Here Are Four Fractions:${ \begin{array}{llll} \frac{1}{50} & \frac{50}{100} & \frac{100}{50} & \frac{1}{5} \end{array} }$Which Fraction Is Equivalent To 0.5 0.5 0.5 ?

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Introduction

Fractions are an essential part of mathematics, and understanding equivalent fractions is crucial for solving various mathematical problems. In this article, we will explore four fractions and determine which one is equivalent to 0.5. We will delve into the world of fractions, learn about equivalent fractions, and apply mathematical concepts to find the correct answer.

What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value, but their numerators and denominators are different. In other words, two fractions are equivalent if they can be simplified to the same value. For example, the fractions 1/2 and 2/4 are equivalent because they both simplify to 1/2.

The Four Fractions

We are given four fractions:

  • 150\frac{1}{50}
  • 50100\frac{50}{100}
  • 10050\frac{100}{50}
  • 15\frac{1}{5}

Our goal is to determine which of these fractions is equivalent to 0.5.

Analyzing the Fractions

Let's start by analyzing each fraction and determining its decimal equivalent.

150\frac{1}{50}

To convert this fraction to a decimal, we can divide the numerator (1) by the denominator (50).

150=0.02\frac{1}{50} = 0.02

50100\frac{50}{100}

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 50.

50100=12=0.5\frac{50}{100} = \frac{1}{2} = 0.5

10050\frac{100}{50}

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 50.

10050=2\frac{100}{50} = 2

15\frac{1}{5}

To convert this fraction to a decimal, we can divide the numerator (1) by the denominator (5).

15=0.2\frac{1}{5} = 0.2

Conclusion

After analyzing each fraction, we can see that only one fraction is equivalent to 0.5, which is 50100\frac{50}{100}. This fraction simplifies to 0.5, making it the correct answer.

Why is 50100\frac{50}{100} Equivalent to 0.5?

50100\frac{50}{100} is equivalent to 0.5 because it can be simplified to 1/2. When we divide 50 by 100, we get 0.5. This is because the numerator (50) is half of the denominator (100), making the fraction equivalent to 1/2.

Real-World Applications

Understanding equivalent fractions is crucial in various real-world applications, such as:

  • Cooking: When a recipe calls for a certain amount of an ingredient, equivalent fractions can help you scale up or down the recipe.
  • Building: When building a structure, equivalent fractions can help you calculate the amount of materials needed.
  • Finance: When investing in stocks or bonds, equivalent fractions can help you calculate the return on investment.

Conclusion

In conclusion, equivalent fractions are an essential part of mathematics, and understanding them is crucial for solving various mathematical problems. By analyzing the four fractions given in the problem, we determined that 50100\frac{50}{100} is equivalent to 0.5. This fraction simplifies to 1/2, making it the correct answer. We also explored the real-world applications of equivalent fractions and why they are important in various fields.

Final Thoughts

Equivalent fractions are a fundamental concept in mathematics, and understanding them can help you solve various mathematical problems. By applying mathematical concepts and analyzing fractions, we can determine which fractions are equivalent to a given value. Whether you're a student, a professional, or simply someone interested in mathematics, understanding equivalent fractions is essential for success.

References

Glossary

  • Equivalent Fractions: Fractions that have the same value, but their numerators and denominators are different.
  • Numerators: The numbers on top of a fraction.
  • Denominators: The numbers on the bottom of a fraction.
  • Greatest Common Divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.
    Equivalent Fractions Q&A ==========================

Introduction

Equivalent fractions are a fundamental concept in mathematics, and understanding them is crucial for solving various mathematical problems. In this article, we will answer some frequently asked questions about equivalent fractions, providing a deeper understanding of this concept.

Q: What are equivalent fractions?

A: Equivalent fractions are fractions that have the same value, but their numerators and denominators are different. In other words, two fractions are equivalent if they can be simplified to the same value.

Q: How do I determine if two fractions are equivalent?

A: To determine if two fractions are equivalent, you can simplify them by dividing both the numerator and the denominator by their greatest common divisor (GCD). If the simplified fractions are the same, then the original fractions are equivalent.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the largest common factor. Another way is to use the Euclidean algorithm, which is a step-by-step process for finding the GCD.

Q: What are some examples of equivalent fractions?

A: Here are a few examples of equivalent fractions:

  • 12\frac{1}{2} and 24\frac{2}{4} are equivalent because they both simplify to 12\frac{1}{2}.
  • 36\frac{3}{6} and 12\frac{1}{2} are equivalent because they both simplify to 12\frac{1}{2}.
  • 48\frac{4}{8} and 12\frac{1}{2} are equivalent because they both simplify to 12\frac{1}{2}.

Q: Why are equivalent fractions important?

A: Equivalent fractions are important because they allow us to simplify complex fractions and make them easier to work with. They also help us to understand the concept of proportionality, which is essential in many areas of mathematics and science.

Q: How do I use equivalent fractions in real-world applications?

A: Equivalent fractions have many real-world applications, including:

  • Cooking: When a recipe calls for a certain amount of an ingredient, equivalent fractions can help you scale up or down the recipe.
  • Building: When building a structure, equivalent fractions can help you calculate the amount of materials needed.
  • Finance: When investing in stocks or bonds, equivalent fractions can help you calculate the return on investment.

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

A: Here are a few common mistakes to avoid when working with equivalent fractions:

  • Not simplifying fractions: Failing to simplify fractions can lead to incorrect answers.
  • Not finding the GCD: Failing to find the GCD can lead to incorrect answers.
  • Not using equivalent fractions: Failing to use equivalent fractions can make it difficult to solve problems.

Conclusion

In conclusion, equivalent fractions are a fundamental concept in mathematics, and understanding them is crucial for solving various mathematical problems. By answering some frequently asked questions about equivalent fractions, we have provided a deeper understanding of this concept and its importance in real-world applications.

Final Thoughts

Equivalent fractions are a powerful tool for simplifying complex fractions and making them easier to work with. By understanding equivalent fractions, you can solve a wide range of mathematical problems and make informed decisions in various areas of life.

References

Glossary

  • Equivalent Fractions: Fractions that have the same value, but their numerators and denominators are different.
  • Numerators: The numbers on top of a fraction.
  • Denominators: The numbers on the bottom of a fraction.
  • Greatest Common Divisor (GCD): The largest number that divides two or more numbers without leaving a remainder.