Add $\frac{5}{8}+\frac{7}{12}$. Simplify The Answer And Write It As A Mixed Number, If Possible.A. $\frac{29}{24}$ B. $1 \frac{20}{96}$ C. $1 \frac{5}{24}$ D. $\frac{12}{20}$

by ADMIN 178 views

Introduction

Adding fractions with different denominators can be a challenging task, especially when dealing with complex numbers. However, with a clear understanding of the concept and a step-by-step approach, it becomes manageable. In this article, we will explore the process of adding fractions with different denominators, simplify the answer, and express it as a mixed number, if possible.

Understanding the Concept

Before we dive into the process, it's essential to understand the concept of adding fractions with different denominators. When we add fractions, we need to have the same denominator, which is the number that appears in the denominator of each fraction. To achieve this, we need to find the least common multiple (LCM) of the two denominators.

Finding the Least Common Multiple (LCM)

The LCM of two numbers is the smallest number that is a multiple of both numbers. To find the LCM, we can list the multiples of each number and find the smallest number that appears in both lists.

For example, let's find the LCM of 8 and 12.

  • Multiples of 8: 8, 16, 24, 32, ...
  • Multiples of 12: 12, 24, 36, 48, ...

As we can see, the smallest number that appears in both lists is 24. Therefore, the LCM of 8 and 12 is 24.

Adding Fractions with Different Denominators

Now that we have found the LCM, we can add the fractions.

Let's add 58\frac{5}{8} and 712\frac{7}{12}.

  • The LCM of 8 and 12 is 24.
  • We need to convert each fraction to have a denominator of 24.
  • 58=5×38×3=1524\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}
  • 712=7×212×2=1424\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}

Now that we have the same denominator, we can add the fractions.

1524+1424=2924\frac{15}{24} + \frac{14}{24} = \frac{29}{24}

Simplifying the Answer

The answer we obtained is an improper fraction, which can be simplified to a mixed number.

2924=1524\frac{29}{24} = 1 \frac{5}{24}

Conclusion

Adding fractions with different denominators requires finding the least common multiple (LCM) of the two denominators and converting each fraction to have the same denominator. Once we have the same denominator, we can add the fractions and simplify the answer to a mixed number, if possible.

Common Mistakes to Avoid

When adding fractions with different denominators, it's essential to avoid common mistakes, such as:

  • Not finding the LCM of the two denominators
  • Not converting each fraction to have the same denominator
  • Not simplifying the answer to a mixed number, if possible

By following the step-by-step guide outlined in this article, you can avoid these common mistakes and become proficient in adding fractions with different denominators.

Practice Problems

To reinforce your understanding of adding fractions with different denominators, try the following practice problems:

  1. Add 34\frac{3}{4} and 56\frac{5}{6}.
  2. Add 23\frac{2}{3} and 79\frac{7}{9}.
  3. Add 45\frac{4}{5} and 310\frac{3}{10}.

Answer Key

  1. 1712\frac{17}{12}
  2. 199\frac{19}{9}
  3. 2310\frac{23}{10}

Final Thoughts

Adding fractions with different denominators may seem challenging, but with practice and patience, you can master this skill. Remember to find the least common multiple (LCM) of the two denominators, convert each fraction to have the same denominator, and simplify the answer to a mixed number, if possible. By following these steps, you can become proficient in adding fractions with different denominators and tackle complex math problems with confidence.