Add The Following Fractions And Answer As A Mixed Number In Simplest Form:$\[ 1 \frac{1}{2} + 4 \frac{5}{6} \\]Enter The Whole Number Part Of The Answer.

Feb 27, 2025 by ADMIN 154 views

**Adding Fractions with Mixed Numbers: A Step-by-Step Guide**

Introduction

Adding fractions with mixed numbers can be a challenging task, especially when dealing with different denominators. However, with a clear understanding of the concept and a step-by-step approach, it becomes manageable. In this article, we will explore how to add fractions with mixed numbers and provide a solution to the given problem.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as 1 1/2 or 4 5/6. To add mixed numbers, we need to first convert them into improper fractions.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For example, let's convert 1 1/2 to an improper fraction:

1 × 2 = 2 2 + 1 = 3

So, 1 1/2 is equal to 3/2.

Similarly, let's convert 4 5/6 to an improper fraction:

4 × 6 = 24 24 + 5 = 29

So, 4 5/6 is equal to 29/6.

Adding Fractions with Different Denominators

To add fractions with different denominators, we need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.

For example, let's find the LCM of 2 and 6:

The multiples of 2 are: 2, 4, 6, 8, 10, ... The multiples of 6 are: 6, 12, 18, 24, 30, ...

The smallest number that both lists have in common is 6. Therefore, the LCM of 2 and 6 is 6.

Adding the Fractions

Now that we have the LCM, we can add the fractions:

3/2 + 29/6

To add these fractions, we need to find a common denominator, which is 6. We can rewrite 3/2 as 9/6:

9/6 + 29/6

Now we can add the numerators:

9 + 29 = 38

So, the sum of the fractions is 38/6.

Converting the Improper Fraction to a Mixed Number

To convert the improper fraction to a mixed number, we divide the numerator by the denominator:

38 ÷ 6 = 6 with a remainder of 2

So, the mixed number is 6 2/6.

Simplifying the Mixed Number

To simplify the mixed number, we can divide the numerator and denominator by their greatest common divisor (GCD). The GCD of 2 and 6 is 2.

38 ÷ 2 = 19 6 ÷ 2 = 3

So, the simplified mixed number is 6 1/3.

Conclusion

Adding fractions with mixed numbers requires a clear understanding of the concept and a step-by-step approach. By converting mixed numbers to improper fractions, finding the LCM, adding the fractions, and converting the improper fraction to a mixed number, we can solve the given problem. The final answer is 6 1/3.

Final Answer

Q: What is the first step in adding fractions with mixed numbers?

A: The first step in adding fractions with mixed numbers is to convert the mixed numbers to improper fractions. This involves multiplying the whole number by the denominator and then adding the numerator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the numerator. For example, to convert 1 1/2 to an improper fraction, you would multiply 1 by 2 and add 1, resulting in 3/2.

Q: What is the least common multiple (LCM) and why is it important?

A: The LCM is the smallest number that both denominators can divide into evenly. It is important because it allows us to add fractions with different denominators by finding a common denominator.

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 smallest number that both lists have in common. Alternatively, you can use a formula or a calculator to find the LCM.

Q: What is the next step after finding the LCM?

A: After finding the LCM, you can rewrite each fraction with the LCM as the denominator. This allows you to add the fractions by adding the numerators.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find the LCM and then rewrite each fraction with the LCM as the denominator. You can then add the fractions by adding the numerators.

Q: What is the final step in adding fractions with mixed numbers?

A: The final step in adding fractions with mixed numbers is to convert the improper fraction to a mixed number. This involves dividing the numerator by the denominator and writing the result as a mixed number.

Q: Can I simplify a mixed number?

A: Yes, you can simplify a mixed number by dividing the numerator and denominator by their greatest common divisor (GCD). This results in a simplified mixed number.

Q: What is the greatest common divisor (GCD) and why is it important?

A: The GCD is the largest number that divides both the numerator and denominator evenly. It is important because it allows us to simplify a mixed number by dividing both the numerator and denominator by the GCD.

Q: How do I simplify a mixed number?

A: To simplify a mixed number, you divide the numerator and denominator by their GCD. This results in a simplified mixed number.

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

A: Some common mistakes to avoid when adding fractions with mixed numbers include:

Forgetting to convert mixed numbers to improper fractions
Not finding the LCM of the denominators
Not rewriting each fraction with the LCM as the denominator
Not adding the numerators correctly
Not simplifying the mixed number correctly

Q: How can I practice adding fractions with mixed numbers?

A: You can practice adding fractions with mixed numbers by working through examples and exercises. You can also use online resources or math software to help you practice and understand the concept.