Calculate:1. $4 \frac{2}{3} + 5 \frac{4}{6} + 1 \frac{3}{4}$

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Introduction

Mixed numbers are a type of complex fraction that consists of a whole number and a fraction. They are commonly used in mathematics, particularly in arithmetic operations such as addition and subtraction. In this article, we will explore how to calculate mixed numbers, focusing on the problem of adding three mixed numbers: $4 \frac{2}{3} + 5 \frac{4}{6} + 1 \frac{3}{4}$

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of $a \frac{b}{c}$, where aa is the whole number, bb is the numerator, and cc is the denominator. For example, $4 \frac{2}{3}$ is a mixed number where 44 is the whole number, 22 is the numerator, and 33 is the denominator.

Converting Mixed Numbers to Improper Fractions

To add mixed numbers, it is often easier 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 by the denominator and add the numerator. The result is then written as a fraction with the product as the numerator and the denominator remaining the same.

For example, to convert $4 \frac{2}{3}$ to an improper fraction, we multiply 44 by 33 and add 22, resulting in $\frac{14}{3}$.

Converting the Given Mixed Numbers to Improper Fractions

Let's convert the given mixed numbers to improper fractions:

  • 4 \frac{2}{3}$ becomes $\frac{14}{3}

  • 5 \frac{4}{6}$ becomes $\frac{34}{6}

  • 1 \frac{3}{4}$ becomes $\frac{7}{4}

Adding the Improper Fractions

Now that we have converted the mixed numbers to improper fractions, we can add them together. To add fractions, we need to have a common denominator. The least common multiple (LCM) of the denominators 33, 66, and 44 is 1212. We can rewrite each fraction with a denominator of 1212:

  • \frac{14}{3}$ becomes $\frac{14 \times 4}{3 \times 4} = \frac{56}{12}

  • \frac{34}{6}$ becomes $\frac{34 \times 2}{6 \times 2} = \frac{68}{12}

  • \frac{7}{4}$ becomes $\frac{7 \times 3}{4 \times 3} = \frac{21}{12}

Now we can add the fractions:

5612+6812+2112=14512\frac{56}{12} + \frac{68}{12} + \frac{21}{12} = \frac{145}{12}

Converting the Result Back to a Mixed Number

To convert the improper fraction $\frac{145}{12}$ back to a mixed number, we divide the numerator by the denominator:

145÷12=12 with a remainder of 1145 \div 12 = 12 \text{ with a remainder of } 1

Therefore, the mixed number equivalent of $\frac{145}{12}$ is $12 \frac{1}{12}$.

Conclusion

In this article, we have explored how to calculate mixed numbers by converting them to improper fractions and adding them together. We have used the problem of adding three mixed numbers: $4 \frac{2}{3} + 5 \frac{4}{6} + 1 \frac{3}{4}$ as an example. By following the steps outlined in this article, you should be able to calculate complex fractions with ease.

Final Answer

The final answer to the problem $4 \frac{2}{3} + 5 \frac{4}{6} + 1 \frac{3}{4}$ is $12 \frac{1}{12}$.

Additional Resources

For more information on mixed numbers and improper fractions, check out the following resources:

  • Khan Academy: Mixed Numbers and Improper Fractions
  • Mathway: Mixed Numbers and Improper Fractions
  • Purplemath: Mixed Numbers and Improper Fractions

Frequently Asked Questions

  • Q: What is a mixed number?
  • A: A mixed number is a combination of a whole number and a fraction.
  • 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 by the denominator and add the numerator.
  • Q: How do I add mixed numbers?
  • A: To add mixed numbers, convert them to improper fractions and add them together.
    Mastering Mixed Numbers: A Step-by-Step Guide to Calculating Complex Fractions ===========================================================

Q&A: Mixed Numbers and Improper Fractions

Frequently Asked Questions

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 of $a \frac{b}{c}$, where aa is the whole number, bb is the numerator, and cc is the denominator.

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 by the denominator and add the numerator. For example, to convert $4 \frac{2}{3}$ to an improper fraction, we multiply 44 by 33 and add 22, resulting in $\frac{14}{3}$.

Q: How do I add mixed numbers?

A: To add mixed numbers, convert them to improper fractions and add them together. For example, to add $4 \frac2}{3}$, $5 \frac{4}{6}$, and $1 \frac{3}{4}$, we first convert them to improper fractions $\frac{143}$, $\frac{34}{6}$, and $\frac{7}{4}$. Then, we find the least common multiple (LCM) of the denominators, which is 1212. We rewrite each fraction with a denominator of 1212 and add them together $\frac{56{12} + \frac{68}{12} + \frac{21}{12} = \frac{145}{12}$.

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

A: To convert an improper fraction back to a mixed number, divide the numerator by the denominator. For example, to convert $\frac145}{12}$ back to a mixed number, we divide 145145 by 1212 $145 \div 12 = 12 \text{ with a remainder of 1$. Therefore, the mixed number equivalent of $\frac{145}{12}$ is $12 \frac{1}{12}$.

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, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $4 \frac{2}{3}$ is a mixed number, while $\frac{14}{3}$ is an improper fraction.

Q: Can I subtract mixed numbers?

A: Yes, you can subtract mixed numbers. To subtract mixed numbers, convert them to improper fractions and subtract them together. For example, to subtract $4 \frac2}{3}$ from $5 \frac{4}{6}$, we first convert them to improper fractions $\frac{143}$ and $\frac{34}{6}$. Then, we find the least common multiple (LCM) of the denominators, which is 66. We rewrite each fraction with a denominator of 66 and subtract them together $\frac{34{6} - \frac{28}{6} = \frac{6}{6} = 1$.

Q: Can I multiply mixed numbers?

A: Yes, you can multiply mixed numbers. To multiply mixed numbers, convert them to improper fractions and multiply them together. For example, to multiply $4 \frac2}{3}$ and $5 \frac{4}{6}$, we first convert them to improper fractions $\frac{143}$ and $\frac{34}{6}$. Then, we multiply them together $\frac{14{3} \times \frac{34}{6} = \frac{476}{18}$.

Q: Can I divide mixed numbers?

A: Yes, you can divide mixed numbers. To divide mixed numbers, convert them to improper fractions and divide them together. For example, to divide $4 \frac2}{3}$ by $5 \frac{4}{6}$, we first convert them to improper fractions $\frac{143}$ and $\frac{34}{6}$. Then, we divide them together $\frac{14{3} \div \frac{34}{6} = \frac{14}{3} \times \frac{6}{34} = \frac{84}{102}$.

Conclusion

In this article, we have explored the world of mixed numbers and improper fractions. We have answered some of the most frequently asked questions about mixed numbers and improper fractions, including how to convert mixed numbers to improper fractions, how to add and subtract mixed numbers, and how to multiply and divide mixed numbers. We hope that this article has been helpful in your understanding of mixed numbers and improper fractions.