From A Piece Of Cloth Which Is A Meter Long, A Man Cuts Off $\frac{3}{5}$. How Much Is $\frac{1}{2}$ Of The Remainder?

by ADMIN 123 views

Introduction

Mathematics is a fascinating subject that surrounds us in every aspect of life. From the intricate patterns on a piece of cloth to the complex calculations in finance, math plays a vital role in understanding and solving problems. In this article, we will delve into a simple yet intriguing problem that involves fractions and remainders. We will explore how a man cuts off a portion of a meter-long cloth and then calculate half of the remaining portion.

The Problem

A man has a piece of cloth that is one meter long. He decides to cut off $\frac{3}{5}$ of the cloth. This leaves him with a remainder, which is the portion of the cloth that is not cut off. The problem asks us to find $\frac{1}{2}$ of the remainder.

Calculating the Remainder

To find the remainder, we first need to calculate the portion of the cloth that is cut off. The man cuts off $\frac{3}{5}$ of the cloth, which is equivalent to $\frac{3}{5} \times 1$ meter. To find the remainder, we subtract the portion cut off from the total length of the cloth.

Remainder=1−35\text{Remainder} = 1 - \frac{3}{5}

To subtract a fraction from a whole number, we need to find a common denominator. In this case, the common denominator is 5. We can rewrite 1 as $\frac{5}{5}$.

Remainder=55−35\text{Remainder} = \frac{5}{5} - \frac{3}{5}

Now, we can subtract the fractions.

Remainder=5−35\text{Remainder} = \frac{5-3}{5}

Remainder=25\text{Remainder} = \frac{2}{5}

Calculating Half of the Remainder

Now that we have found the remainder, we need to calculate half of it. To do this, we multiply the remainder by $\frac{1}{2}$.

Half of the Remainder=12×25\text{Half of the Remainder} = \frac{1}{2} \times \frac{2}{5}

To multiply fractions, we multiply the numerators and the denominators.

Half of the Remainder=1×22×5\text{Half of the Remainder} = \frac{1 \times 2}{2 \times 5}

Half of the Remainder=210\text{Half of the Remainder} = \frac{2}{10}

Simplifying the Fraction

The fraction $\frac{2}{10}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

Half of the Remainder=2÷210÷2\text{Half of the Remainder} = \frac{2 \div 2}{10 \div 2}

Half of the Remainder=15\text{Half of the Remainder} = \frac{1}{5}

Conclusion

In this article, we explored a simple yet intriguing problem that involved fractions and remainders. We calculated the remainder when a man cut off $\frac{3}{5}$ of a meter-long cloth and then found half of the remaining portion. The result was $\frac{1}{5}$ of the original cloth. This problem demonstrates the importance of understanding fractions and remainders in mathematics and how they can be applied to real-world problems.

Applications of Fractions and Remainders

Fractions and remainders are essential concepts in mathematics that have numerous applications in various fields. Here are a few examples:

  • Cooking: When a recipe calls for a certain amount of an ingredient, fractions and remainders can help you measure the exact amount needed.
  • Building and Construction: Fractions and remainders are used to calculate the amount of materials needed for a project, ensuring that the correct amount is ordered and used.
  • Finance: Fractions and remainders are used in financial calculations, such as calculating interest rates and investment returns.
  • Science: Fractions and remainders are used in scientific calculations, such as measuring the concentration of a solution or the amount of a substance present in a sample.

Real-World Examples of Fractions and Remainders

Fractions and remainders are used in various real-world scenarios, including:

  • Measuring Ingredients: When baking a cake, you may need to measure out a certain amount of flour. If the recipe calls for 2 3/4 cups of flour, you can use fractions and remainders to calculate the exact amount needed.
  • Calculating Interest: When calculating interest on a loan or investment, fractions and remainders are used to determine the interest rate and the amount of interest owed.
  • Measuring Time: Fractions and remainders are used to measure time, such as calculating the time it takes to complete a task or the amount of time remaining before a deadline.

Conclusion

Fractions and remainders are essential concepts in mathematics that have numerous applications in various fields. By understanding how to calculate fractions and remainders, you can apply these concepts to real-world problems and make informed decisions. In this article, we explored a simple yet intriguing problem that involved fractions and remainders, and we calculated half of the remaining portion after a man cut off $\frac{3}{5}$ of a meter-long cloth. The result was $\frac{1}{5}$ of the original cloth.

Introduction

In our previous article, we explored a simple yet intriguing problem that involved fractions and remainders. We calculated the remainder when a man cut off $\frac{3}{5}$ of a meter-long cloth and then found half of the remaining portion. The result was $\frac{1}{5}$ of the original cloth. In this article, we will answer some frequently asked questions related to the problem and provide additional insights into the world of fractions and remainders.

Q&A

Q: What is the difference between a fraction and a remainder?

A: A fraction is a way of expressing a part of a whole as a ratio of the part to the whole. A remainder, on the other hand, is the amount left over after a certain operation has been performed. In the context of the problem, the fraction $\frac{3}{5}$ represents the portion of the cloth that is cut off, while the remainder $\frac{2}{5}$ represents the amount of cloth left over.

Q: How do you calculate the remainder when a fraction is subtracted from a whole number?

A: To calculate the remainder when a fraction is subtracted from a whole number, you need to find a common denominator. In the case of the problem, the common denominator is 5. You can rewrite 1 as $\frac{5}{5}$ and then subtract the fraction $\frac{3}{5}$.

Q: What is the significance of the greatest common divisor (GCD) in simplifying fractions?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. In the context of the problem, the GCD of 2 and 10 is 2. By dividing both the numerator and the denominator by the GCD, we can simplify the fraction $\frac{2}{10}$ to $\frac{1}{5}$.

Q: How do you calculate half of a fraction?

A: To calculate half of a fraction, you need to multiply the fraction by $\frac{1}{2}$. In the case of the problem, we multiplied the remainder $\frac{2}{5}$ by $\frac{1}{2}$ to get $\frac{1}{5}$.

Q: What are some real-world applications of fractions and remainders?

A: Fractions and remainders have numerous applications in various fields, including cooking, building and construction, finance, and science. For example, in cooking, fractions and remainders can help you measure the exact amount of ingredients needed for a recipe. In finance, fractions and remainders are used to calculate interest rates and investment returns.

Additional Insights

Fractions and remainders are essential concepts in mathematics that have numerous applications in various fields. By understanding how to calculate fractions and remainders, you can apply these concepts to real-world problems and make informed decisions. Here are some additional insights into the world of fractions and remainders:

  • Fractions can be used to represent parts of a whole: Fractions are a way of expressing a part of a whole as a ratio of the part to the whole. This can be useful in a variety of situations, such as measuring ingredients for a recipe or calculating the amount of materials needed for a project.
  • Remainders can be used to represent the amount left over: Remainders are the amount left over after a certain operation has been performed. This can be useful in a variety of situations, such as calculating the amount of materials left over after a project or determining the amount of time remaining before a deadline.
  • Fractions and remainders can be used to solve problems: Fractions and remainders can be used to solve a variety of problems, such as calculating the amount of materials needed for a project or determining the amount of time remaining before a deadline.
  • Fractions and remainders can be used to make informed decisions: By understanding how to calculate fractions and remainders, you can apply these concepts to real-world problems and make informed decisions.

Conclusion

Fractions and remainders are essential concepts in mathematics that have numerous applications in various fields. By understanding how to calculate fractions and remainders, you can apply these concepts to real-world problems and make informed decisions. In this article, we answered some frequently asked questions related to the problem and provided additional insights into the world of fractions and remainders. We hope that this article has been helpful in understanding the concepts of fractions and remainders and how they can be applied to real-world problems.