What Is The Answer To This Problem? 2 1 3 + 3 1 3 = ? 2 \frac{1}{3} + 3 \frac{1}{3} = ? 2 3 1 ​ + 3 3 1 ​ = ?

What is the Answer to This Problem? $2 \frac{1}{3} + 3 \frac{1}{3} = ?$

In mathematics, we often come across problems that involve adding fractions with different denominators. The problem $2 \frac{1}{3} + 3 \frac{1}{3} = ?$ is a classic example of such a problem. In this article, we will explore the steps involved in solving this problem and provide a clear understanding of the concept.

Understanding the Problem

The problem $2 \frac{1}{3} + 3 \frac{1}{3} = ?$ involves adding two mixed numbers, $2 \frac{1}{3}$ and $3 \frac{1}{3}$. To solve this problem, we need to first understand the concept of mixed numbers and how to add them.

What are 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 part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction. For example, $2 \frac{1}{3}$ is a mixed number where $2$ is the whole number part and $\frac{1}{3}$ is the fraction part.

Adding Mixed Numbers

To add mixed numbers, we need to follow a step-by-step process. Here are the steps involved:

1. Convert the mixed numbers to improper fractions: To add mixed numbers, we need to convert them to 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 part by the denominator and add the numerator. For example, to convert $2 \frac{1}{3}$ to an improper fraction, we multiply $2$ by $3$ and add $1$, which gives us $\frac{7}{3}$.
2. Find a common denominator: Once we have converted the mixed numbers to improper fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two fractions. For example, if we have two fractions $\frac{7}{3}$ and $\frac{10}{3}$, the common denominator is $3$.
3. Add the fractions: Once we have found the common denominator, we can add the fractions. To add fractions, we need to add the numerators and keep the denominator the same. For example, if we have two fractions $\frac{7}{3}$ and $\frac{10}{3}$, we add the numerators $7$ and $10$ to get $17$, and keep the denominator $3$ to get $\frac{17}{3}$.
4. Convert the improper fraction back to a mixed number: Once we have added the fractions, we need to convert the improper fraction back to a mixed number. To convert an improper fraction to a mixed number, we divide the numerator by the denominator and write the remainder as the new numerator. For example, if we have an improper fraction $\frac{17}{3}$, we divide $17$ by $3$ to get $5$ with a remainder of $2$, which gives us $5 \frac{2}{3}$.

Solving the Problem

Now that we have understood the concept of mixed numbers and how to add them, let's solve the problem $2 \frac{1}{3} + 3 \frac{1}{3} = ?$.

1. Convert the mixed numbers to improper fractions: We convert $2 \frac{1}{3}$ to an improper fraction by multiplying $2$ by $3$ and adding $1$, which gives us $\frac{7}{3}$. We convert $3 \frac{1}{3}$ to an improper fraction by multiplying $3$ by $3$ and adding $1$, which gives us $\frac{10}{3}$.
2. Find a common denominator: The common denominator is $3$.
3. Add the fractions: We add the numerators $7$ and $10$ to get $17$, and keep the denominator $3$ to get $\frac{17}{3}$.
4. Convert the improper fraction back to a mixed number: We divide $17$ by $3$ to get $5$ with a remainder of $2$, which gives us $5 \frac{2}{3}$.

In this article, we have explored the concept of mixed numbers and how to add them. We have also solved the problem $2 \frac{1}{3} + 3 \frac{1}{3} = ?$ using the steps involved in adding mixed numbers. We have seen that the answer to the problem is $5 \frac{2}{3}$.

Here are some tips and tricks to help you solve problems involving mixed numbers:

• Make sure to convert the mixed numbers to improper fractions: This is the first step in solving problems involving mixed numbers.
• Find a common denominator: This is an important step in solving problems involving fractions.
• Add the fractions: Once you have found the common denominator, you can add the fractions.
• Convert the improper fraction back to a mixed number: This is the final step in solving problems involving mixed numbers.

Here are some practice problems to help you practice solving problems involving mixed numbers:

• $4 \frac{1}{2} + 2 \frac{1}{2} = ?$
• $6 \frac{2}{3} + 1 \frac{2}{3} = ?$
• $3 \frac{1}{4} + 2 \frac{1}{4} = ?$

• [1] Khan Academy. (n.d.). Adding and Subtracting Fractions. Retrieved from https://www.khanacademy.org/math/fraction-arithmetic/fraction-addition-subtraction/v/adding-and-subtracting-fractions
• [2] Math Open Reference. (n.d.). Mixed Numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html
• [3] Purplemath. (n.d.). Adding and Subtracting Mixed Numbers. Retrieved from https://www.purplemath.com/modules/mixednumb.htm
  Q&A: Mixed Numbers and Adding Fractions =============================================

In our previous article, we explored the concept of mixed numbers and how to add them. We also solved the problem $2 \frac{1}{3} + 3 \frac{1}{3} = ?$ using the steps involved in adding mixed numbers. In this article, we will answer some frequently asked questions about mixed numbers and adding fractions.

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 part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

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

A: To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and add the numerator. For example, to convert $2 \frac{1}{3}$ to an improper fraction, you multiply $2$ by $3$ and add $1$, which gives you $\frac{7}{3}$.

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 denominators of the two fractions. For example, if you have two fractions $\frac{7}{3}$ and $\frac{10}{3}$, the common denominator is $3$.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator and then add the fractions. For example, if you have two fractions $\frac{7}{3}$ and $\frac{10}{3}$, you add the numerators $7$ and $10$ to get $17$, and keep the denominator $3$ to get $\frac{17}{3}$.

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

A: To convert an improper fraction back to a mixed number, you divide the numerator by the denominator and write the remainder as the new numerator. For example, if you have an improper fraction $\frac{17}{3}$, you divide $17$ by $3$ to get $5$ with a remainder of $2$, which gives you $5 \frac{2}{3}$.

Q: What are some tips and tricks for solving problems involving mixed numbers?

A: Here are some tips and tricks to help you solve problems involving mixed numbers:

• Make sure to convert the mixed numbers to improper fractions: This is the first step in solving problems involving mixed numbers.
• Find a common denominator: This is an important step in solving problems involving fractions.
• Add the fractions: Once you have found the common denominator, you can add the fractions.
• Convert the improper fraction back to a mixed number: This is the final step in solving problems involving mixed numbers.

Q: What are some practice problems to help me practice solving problems involving mixed numbers?

A: Here are some practice problems to help you practice solving problems involving mixed numbers:

• $4 \frac{1}{2} + 2 \frac{1}{2} = ?$
• $6 \frac{2}{3} + 1 \frac{2}{3} = ?$
• $3 \frac{1}{4} + 2 \frac{1}{4} = ?$

In this article, we have answered some frequently asked questions about mixed numbers and adding fractions. We have also provided some tips and tricks to help you solve problems involving mixed numbers. We hope that this article has been helpful in clarifying any confusion you may have had about mixed numbers and adding fractions.

• [1] Khan Academy. (n.d.). Adding and Subtracting Fractions. Retrieved from https://www.khanacademy.org/math/fraction-arithmetic/fraction-addition-subtraction/v/adding-and-subtracting-fractions
• [2] Math Open Reference. (n.d.). Mixed Numbers. Retrieved from https://www.mathopenref.com/mixednumbers.html
• [3] Purplemath. (n.d.). Adding and Subtracting Mixed Numbers. Retrieved from https://www.purplemath.com/modules/mixednumb.htm