Add And Simplify The Answer: $\frac{5}{8} + \frac{3}{5}$.Select One:A. $\frac{3}{8}$B. $1 \frac{9}{40}$C. $\frac{49}{40}$D. $\frac{8}{13}$

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**Adding and Simplifying Fractions: A Step-by-Step Guide** ===========================================================

What is the Answer to 58+35\frac{5}{8} + \frac{3}{5}?

In this article, we will explore the concept of adding and simplifying fractions, and provide a step-by-step guide on how to solve the problem 58+35\frac{5}{8} + \frac{3}{5}.

What are Fractions?

A fraction is a way of expressing a part of a whole. It consists of two numbers: a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into.

How to Add Fractions

To add fractions, we need to follow these steps:

  1. Find the Least Common Multiple (LCM): The LCM is the smallest number that both denominators can divide into evenly. In this case, the LCM of 8 and 5 is 40.
  2. Convert the Fractions: We need to convert both fractions to have the same denominator, which is 40. To do this, we multiply the numerator and denominator of each fraction by the necessary number to get the LCM.
    • 58=5×58×5=2540\frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40}
    • 35=3×85×8=2440\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}
  3. Add the Numerators: Now that both fractions have the same denominator, we can add the numerators.
    • 2540+2440=25+2440=4940\frac{25}{40} + \frac{24}{40} = \frac{25 + 24}{40} = \frac{49}{40}

Simplifying the Answer

The answer we got is 4940\frac{49}{40}. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 1.

Conclusion

In conclusion, the answer to 58+35\frac{5}{8} + \frac{3}{5} is 4940\frac{49}{40}. We found the LCM of the denominators, converted the fractions to have the same denominator, added the numerators, and simplified the answer.

Frequently Asked Questions

Q: What is the LCM of 8 and 5?

A: The LCM of 8 and 5 is 40.

Q: How do I convert a fraction to have a different denominator?

A: To convert a fraction to have a different denominator, you need to multiply the numerator and denominator by the necessary number to get the new denominator.

Q: What is the greatest common divisor (GCD) of 49 and 40?

A: The GCD of 49 and 40 is 1.

Q: Can I simplify a fraction by dividing both the numerator and denominator by a number other than the GCD?

A: No, you can only simplify a fraction by dividing both the numerator and denominator by their GCD.

Q: What is the answer to 58+35\frac{5}{8} + \frac{3}{5}?

A: The answer to 58+35\frac{5}{8} + \frac{3}{5} is 4940\frac{49}{40}.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the LCM of the denominators, convert the fractions to have the same denominator, add the numerators, and simplify the answer.

Q: Can I add fractions with unlike denominators?

A: Yes, you can add fractions with unlike denominators by following the steps outlined above.

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

A: The main difference between adding fractions and adding whole numbers is that fractions have a denominator, which represents the total number of parts the whole is divided into. When adding fractions, you need to find the LCM of the denominators and convert the fractions to have the same denominator before adding the numerators.