Answer :
To determine which choices are equivalent to the fraction [tex]\(\frac{24}{30}\)[/tex], we can simplify the fraction and convert it to different representations such as percentages and decimals. Let's go through the choices one by one:
1. Simplify the Fraction:
[tex]\[
\frac{24}{30} \quad \text{can be simplified to} \quad \frac{4}{5}
\][/tex]
We divide both the numerator and the denominator by their greatest common divisor, which is 6.
2. Checking Each Choice:
- A. [tex]\(\frac{8}{10}\)[/tex]:
Let's simplify [tex]\(\frac{8}{10}\)[/tex]:
[tex]\[
\frac{8}{10} = \frac{4}{5}
\][/tex]
This is equivalent to the simplified form of [tex]\(\frac{24}{30}\)[/tex].
- B. [tex]\(60\%\)[/tex]:
Convert [tex]\(\frac{24}{30}\)[/tex] to a percentage:
[tex]\[
\frac{24}{30} = \frac{80}{100} = 80\%
\][/tex]
So, [tex]\(60\%\)[/tex] is not equivalent.
- C. [tex]\(80\%\)[/tex]:
As calculated above, [tex]\(\frac{24}{30} = 80\%\)[/tex].
- D. [tex]\(0.24\)[/tex]:
Convert [tex]\(\frac{24}{30}\)[/tex] to a decimal:
[tex]\[
\frac{24}{30} = 0.8
\][/tex]
So, [tex]\(0.24\)[/tex] is not equivalent.
- E. [tex]\(\frac{10}{8}\)[/tex]:
Let's simplify [tex]\(\frac{10}{8}\)[/tex]:
[tex]\[
\frac{10}{8} = \frac{5}{4}
\][/tex]
This is not equivalent to [tex]\(\frac{4}{5}\)[/tex].
- F. [tex]\(0.8\)[/tex]:
As calculated above, [tex]\(\frac{24}{30} = 0.8\)[/tex].
Based on this analysis, the choices equivalent to [tex]\(\frac{24}{30}\)[/tex] are:
- A. [tex]\(\frac{8}{10}\)[/tex]
- C. [tex]\(80\%\)[/tex]
- F. [tex]\(0.8\)[/tex]
1. Simplify the Fraction:
[tex]\[
\frac{24}{30} \quad \text{can be simplified to} \quad \frac{4}{5}
\][/tex]
We divide both the numerator and the denominator by their greatest common divisor, which is 6.
2. Checking Each Choice:
- A. [tex]\(\frac{8}{10}\)[/tex]:
Let's simplify [tex]\(\frac{8}{10}\)[/tex]:
[tex]\[
\frac{8}{10} = \frac{4}{5}
\][/tex]
This is equivalent to the simplified form of [tex]\(\frac{24}{30}\)[/tex].
- B. [tex]\(60\%\)[/tex]:
Convert [tex]\(\frac{24}{30}\)[/tex] to a percentage:
[tex]\[
\frac{24}{30} = \frac{80}{100} = 80\%
\][/tex]
So, [tex]\(60\%\)[/tex] is not equivalent.
- C. [tex]\(80\%\)[/tex]:
As calculated above, [tex]\(\frac{24}{30} = 80\%\)[/tex].
- D. [tex]\(0.24\)[/tex]:
Convert [tex]\(\frac{24}{30}\)[/tex] to a decimal:
[tex]\[
\frac{24}{30} = 0.8
\][/tex]
So, [tex]\(0.24\)[/tex] is not equivalent.
- E. [tex]\(\frac{10}{8}\)[/tex]:
Let's simplify [tex]\(\frac{10}{8}\)[/tex]:
[tex]\[
\frac{10}{8} = \frac{5}{4}
\][/tex]
This is not equivalent to [tex]\(\frac{4}{5}\)[/tex].
- F. [tex]\(0.8\)[/tex]:
As calculated above, [tex]\(\frac{24}{30} = 0.8\)[/tex].
Based on this analysis, the choices equivalent to [tex]\(\frac{24}{30}\)[/tex] are:
- A. [tex]\(\frac{8}{10}\)[/tex]
- C. [tex]\(80\%\)[/tex]
- F. [tex]\(0.8\)[/tex]
