Evaluate $\frac{6}{7} + \frac{1}{14}$.

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Introduction

In mathematics, fractions are a fundamental concept that is used to represent a part of a whole. When we add fractions, we need to ensure that the denominators are the same. If the denominators are different, we need to find a common denominator before we can add the fractions. In this article, we will evaluate the expression $\frac{6}{7} + \frac{1}{14}$.

Understanding the Problem

To evaluate the expression $\frac{6}{7} + \frac{1}{14}$, we need to find a common denominator for the two fractions. The common denominator is the least common multiple (LCM) of the two denominators. In this case, the denominators are 7 and 14. We can find the LCM by listing the multiples of each denominator and finding the smallest multiple that is common to both.

Finding the Common Denominator

To find the LCM of 7 and 14, we can list the multiples of each denominator.

Multiples of 7: 7, 14, 21, 28, 35, ... Multiples of 14: 14, 28, 42, 56, 70, ...

The smallest multiple that is common to both lists is 14. Therefore, the LCM of 7 and 14 is 14.

Adding the Fractions

Now that we have found the common denominator, we can add the fractions.

$\frac{6}{7} + \frac{1}{14} = \frac{6 \times 2}{7 \times 2} + \frac{1}{14} = \frac{12}{14} + \frac{1}{14} = \frac{13}{14}$

Conclusion

In this article, we evaluated the expression $\frac{6}{7} + \frac{1}{14}$ by finding a common denominator and adding the fractions. We found that the LCM of 7 and 14 is 14, and then we added the fractions to get the final result of $\frac{13}{14}$.

Real-World Applications

Fractions are used in many real-world applications, such as cooking, building, and finance. For example, when a recipe calls for $\frac{3}{4}$ cup of flour, we need to find a common denominator to add the fractions. Similarly, when a builder needs to add $\frac{1}{2}$ inch of wood to a wall, we need to find a common denominator to add the fractions.

Tips and Tricks

When adding fractions, it is essential to find a common denominator. We can find the LCM of the two denominators by listing the multiples of each denominator and finding the smallest multiple that is common to both. We can also use a calculator to find the LCM.

Common Mistakes

When adding fractions, it is easy to make mistakes. Some common mistakes include:

• Not finding a common denominator
• Adding the numerators instead of the fractions
• Not simplifying the fraction after adding

Simplifying Fractions

When we add fractions, we need to simplify the fraction to get the final result. We can simplify a fraction by dividing the numerator and denominator by their greatest common divisor (GCD).

Final Result

The final result of the expression $\frac{6}{7} + \frac{1}{14}$ is $\frac{13}{14}$.

Frequently Asked Questions

Q: What is the common denominator of 7 and 14? A: The LCM of 7 and 14 is 14.

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.

Q: What is the final result of the expression $\frac{6}{7} + \frac{1}{14}$? A: The final result of the expression $\frac{6}{7} + \frac{1}{14}$ is $\frac{13}{14}$.

Conclusion

In this article, we evaluated the expression $\frac{6}{7} + \frac{1}{14}$ by finding a common denominator and adding the fractions. We found that the LCM of 7 and 14 is 14, and then we added the fractions to get the final result of $\frac{13}{14}$. We also discussed the importance of finding a common denominator when adding fractions and provided tips and tricks for simplifying fractions.

Introduction

Adding fractions with different denominators 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 fractions with different denominators.

Q: What is the common denominator of 7 and 14?

A: The least common multiple (LCM) of 7 and 14 is 14.

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. You can find the common denominator by listing the multiples of each denominator and finding the smallest multiple that is common to both.

Q: What is the final result of the expression $\frac{6}{7} + \frac{1}{14}$?

A: The final result of the expression $\frac{6}{7} + \frac{1}{14}$ is $\frac{13}{14}$.

Q: How do I find the common denominator of two fractions?

A: To find the common denominator of two fractions, you can list the multiples of each denominator and find the smallest multiple that is common to both. Alternatively, you can use a calculator to find the least common multiple (LCM) of the two denominators.

Q: What is the difference between adding fractions and adding whole numbers?

A: Adding fractions and adding whole numbers are two different operations. When you add fractions, you need to find a common denominator and then add the fractions. When you add whole numbers, you simply add the numbers together.

Q: Can I add fractions with different signs?

A: Yes, you can add fractions with different signs. When you add fractions with different signs, you need to find a common denominator and then add the fractions. The sign of the result will be the same as the sign of the fraction with the larger absolute value.

Q: How do I simplify a fraction after adding?

A: To simplify a fraction after adding, you need to divide the numerator and denominator by their greatest common divisor (GCD). This will give you the simplest form of the fraction.

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.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can list the factors of each number and find the largest factor that is common to both. Alternatively, you can use a calculator to find the GCD.

Q: Can I add fractions with negative numbers?

A: Yes, you can add fractions with negative numbers. When you add fractions with negative numbers, you need to find a common denominator and then add the fractions. The sign of the result will be the same as the sign of the fraction with the larger absolute value.

Q: How do I add fractions with decimals?

A: To add fractions with decimals, you need to convert the decimals to fractions and then add the fractions. You can convert a decimal to a fraction by writing it as a fraction with a denominator of 10 or 100.

Q: What is the difference between adding fractions and subtracting fractions?

A: Adding fractions and subtracting fractions are two different operations. When you add fractions, you need to find a common denominator and then add the fractions. When you subtract fractions, you need to find a common denominator and then subtract the fractions.

Q: Can I subtract fractions with different signs?

A: Yes, you can subtract fractions with different signs. When you subtract fractions with different signs, you need to find a common denominator and then subtract the fractions. The sign of the result will be the same as the sign of the fraction with the larger absolute value.

Q: How do I simplify a fraction after subtracting?

A: To simplify a fraction after subtracting, you need to divide the numerator and denominator by their greatest common divisor (GCD). This will give you the simplest form of the fraction.

Q: What is the final result of the expression $\frac{6}{7} - \frac{1}{14}$?

A: The final result of the expression $\frac{6}{7} - \frac{1}{14}$ is $\frac{11}{14}$.

Conclusion

In this article, we answered some of the most frequently asked questions about adding fractions with different denominators. We discussed the importance of finding a common denominator and simplifying fractions after adding or subtracting. We also provided tips and tricks for adding and subtracting fractions with different signs and decimals.