Complete The Following Fractions:${ \begin{tabular}{rl} 3 1 6 3 \frac{1}{6} 3 6 1 ​ & = 3 6 =3 \frac{}{6} = 3 6 ​ \ + 5 2 3 +5 \frac{2}{3} + 5 3 2 ​ & = 5 □ 6 =5 \frac{\square}{6} = 5 6 □ ​ \ \hline \end{tabular} }$

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Solving Mixed Fractions: A Step-by-Step Guide to Completing the Given Fractions

When dealing with mixed fractions, it's essential to understand how to add and subtract them. In this article, we will focus on completing the given fractions, specifically 3163 \frac{1}{6} and 5235 \frac{2}{3}. We will break down the process into manageable steps, making it easier to understand and apply the concepts.

Understanding Mixed Fractions

A mixed fraction is a combination of a whole number and a fraction. It's denoted by a whole number followed by a fraction, such as 3163 \frac{1}{6}. The whole number represents the part of the fraction that is already completed, while the fraction represents the remaining part.

Adding Mixed Fractions

To add mixed fractions, we need to follow a specific process. Here's a step-by-step guide:

  1. Convert the mixed fractions to improper fractions: To add mixed fractions, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.

    • 3163 \frac{1}{6} can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 3×6+1=193 \times 6 + 1 = 19. So, 3163 \frac{1}{6} becomes 196\frac{19}{6}.
    • 5235 \frac{2}{3} can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 5×3+2=175 \times 3 + 2 = 17. So, 5235 \frac{2}{3} becomes 173\frac{17}{3}.

  2. Find a common denominator: To add fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators of the two fractions.

    • The LCM of 6 and 3 is 6.

  3. Convert the fractions to have the common denominator: We need to convert both fractions to have the common denominator.

    • 196\frac{19}{6} already has the common denominator, so we don't need to do anything.
    • 173\frac{17}{3} needs to be converted to have the common denominator. We can do this by multiplying the numerator and denominator by 2: 17×23×2=346\frac{17 \times 2}{3 \times 2} = \frac{34}{6}.

  4. Add the fractions: Now that both fractions have the common denominator, we can add them.

    • 196+346=536\frac{19}{6} + \frac{34}{6} = \frac{53}{6}

  5. Convert the improper fraction back to a mixed fraction: Finally, we need to convert the improper fraction back to a mixed fraction.

    • 536\frac{53}{6} can be converted to a mixed fraction by dividing the numerator by the denominator: 53÷6=853 \div 6 = 8 with a remainder of 5. So, 536\frac{53}{6} becomes 8568 \frac{5}{6}.

In this article, we have learned how to complete the given fractions, specifically 3163 \frac{1}{6} and 5235 \frac{2}{3}. We have broken down the process into manageable steps, making it easier to understand and apply the concepts. By following these steps, we can add mixed fractions and convert them back to mixed fractions.

  • When adding mixed fractions, make sure to convert them to improper fractions first.
  • Find a common denominator by finding the LCM of the denominators.
  • Convert the fractions to have the common denominator.
  • Add the fractions.
  • Convert the improper fraction back to a mixed fraction.
  • 234+114=?2 \frac{3}{4} + 1 \frac{1}{4} = ?
  • 425+335=?4 \frac{2}{5} + 3 \frac{3}{5} = ?
  • 612+212=?6 \frac{1}{2} + 2 \frac{1}{2} = ?
  • 234+114=4122 \frac{3}{4} + 1 \frac{1}{4} = 4 \frac{1}{2}
  • 425+335=8154 \frac{2}{5} + 3 \frac{3}{5} = 8 \frac{1}{5}
  • 612+212=9126 \frac{1}{2} + 2 \frac{1}{2} = 9 \frac{1}{2}
    Frequently Asked Questions: Mixed Fractions =============================================

Q: What is a mixed fraction?

A: A mixed fraction is a combination of a whole number and a fraction. It's denoted by a whole number followed by a fraction, such as 3163 \frac{1}{6}.

Q: How do I add mixed fractions?

A: To add mixed fractions, you need to follow these steps:

  1. Convert the mixed fractions to improper fractions.
  2. Find a common denominator by finding the LCM of the denominators.
  3. Convert the fractions to have the common denominator.
  4. Add the fractions.
  5. Convert the improper fraction back to a mixed fraction.

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than the denominator. For example, 196\frac{19}{6} is an improper fraction.

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

A: To convert a mixed fraction to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. For example, 3163 \frac{1}{6} can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator: 3×6+1=193 \times 6 + 1 = 19. So, 3163 \frac{1}{6} becomes 196\frac{19}{6}.

Q: How do I find a common denominator?

A: To find a common denominator, you need to find the LCM of the denominators. For example, the LCM of 6 and 3 is 6.

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

A: To convert a fraction to have a common denominator, you need to multiply the numerator and denominator by the necessary factor. For example, 173\frac{17}{3} needs to be converted to have the common denominator of 6. We can do this by multiplying the numerator and denominator by 2: 17×23×2=346\frac{17 \times 2}{3 \times 2} = \frac{34}{6}.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to follow these steps:

  1. Find a common denominator by finding the LCM of the denominators.
  2. Convert the fractions to have the common denominator.
  3. Add the fractions.

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

A: To convert an improper fraction to a mixed fraction, you need to divide the numerator by the denominator. For example, 536\frac{53}{6} can be converted to a mixed fraction by dividing the numerator by the denominator: 53÷6=853 \div 6 = 8 with a remainder of 5. So, 536\frac{53}{6} becomes 8568 \frac{5}{6}.

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

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

  • Not converting the mixed fractions to improper fractions before adding or subtracting.
  • Not finding a common denominator before adding or subtracting fractions.
  • Not converting the fractions to have the common denominator before adding or subtracting.
  • Not adding or subtracting the fractions correctly.
  • Not converting the improper fraction back to a mixed fraction after adding or subtracting.

Q: How can I practice working with mixed fractions?

A: You can practice working with mixed fractions by:

  • Using online resources and worksheets to practice adding and subtracting mixed fractions.
  • Working with real-world examples, such as measuring ingredients for a recipe or calculating the cost of items.
  • Creating your own practice problems and solutions.
  • Asking a teacher or tutor for help and guidance.

In this article, we have answered some frequently asked questions about mixed fractions. We have covered topics such as what a mixed fraction is, how to add mixed fractions, and how to convert improper fractions to mixed fractions. We have also provided some tips and tricks for working with mixed fractions and some common mistakes to avoid. By following these steps and practicing regularly, you can become more confident and proficient in working with mixed fractions.