
3. Add the fractions.
4. Convert the result 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, $\frac{3}{2}$ 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 part by the denominator and add the numerator. Then, you write the result as an improper fraction.

For example, to convert $2 \frac{1}{4}$ to an improper fraction, you multiply 2 by 4 to get 8, and then add 1 to get 9. So, $2 \frac{1}{4}$ becomes $\frac{9}{4}$.

Q: How do I find a common denominator?

A: To find a common denominator, you 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.

For example, to find the common denominator of 4 and 6, you need to find the LCM of 4 and 6. The LCM of 4 and 6 is 12.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator. Then, you multiply the numerator of each fraction by the denominator of the other fraction, and then add the results.

For example, to add $\frac{1}{4}$ and $\frac{1}{6}$, you need to find a common denominator, which is 12. Then, you multiply the numerator of each fraction by the denominator of the other fraction, and then add the results.

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 mixed number.

For example, to convert $\frac{7}{4}$ to a mixed number, you divide 7 by 4 to get 1 with a remainder of 3. So, $\frac{7}{4}$ becomes $1 \frac{3}{4}$.

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 numbers to improper fractions before adding them.
• Not finding a common denominator before adding the fractions.
• Not adding the numerators after finding a common denominator.
• Not converting the result to a mixed number after adding the fractions.

Q: How can I practice adding mixed numbers?

A: You can practice adding mixed numbers by using online resources such as math problem solvers, video lessons, and practice exercises. You can also practice by working on your own problems and checking your answers with a calculator or a math teacher.

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

A: Adding mixed numbers has many real-world applications, including:

• Cooking: When you're cooking, you may need to add fractions of ingredients to a recipe. For example, if a recipe calls for 2 cups of flour and 1/4 cup of sugar, you need to add 2 1/4 cups of flour and sugar together.
• Building: When you're building a structure, you may need to add fractions of materials to a blueprint. For example, if a blueprint calls for 3/4 inch of wood and 1/2 inch of nails, you need to add 3/4 inch and 1/2 inch together.
• Science: When you're conducting a science experiment, you may need to add fractions of chemicals to a solution. For example, if a recipe calls for 2/3 cup of water and 1/4 cup of acid, you need to add 2/3 cup and 1/4 cup together.

Q: How can I use technology to help me add mixed numbers?

A: You can use technology such as calculators, math software, and online resources to help you add mixed numbers. For example, you can use a calculator to convert mixed numbers to improper fractions and then add them together.

Q: What are some tips for adding mixed numbers?

A: Some tips for adding mixed numbers include:

• Make sure to convert the mixed numbers to improper fractions before adding them.
• Find a common denominator before adding the fractions.
• Add the numerators after finding a common denominator.
• Convert the result to a mixed number after adding the fractions.
• Practice, practice, practice!

Q: How can I use visual aids to help me add mixed numbers?

A: You can use visual aids such as diagrams, charts, and graphs to help you add mixed numbers. For example, you can use a diagram to show the different parts of a mixed number and how they add up.

Q: What are some common misconceptions about adding mixed numbers?

A: Some common misconceptions about adding mixed numbers include:

• Thinking that you can add mixed numbers without converting them to improper fractions.
• Thinking that you can add mixed numbers without finding a common denominator.
• Thinking that you can add mixed numbers without converting the result to a mixed number.

Q: How can I use real-world examples to help me add mixed numbers?

A: You can use real-world examples such as cooking, building, and science to help you add mixed numbers. For example, you can use a recipe to practice adding mixed numbers.

Q: What are some resources for learning more about adding mixed numbers?

A: Some resources for learning more about adding mixed numbers include:

• Math textbooks and workbooks
• Online resources such as math problem solvers and video lessons
• Math software and apps
• Math teachers and tutors

Q: How can I use games and activities to help me add mixed numbers?

A: You can use games and activities such as math puzzles, brain teasers, and math games to help you add mixed numbers. For example, you can use a math puzzle to practice adding mixed numbers.

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

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

• Not converting the mixed numbers to improper fractions before subtracting them.
• Not finding a common denominator before subtracting the fractions.
• Not subtracting the numerators after finding a common denominator.
• Not converting the result to a mixed number after subtracting the fractions.

Q: How can I practice subtracting mixed numbers?

A: You can practice subtracting mixed numbers by using online resources such as math problem solvers, video lessons, and practice exercises. You can also practice by working on your own problems and checking your answers with a calculator or a math teacher.

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

A: Subtracting mixed numbers has many real-world applications, including:

• Cooking: When you're cooking, you may need to subtract fractions of ingredients from a recipe. For example, if a recipe calls for 2 cups of flour and 1/4 cup of sugar, and you only need 1 3/4 cups of flour and sugar, you need to subtract 1 3/4 cups from 2 1/4 cups.
• Building: When you're building a structure, you may need to subtract fractions of materials from a blueprint. For example, if a blueprint calls for 3/4 inch of wood and 1/2 inch of nails, and you only need 1/2 inch of wood and nails, you need to subtract 1/2 inch from 3/4 inch.
• Science: When you're conducting a science experiment, you may need to subtract fractions of chemicals from a solution. For example, if a recipe calls for 2/3 cup of water and 1/4 cup of acid, and you only need 1/2 cup of water and acid, you need to subtract 1/2 cup from 2/3 cup.

Q: How can I use technology to help me subtract mixed numbers?

A: You can use technology such as calculators, math software, and online resources to help you subtract mixed numbers. For example, you can use a calculator to convert mixed numbers to improper fractions and then subtract them together.

Q: What are some tips for subtracting mixed numbers?

A: Some tips for subtracting mixed numbers include:

• Make sure to convert the mixed numbers to improper fractions before subtracting them.
• Find a common denominator before subtracting the fractions.
• Subtract the numerators after finding a common denominator.
• Convert the result to a mixed number after subtracting the fractions.
• Practice, practice, practice!

Q: How can I use visual aids to help me subtract mixed numbers?

A: You can use visual aids such as diagrams, charts, and graphs to help you subtract mixed numbers. For example, you can use a diagram to show the different parts of a mixed number and how they subtract.