Let's solve the problem step-by-step to complete the table by finding the missing equivalent forms for each row.
Step 1: Interpreting the given values.
- For the first row, the unit fraction is [tex]\( \frac{1}{10} \)[/tex], and its equivalent fraction with a denominator of 100 is [tex]\( \frac{10}{100} \)[/tex]. We need to find the equivalent percentage [tex]\( a \)[/tex].
- For the second row, the unit fraction is [tex]\( \frac{1}{4} \)[/tex], and its equivalent percentage is given as [tex]\( 25\% \)[/tex]. We need to find the equivalent fraction with a denominator of 100, which is [tex]\( b \)[/tex].
- For the third row, the equivalent fraction with a denominator of 100 is [tex]\( \frac{50}{100} \)[/tex], and the equivalent percentage is [tex]\( 50\% \)[/tex]. We need to find the unit fraction [tex]\( c \)[/tex].
Step 2: Converting the unit fraction to a percentage.
- First Row ([tex]\( \frac{1}{10} \)[/tex]):
- To convert a fraction to a percentage, multiply it by 100.
- [tex]\( a = \frac{1}{10} \times 100 = 10 \% \)[/tex].
- So, [tex]\( a = 10 \% \)[/tex].
- Second Row ([tex]\( \frac{1}{4} \)[/tex]):
- The percentage given is 25\%.
- To convert the percentage to a fraction with a denominator of 100, divide by 100.
- [tex]\( \frac{25}{100} = b \)[/tex].
- So, [tex]\( b = \frac{25}{100} \)[/tex].
- Third Row ([tex]\( \frac{50}{100} \)[/tex]):
- The fraction given is [tex]\( \frac{50}{100} \)[/tex], which simplifies as [tex]\( \frac{1}{2} \)[/tex].
- So, [tex]\( c = \frac{1}{2} \)[/tex].
Step 3: Summarizing the values.
- [tex]\( a = 10\% \)[/tex]
- [tex]\( b = \frac{25}{100} \)[/tex]
- [tex]\( c = \frac{1}{2} \)[/tex]
So the complete table with missing equivalent forms is:
\begin{tabular}{|c|c|c|}
\hline \begin{tabular}{c}
Unit \\
Fraction
\end{tabular} & \begin{tabular}{c}
Fraction with \\
100 in the \\
Denominator
\end{tabular} & Percent \\
\hline[tex]$\frac{1}{10}$[/tex] & [tex]$\frac{10}{100}$[/tex] & [tex]$10\%$[/tex] \\
\hline[tex]$\frac{1}{4}$[/tex] & [tex]$\frac{25}{100}$[/tex] & [tex]$25\%$[/tex] \\
\hline[tex]$\frac{1}{2}$[/tex] & [tex]$\frac{50}{100}$[/tex] & [tex]$50\%$[/tex] \\
\hline
\end{tabular}
And therefore:
[tex]\[ a = 10 \][/tex]
[tex]\[ b = \frac{25}{100} \][/tex]
[tex]\[ c = \frac{1}{2} \][/tex]
