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Which fraction is equivalent to [tex]$48 \%$[/tex]?

A. [tex]$\frac{4}{5}$[/tex]
B. [tex]$\frac{4}{8}$[/tex]
C. [tex]$\frac{12}{25}$[/tex]
D. [tex]$\frac{8}{25}$[/tex]

Answer :

To find which fraction is equivalent to 48%, we first need to convert 48% into a fraction. Here's how we can do it step by step:

1. Understand the percentage: The percentage 48% means 48 out of 100. This can initially be written as the fraction [tex]\(\frac{48}{100}\)[/tex].

2. Simplify the fraction: To simplify [tex]\(\frac{48}{100}\)[/tex], we need to find the greatest common divisor (GCD) of 48 and 100.

3. Find the GCD of 48 and 100: The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. The greatest common factor they share is 4.

4. Divide both the numerator and denominator by the GCD:
- Divide 48 by 4, which equals 12.
- Divide 100 by 4, which equals 25.

So, [tex]\(\frac{48}{100}\)[/tex] simplifies to [tex]\(\frac{12}{25}\)[/tex].

5. Compare with the options: Now we compare [tex]\(\frac{12}{25}\)[/tex] to the given options:
- A. [tex]\(\frac{4}{5}\)[/tex]
- B. [tex]\(\frac{4}{8}\)[/tex]
- C. [tex]\(\frac{12}{25}\)[/tex]
- D. [tex]\(\frac{8}{25}\)[/tex]

The fraction [tex]\(\frac{12}{25}\)[/tex] matches option C.

Therefore, the fraction equivalent to 48% is [tex]\(\frac{12}{25}\)[/tex], which corresponds to option C.

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