What Is The Difference Of The Fractions Below?${ \frac{6x}{7} - \frac{2x}{7} }$A. ${ 4x\$} B. { \frac{4x}{7}$}$ C. 4 D. { \frac{4}{7}$}$

What is the Difference of the Fractions Below?

Understanding the Problem

When dealing with fractions, it's essential to understand the concept of difference, which is a fundamental operation in mathematics. The difference of two fractions is obtained by subtracting the second fraction from the first fraction. In this problem, we are given two fractions: $\frac{6x}{7}$ and $\frac{2x}{7}$. We need to find the difference between these two fractions.

Subtracting Fractions with the Same Denominator

To subtract fractions with the same denominator, we simply subtract the numerators while keeping the denominator the same. In this case, both fractions have a denominator of 7. Therefore, we can subtract the numerators as follows:

$\frac{6x}{7} - \frac{2x}{7} = \frac{6x - 2x}{7}$

Simplifying the Expression

Now that we have subtracted the numerators, we can simplify the expression by combining like terms. In this case, we have $6x - 2x$, which can be simplified to $4x$.

$\frac{6x - 2x}{7} = \frac{4x}{7}$

Evaluating the Answer Choices

Now that we have found the difference of the fractions, we can evaluate the answer choices to determine which one is correct.

A. $4x$ - This is not the correct answer because the difference of the fractions is not an integer.

B. $\frac{4x}{7}$ - This is the correct answer because it matches the expression we obtained by subtracting the fractions.

C. 4 - This is not the correct answer because the difference of the fractions is not an integer.

D. $\frac{4}{7}$ - This is not the correct answer because the difference of the fractions is not a constant.

Conclusion

In conclusion, the difference of the fractions $\frac{6x}{7}$ and $\frac{2x}{7}$ is $\frac{4x}{7}$. This can be obtained by subtracting the numerators while keeping the denominator the same, and then simplifying the expression by combining like terms.

Understanding the Concept of Difference

The concept of difference is a fundamental operation in mathematics that involves finding the result of subtracting one quantity from another. In the context of fractions, the difference of two fractions is obtained by subtracting the second fraction from the first fraction. This can be done by subtracting the numerators while keeping the denominator the same, and then simplifying the expression by combining like terms.

Real-World Applications of the Concept of Difference

The concept of difference has numerous real-world applications in various fields, including finance, engineering, and science. For example, in finance, the difference between two stock prices can be used to determine the profit or loss of an investment. In engineering, the difference between two measurements can be used to determine the accuracy of a device. In science, the difference between two experimental results can be used to determine the validity of a hypothesis.

Common Mistakes to Avoid

When working with fractions, there are several common mistakes to avoid. One of the most common mistakes is to subtract the denominators instead of the numerators. This can result in an incorrect answer. Another common mistake is to forget to simplify the by combining like terms. This can also result in an incorrect answer.

Tips for Solving Problems Involving Fractions

When solving problems involving fractions, there are several tips to keep in mind. One of the most important tips is to read the problem carefully and understand what is being asked. Another important tip is to identify the operation that needs to be performed, such as addition, subtraction, multiplication, or division. Finally, it's essential to simplify the expression by combining like terms to ensure that the answer is correct.

Conclusion

In conclusion, the difference of the fractions $\frac{6x}{7}$ and $\frac{2x}{7}$ is $\frac{4x}{7}$. This can be obtained by subtracting the numerators while keeping the denominator the same, and then simplifying the expression by combining like terms. The concept of difference is a fundamental operation in mathematics that has numerous real-world applications in various fields. By understanding the concept of difference and avoiding common mistakes, we can solve problems involving fractions with confidence.

Final Answer

The final answer is $\boxed{\frac{4x}{7}}$.
Frequently Asked Questions (FAQs) About Fractions

Q: What is a fraction?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, the fraction $\frac{1}{2}$ represents one half of a whole.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a way of expressing a part of a whole as a ratio of two numbers, while a decimal is a way of expressing a number as a sum of powers of 10. For example, the fraction $\frac{1}{2}$ is equivalent to the decimal 0.5.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the two denominators. Then, you can convert both fractions to have the LCM as the denominator, and add the numerators.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, you need to find the least common multiple (LCM) of the two denominators. Then, you can convert both fractions to have the LCM as the denominator, and subtract the numerators.

Q: How do I multiply fractions?

A: To multiply fractions, you simply multiply the numerators and multiply the denominators.

Q: How do I divide fractions?

A: To divide fractions, you need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply.

Q: What is the least common multiple (LCM) of two numbers?

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 4 and 6 is 12.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and denominator, and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator.

Q: How do I convert a decimal to a fraction?

A: To convert a decimal to a fraction, you need to express the decimal as a sum of powers of 10, and then simplify the resulting fraction.

Q: What is the difference between a proper fraction and an improper fraction?

A: A proper fraction is a fraction where the numerator is less than the denominator, while an improper fraction is a fraction where the numerator is greater than or equal to 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 need to multiply the whole number by the denominator, add the numerator, and then write the result as an improper fraction.

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 then write the result as a mixed number.

Conclusion

In conclusion, fractions are a fundamental concept in mathematics that have numerous real-world applications. By understanding the basics of fractions, including adding, subtracting, multiplying, and dividing fractions, you can solve problems with confidence. Additionally, by knowing how to simplify fractions, convert fractions to decimals, and convert decimals to fractions, you can perform a wide range of mathematical operations.