Calculate The Result Of The Expression:${ 7 \frac{5}{6} - 4 \frac{3}{7} }$

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that are not whole, but can be expressed as a combination of a whole number and a fraction. In this article, we will explore how to calculate the result of the expression $7 \frac{5}{6} - 4 \frac{3}{7}$.

Understanding 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, $b$ is the numerator, and $c$ is the denominator. For example, $3 \frac{2}{3}$ is a mixed number that represents the quantity $3 + \frac{2}{3}$.

Converting Mixed Numbers to Improper Fractions

To calculate the result of the expression $7 \frac{5}{6} - 4 \frac{3}{7}$, we need to convert the mixed numbers 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. We then write the result as a fraction with the denominator.

For example, to convert $7 \frac{5}{6}$ to an improper fraction, we multiply $7$ by $6$ and add $5$. This gives us $42 + 5 = 47$. We then write the result as a fraction with the denominator: $\frac{47}{6}$.

Converting $7 \frac{5}{6}$ to an Improper Fraction

To convert $7 \frac{5}{6}$ to an improper fraction, we multiply $7$ by $6$ and add $5$. This gives us $42 + 5 = 47$. We then write the result as a fraction with the denominator: $\frac{47}{6}$.

Converting $4 \frac{3}{7}$ to an Improper Fraction

To convert $4 \frac{3}{7}$ to an improper fraction, we multiply $4$ by $7$ and add $3$. This gives us $28 + 3 = 31$. We then write the result as a fraction with the denominator: $\frac{31}{7}$.

Calculating the Result of the Expression

Now that we have converted the mixed numbers to improper fractions, we can calculate the result of the expression $7 \frac{5}{6} - 4 \frac{3}{7}$. To do this, we subtract the two improper fractions: $\frac{47}{6} - \frac{31}{7}$.

Finding a Common Denominator

To subtract the two improper fractions, we need to find a common denominator. The least common multiple (LCM) of $6$ and $7$ is $42$. We can rewrite the fractions with the common denominator: $\frac{47}{6} = \frac{47 \times 7}{6 \times 7} = \frac{329}{42}$ and $\frac{31}{7} = \frac{31 \times 6}{7 \times 6} = \frac{186}{42}$.

Subtracting the Fractions

Now that we have rewritten the fractions with the common denominator, we can subtract them: $\frac{329}{42} - \frac{186}{42} = \frac{329 - 186}{42} = \frac{143}{42}$.

Reducing the Fraction

The fraction $\frac{143}{42}$ can be reduced by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of $143$ and $42$ is $1$. Therefore, the fraction $\frac{143}{42}$ is already in its simplest form.

Conclusion

In this article, we have explored how to calculate the result of the expression $7 \frac{5}{6} - 4 \frac{3}{7}$. We first converted the mixed numbers to improper fractions, then found a common denominator, subtracted the fractions, and finally reduced the resulting fraction. The result of the expression is $\frac{143}{42}$.

Final Answer

The final answer is $\boxed{\frac{143}{42}}$.

Additional Resources

For more information on mixed numbers and improper fractions, please see the following resources:

• Wikipedia: Mixed number
• Wikipedia: Improper fraction
• Math Is Fun: Mixed Numbers
• Math Is Fun: Improper Fractions
  Frequently Asked Questions: Mixed Numbers and Improper 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, $b$ is the numerator, and $c$ 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, you multiply the whole number by the denominator and add the numerator. You then write the result as a fraction with the denominator.

Q: What is an improper fraction?

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

Q: How do I find a common denominator for two fractions?

A: To find a common denominator for two fractions, 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.

Q: How do I subtract two fractions with different denominators?

A: To subtract two fractions with different denominators, you need to find a common denominator and then subtract the fractions. You can find a common denominator by finding the least common multiple (LCM) of the two denominators.

Q: Can I simplify a fraction?

A: Yes, you can simplify a fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD is the largest number that both the numerator and the denominator can divide into evenly.

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.

Q: How do I add two mixed numbers?

A: To add two mixed numbers, you need to convert them to improper fractions, find a common denominator, add the fractions, and then convert the result back to a mixed number.

Q: How do I subtract two mixed numbers?

A: To subtract two mixed numbers, you need to convert them to improper fractions, find a common denominator, subtract the fractions, and then convert the result back to a mixed number.

Q: Can I multiply two mixed numbers?

A: Yes, you can multiply two mixed numbers by converting them to improper fractions, multiplying the fractions, and then converting the result back to a mixed number.

Q: Can I divide two mixed numbers?

A: Yes, you can divide two mixed numbers by converting them to improper fractions, dividing the fractions, and then converting the result back to a mixed number.

Q: What are some real-world applications of mixed numbers and improper fractions?

A: Mixed numbers and improper fractions are used in many real-world applications, such as:

• Measuring ingredients in cooking and baking
• Calculating areas and volumes of shapes
• Determining the cost of items
• Calculating the amount of time it takes to complete a task

Conclusion

In this article, we have answered some frequently asked questions about mixed numbers and improper fractions. We have covered topics such as converting mixed numbers to improper fractions, finding common denominators, subtracting fractions, simplifying fractions, and adding and subtracting mixed numbers. We have also discussed some real-world applications of mixed numbers and improper fractions.