Which Number Is Closer To $\frac{1}{2}$?A. $\frac{2}{2}$ B. $\frac{3}{4}$

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Introduction

When comparing two fractions, it's essential to understand how to determine which one is closer to a given value. In this case, we're comparing the fractions 22\frac{2}{2} and 34\frac{3}{4} to determine which one is closer to 12\frac{1}{2}. To do this, we need to understand the concept of equivalent fractions and how to compare them.

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but may have different numerators and denominators. For example, the fractions 12\frac{1}{2} and 24\frac{2}{4} are equivalent because they both represent the same value. To determine if two fractions are equivalent, we can multiply or divide both the numerator and denominator by the same number.

Comparing Fractions

To compare two fractions, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. Once we have a common denominator, we can compare the fractions by comparing the numerators.

Finding the Common Denominator

To find the common denominator of 22\frac{2}{2} and 34\frac{3}{4}, we need to find the LCM of 2 and 4. The LCM of 2 and 4 is 4. Therefore, the common denominator is 4.

Converting Fractions to Have a Common Denominator

To convert 22\frac{2}{2} to have a denominator of 4, we can multiply both the numerator and denominator by 2. This gives us 44\frac{4}{4}. To convert 34\frac{3}{4} to have a denominator of 4, we don't need to do anything because it already has a denominator of 4.

Comparing the Fractions

Now that we have both fractions with a common denominator of 4, we can compare them. The fraction 44\frac{4}{4} is equal to 1, and the fraction 34\frac{3}{4} is equal to 0.75. Since 0.75 is closer to 0.5 than 1 is, the fraction 34\frac{3}{4} is closer to 12\frac{1}{2}.

Conclusion

In conclusion, to determine which number is closer to 12\frac{1}{2}, we need to compare the fractions 22\frac{2}{2} and 34\frac{3}{4}. By finding the common denominator and converting both fractions to have the same denominator, we can compare them and determine that 34\frac{3}{4} is closer to 12\frac{1}{2}.

Why is 34\frac{3}{4} Closer to 12\frac{1}{2}?

34\frac{3}{4} is closer to 12\frac{1}{2} because it has a smaller difference between the two fractions. The difference between 34\frac{3}{4} and 12\frac{1}{2} is 0.125, while the difference between 22\frac{2}{2} and 12\frac{1}{2} is 0.5. Therefore, 34\frac{3}{4} is closer to 12\frac{1}{2}.

What is the Significance of Comparing Fractions?

Comparing fractions is an essential skill in mathematics, particularly in algebra and geometry. It allows us to determine which fractions are equivalent, which ones are greater than or less than each other, and which ones are closer to a given value. This skill is also important in real-world applications, such as finance, engineering, and science.

How to Compare Fractions in Real-World Applications

Comparing fractions is an essential skill in many real-world applications. For example, in finance, comparing fractions can help us determine which investment is more profitable. In engineering, comparing fractions can help us determine which design is more efficient. In science, comparing fractions can help us determine which experiment is more accurate.

Conclusion

In conclusion, comparing fractions is an essential skill in mathematics and real-world applications. By understanding how to compare fractions, we can determine which ones are equivalent, which ones are greater than or less than each other, and which ones are closer to a given value. This skill is also important in real-world applications, such as finance, engineering, and science.

Final Thoughts

Comparing fractions is a fundamental concept in mathematics that has many real-world applications. By understanding how to compare fractions, we can make informed decisions in finance, engineering, and science. Therefore, it's essential to practice comparing fractions to develop this skill.

References

Keywords

  • Comparing fractions
  • Equivalent fractions
  • Common denominator
  • Least common multiple (LCM)
  • Real-world applications
  • Finance
  • Engineering
  • Science

Introduction

Comparing fractions is a fundamental concept in mathematics that has many real-world applications. However, it can be a challenging topic for many students and professionals. In this article, we will answer some frequently asked questions (FAQs) about comparing fractions to help you better understand this concept.

Q: What is the difference between comparing fractions and equivalent fractions?

A: Comparing fractions refers to determining which fraction is greater than or less than another fraction. Equivalent fractions, on the other hand, are fractions that have the same value but may have different numerators and denominators.

Q: How do I compare two fractions with different denominators?

A: To compare two fractions with different denominators, you need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. Once you have a common denominator, you can compare the fractions by comparing the numerators.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 2 and 4 is 4, because 4 is the smallest number that is a multiple of both 2 and 4.

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

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the formula: LCM(a, b) = (a Γ— b) / GCD(a, b), where GCD is the greatest common divisor.

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 compare fractions with decimals?

A: To compare fractions with decimals, you can convert the fractions to decimals by dividing the numerator by the denominator. For example, the fraction 3/4 can be converted to a decimal by dividing 3 by 4, which equals 0.75.

Q: What is the significance of comparing fractions in real-world applications?

A: Comparing fractions is an essential skill in many real-world applications, such as finance, engineering, and science. It allows us to determine which investments are more profitable, which designs are more efficient, and which experiments are more accurate.

Q: How do I apply comparing fractions in finance?

A: Comparing fractions can be applied in finance by determining which investment is more profitable. For example, if you have two investment options with different interest rates, you can compare the fractions to determine which one is more profitable.

Q: How do I apply comparing fractions in engineering?

A: Comparing fractions can be applied in engineering by determining which design is more efficient. For example, if you have two design options with different dimensions, you can compare the fractions to determine which one is more efficient.

Q: How do I apply comparing fractions in science?

A: Comparing fractions can be applied in science by determining which experiment is more accurate. For example, if you have two experimental results with different measurements, you can compare the fractions to determine which one is more accurate.

Conclusion

Comparing fractions is a fundamental concept in mathematics that has many real-world applications. By understanding how to compare fractions, we can make informed decisions in finance, engineering, and science. We hope that this article has helped you better understand the concept of comparing fractions and how to apply it in real-world applications.

References

Keywords

  • Comparing fractions
  • Equivalent fractions
  • Common denominator
  • Least common multiple (LCM)
  • Greatest common divisor (GCD)
  • Real-world applications
  • Finance
  • Engineering
  • Science