Mark Has $4 \frac{1}{5}$ Yards Of Rope And Gives $\frac{1}{3}$ Of It To His Friend.How Many Yards Of Rope Did Mark Give His Friend?A. $1 \frac{6}{15}$B. $2 \frac{5}{8}$C. $4 \frac{1}{15}$D. $4

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Introduction

Fractions are an essential part of mathematics, and solving problems involving fractions can be a challenging task for many students. In this article, we will focus on solving a specific problem that involves fractions, and we will provide a step-by-step guide on how to solve it.

The Problem

Mark has 4154 \frac{1}{5} yards of rope and gives 13\frac{1}{3} of it to his friend. We need to find out how many yards of rope Mark gave to his friend.

Step 1: Convert the Mixed Number to an Improper Fraction

To solve this problem, we first need to convert the mixed number 4154 \frac{1}{5} to an improper fraction. To do this, we multiply the whole number part (4) by the denominator (5) and then add the numerator (1).

415=(4×5)+15=20+15=2154 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5}

Step 2: Multiply the Improper Fraction by the Fraction Given to the Friend

Now that we have the improper fraction 215\frac{21}{5}, we need to multiply it by the fraction 13\frac{1}{3} that Mark gave to his friend.

215×13=215×13=21×15×3=2115\frac{21}{5} \times \frac{1}{3} = \frac{21}{5} \times \frac{1}{3} = \frac{21 \times 1}{5 \times 3} = \frac{21}{15}

Step 3: Simplify the Result

The result we obtained in the previous step is 2115\frac{21}{15}. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3.

2115=21÷315÷3=75\frac{21}{15} = \frac{21 \div 3}{15 \div 3} = \frac{7}{5}

Step 4: Convert the Improper Fraction to a Mixed Number

Now that we have the simplified improper fraction 75\frac{7}{5}, we need to convert it to a mixed number. To do this, we divide the numerator (7) by the denominator (5) and then write the result as a mixed number.

7÷5=1 with a remainder of 27 \div 5 = 1 \text{ with a remainder of } 2

So, the mixed number is 1251 \frac{2}{5}.

Conclusion

In this article, we solved a problem that involved fractions. We converted a mixed number to an improper fraction, multiplied the improper fraction by a fraction, simplified the result, and finally converted the improper fraction to a mixed number. The final answer is 1251 \frac{2}{5}.

Answer Key

Q&A: Frequently Asked Questions

Q: What is the difference between a mixed number and an improper fraction? A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to 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 multiply the whole number part by the denominator and then add the numerator. For example, 415=(4×5)+15=20+15=2154 \frac{1}{5} = \frac{(4 \times 5) + 1}{5} = \frac{20 + 1}{5} = \frac{21}{5}.

Q: How do I multiply fractions? A: To multiply fractions, you multiply the numerators together and the denominators together. For example, 215×13=21×15×3=2115\frac{21}{5} \times \frac{1}{3} = \frac{21 \times 1}{5 \times 3} = \frac{21}{15}.

Q: How do I simplify a fraction? A: To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD). For example, 2115=21÷315÷3=75\frac{21}{15} = \frac{21 \div 3}{15 \div 3} = \frac{7}{5}.

Q: How do I convert an improper fraction to a mixed number? A: To convert an improper fraction to a mixed number, you divide the numerator by the denominator and then write the result as a mixed number. For example, 7÷5=1 with a remainder of 27 \div 5 = 1 \text{ with a remainder of } 2, so the mixed number is 1251 \frac{2}{5}.

Q: What are some common mistakes to avoid when working with fractions? A: Some common mistakes to avoid when working with fractions include:

  • Not converting mixed numbers to improper fractions before multiplying
  • Not simplifying fractions after multiplying
  • Not converting improper fractions to mixed numbers when the result is a mixed number
  • Not checking for common factors between the numerator and denominator

Q: How can I practice solving fractional problems? A: You can practice solving fractional problems by working through examples and exercises in a textbook or online resource. You can also try creating your own problems and solving them on your own.

Q: What are some real-world applications of fractions? A: Fractions have many real-world applications, including:

  • Cooking and measuring ingredients
  • Building and construction
  • Finance and accounting
  • Science and engineering
  • Music and art

Conclusion

In this article, we provided a step-by-step guide to solving fractional problems, including converting mixed numbers to improper fractions, multiplying fractions, simplifying fractions, and converting improper fractions to mixed numbers. We also answered some frequently asked questions about fractions and provided some tips for practicing and applying fractions in real-world situations.

Additional Resources

  • Khan Academy: Fractions
  • Mathway: Fractions
  • IXL: Fractions
  • Wolfram Alpha: Fractions

Answer Key

The correct answers to the Q&A section are:

  • A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.
  • To convert a mixed number to an improper fraction, you multiply the whole number part by the denominator and then add the numerator.
  • To multiply fractions, you multiply the numerators together and the denominators together.
  • To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD).
  • To convert an improper fraction to a mixed number, you divide the numerator by the denominator and then write the result as a mixed number.
  • Some common mistakes to avoid when working with fractions include not converting mixed numbers to improper fractions before multiplying, not simplifying fractions after multiplying, not converting improper fractions to mixed numbers when the result is a mixed number, and not checking for common factors between the numerator and denominator.
  • You can practice solving fractional problems by working through examples and exercises in a textbook or online resource, or by creating your own problems and solving them on your own.
  • Fractions have many real-world applications, including cooking and measuring ingredients, building and construction, finance and accounting, science and engineering, and music and art.