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Introduction

In this article, we will delve into the world of fractions and learn how to add them together. We will focus on finding the sum of two fractions, $\frac{2}{3}$ and $\frac{5}{8}$, and express the result as a mixed number in its simplest form.

Understanding Fractions

Fractions are a way to represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

For example, in the fraction $\frac{2}{3}$, the numerator is 2 and the denominator is 3. This means that we have 2 equal parts out of a total of 3 parts.

Adding Fractions with Different Denominators

When adding fractions with different denominators, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators.

In our example, the denominators are 3 and 8. To find the LCM, we can list the multiples of each number:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ... Multiples of 8: 8, 16, 24, 32, 40, ...

As we can see, the first number that appears in both lists is 24. Therefore, the LCM of 3 and 8 is 24.

Finding the Common Denominator

Now that we have found the common denominator, we can rewrite each fraction with the common denominator.

$\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}$

$\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}$

Adding the Fractions

Now that we have rewritten each fraction with the common denominator, we can add them together.

$\frac{16}{24} + \frac{15}{24} = \frac{16 + 15}{24} = \frac{31}{24}$

Converting to a Mixed Number

To convert the improper fraction $\frac{31}{24}$ to a mixed number, we need to divide the numerator by the denominator.

$31 \div 24 = 1$ with a remainder of 7

Therefore, the mixed number is $1\frac{7}{24}$.

Conclusion

In this article, we learned how to add fractions with different denominators. We found the common denominator, rewrote each fraction with the common denominator, added the fractions, and finally converted the improper fraction to a mixed number. The result is $1\frac{7}{24}$.

Final Answer

The final answer is $\boxed{1\frac{7}{24}}$.

Introduction

In our previous article, we learned how to add fractions with different denominators. However, we may still have some questions about this process. In this article, we will address some of the most frequently asked questions about adding fractions.

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

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. In the context of adding fractions, the LCM is the common denominator that we use to add the fractions.

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

A: To find the LCM of two numbers, you can list the multiples of each number and find the first number that appears in both lists. Alternatively, you can use the following formula:

LCM(a, b) = (a × b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of a and b.

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

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. In the context of adding fractions, the GCD is used to find the LCM.

Q: How do I add fractions with unlike denominators?

A: To add fractions with unlike denominators, you need to find the LCM of the two denominators and rewrite each fraction with the LCM as the denominator. Then, you can add the fractions by adding the numerators and keeping the same denominator.

Q: Can I add fractions with unlike denominators by converting them to equivalent fractions?

A: Yes, you can add fractions with unlike denominators by converting them to equivalent fractions with a common denominator. However, this method may not be as efficient as finding the LCM and rewriting the fractions.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $\frac{5}{2}$ is 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 write the result as a mixed number. For example, $\frac{17}{4}$ can be converted to $4\frac{1}{4}$.

Q: Can I add fractions with unlike denominators by using a calculator?

A: Yes, you can add fractions with unlike denominators by using a calculator. However, it's always a good idea to understand the underlying math and be able to do the calculation by hand.

Q: What are some common mistakes to avoid when adding fractions?

A: Some common mistakes to avoid when adding fractions include:

• Not finding the LCM of the denominators
• Not rewriting the fractions with the LCM as the denominator
• Not adding the numerators correctly
• Not converting improper fractions to mixed numbers correctly

Conclusion

In this article, we addressed some of the most frequently asked questions about adding fractions. We hope that this article has helped to clarify any confusion and provide a better understanding of the process.

Final Answer

The final answer is $\boxed{1\frac{7}{24}}$.