Which Of The Following Has The Lowest Value?A. \[$\frac{2}{13}\$\] B. \[$\frac{1}{8}\$\] C. \[$\frac{4}{30}\$\] D. \[$\frac{3}{25}\$\]

Feb 25, 2025 by ADMIN 140 views

Comparing Fractions: Which One Has the Lowest Value?

When comparing fractions, it's essential to understand that the value of a fraction is determined by the ratio of its numerator to its denominator. In this article, we will compare four fractions: $\frac{2}{13}$ , $\frac{1}{8}$ , $\frac{4}{30}$ , and $\frac{3}{25}$ . Our goal is to determine which of these fractions has the lowest value.

Understanding Fraction Values

To compare fractions, we need to understand that a fraction with a smaller numerator and a larger denominator has a lower value. Conversely, a fraction with a larger numerator and a smaller denominator has a higher value. This is because the numerator represents the number of equal parts we have, while the denominator represents the total number of parts.

Comparing the Fractions

Let's compare the fractions one by one:

A. $\frac{2}{13}$

$A. $\frac{2}{13}$$

The numerator of this fraction is 2, and the denominator is 13. This fraction represents 2 equal parts out of a total of 13 parts.

B. $\frac{1}{8}$

The numerator of this fraction is 1, and the denominator is 8. This fraction represents 1 equal part out of a total of 8 parts.

C. $\frac{4}{30}$

The numerator of this fraction is 4, and the denominator is 30. This fraction represents 4 equal parts out of a total of 30 parts.

D. $\frac{3}{25}$

The numerator of this fraction is 3, and the denominator is 25. This fraction represents 3 equal parts out of a total of 25 parts.

Simplifying the Fractions

To make it easier to compare the fractions, let's simplify them by dividing both the numerator and the denominator by their greatest common divisor (GCD).

A. $\frac{2}{13}$

The GCD of 2 and 13 is 1, so this fraction cannot be simplified further.

B. $\frac{1}{8}$

The GCD of 1 and 8 is 1, so this fraction cannot be simplified further.

C. $\frac{4}{30}$

The GCD of 4 and 30 is 2, so we can simplify this fraction by dividing both the numerator and the denominator by 2:

$\frac{4}{30} = \frac{2}{15}$

D. $\frac{3}{25}$

The GCD of 3 and 25 is 1, so this fraction cannot be simplified further.

Comparing the Simplified Fractions

Now that we have simplified the fractions, let's compare them:

A. $\frac{2}{13}$

B. $\frac{1}{8}$

C. $\frac{2}{15}$

D. $\frac{3}{25}$

To compare these fractions, we can convert them to equivalent decimals:

A. $\frac{2}{13} \approx 0.1538$

B. $\frac{1}{8} = 0.125$

C. $\frac{2}{15} \approx 0.1333$

D. $\frac{3}{25} = 0.12$

Conclusion

Based on our comparison, we can see that $\frac{3}{25}$ has the lowest value, followed by $\frac{2}{15}$ , $\frac{1}{8}$ , and finally $\frac{2}{13}$ . Therefore, the correct answer is:

The final answer is D. $\frac{3}{25}$ .

Additional Tips

When comparing fractions, it's essential to simplify them by dividing both the numerator and the denominator by their greatest common divisor (GCD). This will make it easier to compare the fractions and determine which one has the lowest value. Additionally, converting fractions to equivalent decimals can also help you compare them more easily.
Frequently Asked Questions: Comparing Fractions

In our previous article, we compared four fractions: $\frac{2}{13}$ , $\frac{1}{8}$ , $\frac{4}{30}$ , and $\frac{3}{25}$ . We determined that $\frac{3}{25}$ has the lowest value. In this article, we will answer some frequently asked questions about comparing fractions.

Q: How do I compare fractions with different denominators?

A: To compare fractions with different denominators, you need to find a common denominator. The common denominator is the smallest multiple of both denominators. Once you have the common denominator, you can convert both fractions to have the same denominator.

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

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction. To find the GCD, you can use the Euclidean algorithm or list the factors of both numbers.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). This will reduce the fraction to its simplest form.

Q: Can I compare fractions with different signs?

A: Yes, you can compare fractions with different signs. However, you need to consider the sign of the fraction when comparing them. For example, if you have two fractions with opposite signs, the fraction with the positive sign will be greater than the fraction with the negative sign.

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

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator. This will give you the decimal equivalent of the fraction.

Q: Can I compare fractions with different units?

A: No, you cannot compare fractions with different units. Fractions are used to compare quantities with the same unit. If you have fractions with different units, you need to convert them to the same unit before comparing them.

Q: How do I compare mixed numbers?

A: To compare mixed numbers, you need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator. Once you have the improper fractions, you can compare them using the same methods as comparing fractions.

Q: Can I compare fractions with different exponents?

A: No, you cannot compare fractions with different exponents. Fractions are used to compare quantities with the same exponent. If you have fractions with different exponents, you need to convert them to the same exponent before comparing them.

Q: How do I compare fractions with negative exponents?

A: To compare fractions with negative exponents, you need to convert them to positive exponents. A negative exponent is equivalent to taking the reciprocal of the fraction.

Q: Can I compare fractions with complex numbers?

A: No, you cannot compare fractions with complex numbers. Fractions are used to compare real numbers. If you have fractions with complex numbers, you need to convert them to real numbers before comparing them.

Conclusion

Comparing fractions can be a challenging task, but with the right techniques and strategies, you can easily compare them. Remember to simplify fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD), and convert fractions to equivalent decimals to make comparison easier. Additionally, be aware of the different types of fractions, such as mixed numbers and improper fractions, and how to compare them. By following these tips and techniques, you will become a pro at comparing fractions in no time.

Additional Resources

If you want to learn more about comparing fractions, here are some additional resources:

Khan Academy: Comparing Fractions
Mathway: Comparing Fractions
Wolfram Alpha: Comparing Fractions

These resources will provide you with more information and practice exercises to help you master the art of comparing fractions.

A. 213\frac{2}{13}132​

B. 18\frac{1}{8}81​

C. 430\frac{4}{30}304​

D. 325\frac{3}{25}253​

A. 213\frac{2}{13}132​

B. 18\frac{1}{8}81​

C. 430\frac{4}{30}304​

D. 325\frac{3}{25}253​

A. 213\frac{2}{13}132​

B. 18\frac{1}{8}81​

C. 215\frac{2}{15}152​

D. 325\frac{3}{25}253​

A. 213≈0.1538\frac{2}{13} \approx 0.1538132​≈0.1538

B. 18=0.125\frac{1}{8} = 0.12581​=0.125

C. 215≈0.1333\frac{2}{15} \approx 0.1333152​≈0.1333

D. 325=0.12\frac{3}{25} = 0.12253​=0.12

A. $\frac{2}{13}$

B. $\frac{1}{8}$

C. $\frac{4}{30}$

D. $\frac{3}{25}$

A. $\frac{2}{13}$

B. $\frac{1}{8}$

C. $\frac{4}{30}$

D. $\frac{3}{25}$

A. $\frac{2}{13}$

B. $\frac{1}{8}$

C. $\frac{2}{15}$

D. $\frac{3}{25}$

A. $\frac{2}{13} \approx 0.1538$

B. $\frac{1}{8} = 0.125$

C. $\frac{2}{15} \approx 0.1333$

D. $\frac{3}{25} = 0.12$