21. Choose All That Are True.A. $4 \frac{1}{12} \times \frac{3}{4} = \frac{49}{16}$ B. $8 \frac{5}{6} \times 2 = 17 \frac{2}{3}$ C. $5 \frac{1}{2} \times 5 \frac{1}{2} = 30 \frac{1}{4}$ D. $9 \frac{1}{5} \times

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21. Choose all that are true: Multiplying Mixed Numbers and Fractions

In mathematics, multiplying mixed numbers and fractions can be a challenging task, especially for students who are new to this concept. However, with the right approach and practice, it can become a breeze. In this article, we will explore the concept of multiplying mixed numbers and fractions, and we will examine four statements to determine which ones are true.

Understanding Mixed Numbers and Fractions

Before we dive into the multiplication of mixed numbers and fractions, let's first understand what they are. A mixed number is a combination of a whole number and a fraction, while a fraction is a part of a whole. For example, 2 3/4 is a mixed number, where 2 is the whole number and 3/4 is the fraction. On the other hand, 3/4 is a fraction, where 3 is the numerator and 4 is the denominator.

Multiplying Mixed Numbers and Fractions

To multiply mixed numbers and fractions, we need to follow a specific set of rules. The first rule is to convert the mixed number to an improper fraction. This involves multiplying the whole number by the denominator and then adding the numerator. For example, to convert 2 3/4 to an improper fraction, we multiply 2 by 4 and add 3, which gives us 11/4.

Once we have converted the mixed number to an improper fraction, we can multiply it by the other fraction. To do this, we multiply the numerators together and the denominators together. For example, to multiply 11/4 by 3/4, we multiply 11 by 3 and 4 by 4, which gives us 33/16.

Evaluating the Statements

Now that we have a good understanding of multiplying mixed numbers and fractions, let's evaluate the four statements:

A. 4112×34=49164 \frac{1}{12} \times \frac{3}{4} = \frac{49}{16}

To evaluate this statement, we need to convert the mixed number to an improper fraction. We multiply 4 by 12 and add 1, which gives us 49/12. Then, we multiply 49/12 by 3/4, which gives us 147/48. This is not equal to 49/16, so statement A is false.

B. 856×2=17238 \frac{5}{6} \times 2 = 17 \frac{2}{3}

To evaluate this statement, we need to convert the mixed number to an improper fraction. We multiply 8 by 6 and add 5, which gives us 53/6. Then, we multiply 53/6 by 2, which gives us 106/6. This simplifies to 53/3, which is equal to 17 2/3. Therefore, statement B is true.

C. 512×512=30145 \frac{1}{2} \times 5 \frac{1}{2} = 30 \frac{1}{4}

To evaluate this statement, we need to convert the mixed numbers to improper fractions. We multiply 5 by 2 and add 1, which gives us 11/2. Then, we multiply 11/2 by 11/2, which gives us 121/4. This is not equal to 30 1/4, so statement C is false.

D. 915×34=27209 \frac{1}{5} \times \frac{3}{4} = \frac{27}{20}

To evaluate this statement, we need to convert the mixed number to an improper fraction. We multiply 9 by 5 and add 1, which gives us 46/5. Then, we multiply 46/5 by 3/4, which gives us 138/20. This simplifies to 69/10, which is not equal to 27/20. Therefore, statement D is false.

Conclusion

In conclusion, we have evaluated four statements about multiplying mixed numbers and fractions. We found that statement B is true, while statements A, C, and D are false. By following the rules of multiplying mixed numbers and fractions, we can determine which statements are true and which are false.

Common Mistakes to Avoid

When multiplying mixed numbers and fractions, there are several common mistakes to avoid. One mistake is to forget to convert the mixed number to an improper fraction. Another mistake is to multiply the whole numbers together and then multiply the fractions together. This can lead to incorrect answers.

Tips for Success

To succeed in multiplying mixed numbers and fractions, it's essential to follow the rules and practice regularly. Here are some tips to help you succeed:

  • Make sure to convert the mixed number to an improper fraction before multiplying.
  • Multiply the numerators together and the denominators together.
  • Simplify the answer by dividing both the numerator and the denominator by their greatest common divisor.
  • Practice regularly to build your confidence and skills.

Conclusion

In conclusion, multiplying mixed numbers and fractions can be a challenging task, but with the right approach and practice, it can become a breeze. By following the rules and avoiding common mistakes, you can succeed in multiplying mixed numbers and fractions. Remember to practice regularly and to simplify your answers to get the correct results.

Final Thoughts

Multiplying mixed numbers and fractions is an essential skill in mathematics, and it's used in many real-world applications. By mastering this skill, you can solve problems in algebra, geometry, and other areas of mathematics. So, don't be afraid to practice and challenge yourself to become proficient in multiplying mixed numbers and fractions.

References

  • [1] "Multiplying Mixed Numbers and Fractions" by Math Open Reference
  • [2] "Multiplying Fractions and Mixed Numbers" by Khan Academy
  • [3] "Multiplying Mixed Numbers and Fractions" by Purplemath

Additional Resources

  • [1] "Multiplying Mixed Numbers and Fractions" worksheet by Math Drills
  • [2] "Multiplying Fractions and Mixed Numbers" practice problems by IXL
  • [3] "Multiplying Mixed Numbers and Fractions" video tutorial by Crash Course
    21. Choose all that are true: Multiplying Mixed Numbers and Fractions - Q&A

In our previous article, we explored the concept of multiplying mixed numbers and fractions, and we evaluated four statements to determine which ones are true. In this article, we will answer some frequently asked questions about multiplying mixed numbers and fractions.

Q: What is the difference between a mixed number and a fraction?

A: A mixed number is a combination of a whole number and a fraction, while a fraction is a part of a whole. For example, 2 3/4 is a mixed number, where 2 is the whole number and 3/4 is the fraction. On the other hand, 3/4 is a fraction, where 3 is the numerator and 4 is the denominator.

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, to convert 2 3/4 to an improper fraction, you multiply 2 by 4 and add 3, which gives you 11/4.

Q: What is the rule for multiplying mixed numbers and fractions?

A: The rule for multiplying mixed numbers and fractions is to convert the mixed number to an improper fraction, multiply the numerators together, and multiply the denominators together. For example, to multiply 2 3/4 by 3/4, you convert 2 3/4 to an improper fraction (11/4), multiply the numerators together (11 x 3 = 33), and multiply the denominators together (4 x 4 = 16), which gives you 33/16.

Q: How do I simplify a fraction after multiplying mixed numbers and fractions?

A: To simplify a fraction after multiplying mixed numbers and fractions, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 33/16, you divide both the numerator and the denominator by their GCD (1), which gives you 33/16.

Q: What are some common mistakes to avoid when multiplying mixed numbers and fractions?

A: Some common mistakes to avoid when multiplying mixed numbers and fractions include forgetting to convert the mixed number to an improper fraction, multiplying the whole numbers together and then multiplying the fractions together, and not simplifying the answer. By avoiding these mistakes, you can ensure that your answers are accurate.

Q: How can I practice multiplying mixed numbers and fractions?

A: You can practice multiplying mixed numbers and fractions by using worksheets, online resources, and practice problems. Some popular resources include Math Drills, IXL, and Khan Academy. You can also practice by creating your own problems and solving them.

Q: What are some real-world applications of multiplying mixed numbers and fractions?

A: Multiplying mixed numbers and fractions has many real-world applications, including algebra, geometry, and other areas of mathematics. For example, you may need to multiply mixed numbers and fractions to solve problems involving area, volume, and rate. By mastering this skill, you can solve problems in a variety of contexts.

Q: How can I improve my skills in multiplying mixed numbers and fractions?

A: To improve your skills in multiplying mixed numbers and fractions, you need to practice regularly and consistently. You can also try to challenge yourself by creating your own problems and solving them. Additionally, you can seek help from a teacher or tutor if you are struggling with this concept.

Conclusion

In conclusion, multiplying mixed numbers and fractions is an essential skill in mathematics, and it has many real-world applications. By following the rules and avoiding common mistakes, you can succeed in multiplying mixed numbers and fractions. Remember to practice regularly and to simplify your answers to get the correct results.

Final Thoughts

Multiplying mixed numbers and fractions is a challenging concept, but with practice and patience, you can master it. By following the rules and avoiding common mistakes, you can ensure that your answers are accurate. Remember to practice regularly and to challenge yourself to become proficient in multiplying mixed numbers and fractions.

References

  • [1] "Multiplying Mixed Numbers and Fractions" by Math Open Reference
  • [2] "Multiplying Fractions and Mixed Numbers" by Khan Academy
  • [3] "Multiplying Mixed Numbers and Fractions" by Purplemath

Additional Resources

  • [1] "Multiplying Mixed Numbers and Fractions" worksheet by Math Drills
  • [2] "Multiplying Fractions and Mixed Numbers" practice problems by IXL
  • [3] "Multiplying Mixed Numbers and Fractions" video tutorial by Crash Course