College

A nutrition label states the item contains [tex]$48\%$[/tex] of the daily recommended amount of Vitamin B12. Rewrite this percent as a fraction in simplest form.

A. [tex]\frac{7}{20}[/tex]
B. [tex]\frac{12}{25}[/tex]
C. [tex]\frac{6}{13}[/tex]
D. [tex]\frac{10}{25}[/tex]

Answer :

To rewrite 48% as a fraction in simplest form, let's break it down step-by-step:

1. Understand the percent: The given percentage is 48%, which means 48 out of 100.

2. Convert the percent to a fraction: You can express 48% as a fraction by writing it over 100. So, 48% becomes [tex]\(\frac{48}{100}\)[/tex]. This fraction means "48 parts out of 100 parts."

3. Simplify the fraction: To simplify [tex]\(\frac{48}{100}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 48 and 100 is 4.

4. Divide both the numerator and the denominator by the GCD:

[tex]\[
\frac{48 \div 4}{100 \div 4} = \frac{12}{25}
\][/tex]

5. Final simplified fraction: So, 48% is equivalent to [tex]\(\frac{12}{25}\)[/tex] in simplest form.

Now, look at the answer choices provided:

- [tex]\(\frac{7}{20}\)[/tex]
- [tex]\(\frac{12}{25}\)[/tex]
- [tex]\(\frac{6}{13}\)[/tex]
- [tex]\(\frac{10}{25}\)[/tex]

The fraction [tex]\(\frac{12}{25}\)[/tex] matches the simplified form of 48%. Therefore, the correct answer is [tex]\(\frac{12}{25}\)[/tex].