Which Of The Following Values Is The Largest?A. 7 2 \frac{7}{2} 2 7 ​ B. 4 C. 25 10 \frac{25}{10} 10 25 ​ D. 3 1 5 3 \frac{1}{5} 3 5 1 ​

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When comparing fractions and whole numbers, it's essential to understand the concept of equivalent ratios and how to convert between different forms. In this article, we'll explore the given options and determine which value is the largest.

Understanding the Options

We have four options to compare:

A. 72\frac{7}{2} B. 4 C. 2510\frac{25}{10} D. 3153 \frac{1}{5}

To compare these values, we need to convert them to a common form. Let's start by converting the fractions to decimal form.

Converting Fractions to Decimal Form

To convert a fraction to decimal form, we divide the numerator by the denominator.

  • Option A: 72=3.5\frac{7}{2} = 3.5
  • Option C: 2510=2.5\frac{25}{10} = 2.5

Now, let's convert the mixed number to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator.

  • Option D: 315=(3×5)+15=15+15=165=3.23 \frac{1}{5} = \frac{(3 \times 5) + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5} = 3.2

Now that we have all the options in decimal form, let's compare them.

Comparing the Values

We have the following values in decimal form:

  • Option A: 3.5
  • Option B: 4
  • Option C: 2.5
  • Option D: 3.2

To determine which value is the largest, we can see that Option B is the largest whole number. However, we also need to consider the decimal values.

Comparing Decimal Values

When comparing decimal values, we can see that Option A (3.5) is greater than Option D (3.2). However, Option B (4) is greater than both Option A and Option D.

Conclusion

In conclusion, the largest value among the given options is Option B, which is equal to 4.

Key Takeaways

  • When comparing fractions and whole numbers, it's essential to convert them to a common form.
  • Converting fractions to decimal form can help us compare them easily.
  • Mixed numbers can be converted to improper fractions to make comparison easier.
  • When comparing decimal values, we can see which value is greater.

Final Answer

In our previous article, we explored the concept of comparing fractions and whole numbers. We discussed how to convert fractions to decimal form, mixed numbers to improper fractions, and how to compare decimal values. In this article, we'll answer some frequently asked questions related to this topic.

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

A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). For example, 12\frac{1}{2} is a fraction where 1 is the numerator and 2 is the denominator.

A whole number, on the other hand, is a number that is not a fraction. It is a number that is equal to itself, without any remainder. For example, 4 is a whole number.

Q: How do I convert a fraction to decimal form?

To convert a fraction to decimal form, you divide the numerator by the denominator. For example, to convert 12\frac{1}{2} to decimal form, you would divide 1 by 2, which equals 0.5.

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

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. For example, to convert 3123 \frac{1}{2} to an improper fraction, you would multiply 3 by 2 and add 1, which equals 72\frac{7}{2}.

Q: How do I compare fractions and whole numbers?

To compare fractions and whole numbers, you need to convert them to a common form. You can convert fractions to decimal form, and whole numbers can be left as they are. Then, you can compare the decimal values to determine which one is larger.

Q: What is the largest value among the following options: 12\frac{1}{2}, 2, and 34\frac{3}{4}?

To determine the largest value, you need to convert the fractions to decimal form. 12\frac{1}{2} equals 0.5, and 34\frac{3}{4} equals 0.75. Since 2 is greater than both 0.5 and 0.75, the largest value is 2.

Q: How do I determine if a fraction is greater than or less than a whole number?

To determine if a fraction is greater than or less than a whole number, you need to convert the fraction to decimal form. If the decimal value is greater than the whole number, the fraction is greater. If the decimal value is less than the whole number, the fraction is less.

Q: Can you provide an example of a fraction that is greater than a whole number?

Yes, an example of a fraction that is greater than a whole number is 32\frac{3}{2}. When converted to decimal form, it equals 1.5, which is greater than 1.

Q: Can you provide an example of a fraction that is less than a whole number?

Yes, an example of a fraction that is less than a whole number is 12\frac{1}{2}. When converted to decimal form, it equals 0.5, which is less than 1.

Conclusion

In conclusion, comparing fractions and whole numbers requires converting them to a common form. You can convert fractions to decimal form, and whole numbers can be left as they are. Then, you can compare the decimal values to determine which one is larger. We hope this article has provided you with a better understanding of how to compare fractions and whole numbers.