Answer :
To find which ratio is equivalent to [tex]\(4:5\)[/tex], we must determine if any given fractions simplify to the same value as [tex]\(4:5\)[/tex].
Let's go through each option:
1. Option [tex]\(\frac{10}{15}\)[/tex]:
To check if [tex]\(\frac{10}{15}\)[/tex] is equivalent to [tex]\(4:5\)[/tex], we can simplify [tex]\(\frac{10}{15}\)[/tex].
[tex]\[
\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}
\][/tex]
Since [tex]\(\frac{2}{3}\)[/tex] is not the same as [tex]\(4:5\)[/tex], this ratio is not equivalent.
2. Option [tex]\(\frac{4}{10}\)[/tex]:
Simplify [tex]\(\frac{4}{10}\)[/tex]:
[tex]\[
\frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{5}\)[/tex] is also not equal to [tex]\(4:5\)[/tex], this ratio is not equivalent.
3. Option [tex]\(\frac{18}{20}\)[/tex]:
Simplify [tex]\(\frac{18}{20}\)[/tex]:
[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
Since [tex]\(\frac{9}{10}\)[/tex] does not equal [tex]\(4:5\)[/tex], this ratio is not equivalent.
4. Option [tex]\(\frac{15}{8}\)[/tex]:
Since [tex]\(\frac{15}{8}\)[/tex] is greater than 1 and [tex]\(4:5\)[/tex] is less than 1, they cannot be equivalent. Thus, this ratio is not equivalent.
After evaluating each option, we find that none of the given ratios is equivalent to [tex]\(4:5\)[/tex].
Let's go through each option:
1. Option [tex]\(\frac{10}{15}\)[/tex]:
To check if [tex]\(\frac{10}{15}\)[/tex] is equivalent to [tex]\(4:5\)[/tex], we can simplify [tex]\(\frac{10}{15}\)[/tex].
[tex]\[
\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}
\][/tex]
Since [tex]\(\frac{2}{3}\)[/tex] is not the same as [tex]\(4:5\)[/tex], this ratio is not equivalent.
2. Option [tex]\(\frac{4}{10}\)[/tex]:
Simplify [tex]\(\frac{4}{10}\)[/tex]:
[tex]\[
\frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\][/tex]
Since [tex]\(\frac{2}{5}\)[/tex] is also not equal to [tex]\(4:5\)[/tex], this ratio is not equivalent.
3. Option [tex]\(\frac{18}{20}\)[/tex]:
Simplify [tex]\(\frac{18}{20}\)[/tex]:
[tex]\[
\frac{18}{20} = \frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
Since [tex]\(\frac{9}{10}\)[/tex] does not equal [tex]\(4:5\)[/tex], this ratio is not equivalent.
4. Option [tex]\(\frac{15}{8}\)[/tex]:
Since [tex]\(\frac{15}{8}\)[/tex] is greater than 1 and [tex]\(4:5\)[/tex] is less than 1, they cannot be equivalent. Thus, this ratio is not equivalent.
After evaluating each option, we find that none of the given ratios is equivalent to [tex]\(4:5\)[/tex].
