To determine which ratios are equivalent to [tex]\(8:20\)[/tex], we need to compare each given ratio to the simplified form of [tex]\(8:20\)[/tex].
First, simplify the ratio [tex]\( 8:20 \)[/tex]:
[tex]\[ \frac{8}{20} = \frac{8 \div 4}{20 \div 4} = \frac{2}{5} \][/tex]
Now, let's compare each given ratio to [tex]\(\frac{2}{5}\)[/tex].
1. A [tex]\(1:4\)[/tex]
[tex]\[ \frac{1}{4} \][/tex]
[tex]\[\frac{1}{4} \neq \frac{2}{5}\][/tex]
2. B [tex]\(4:10\)[/tex]
[tex]\[ \frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \][/tex]
[tex]\[\frac{4}{10} = \frac{2}{5}\][/tex]
This ratio is equivalent.
3. C [tex]\(24:60\)[/tex]
[tex]\[ \frac{24}{60} = \frac{24 \div 12}{60 \div 12} = \frac{2}{5} \][/tex]
[tex]\[\frac{24}{60} = \frac{2}{5}\][/tex]
This ratio is equivalent.
4. D [tex]\(2:5\)[/tex]
[tex]\[ \frac{2}{5} \][/tex]
[tex]\[\frac{2}{5} = \frac{2}{5}\][/tex]
This ratio is equivalent.
5. E [tex]\(10:24\)[/tex]
[tex]\[ \frac{10}{24} = \frac{10 \div 2.4}{24 \div 2.4} = \frac{5}{12} \][/tex]
[tex]\[\frac{10}{24} \neq \frac{2}{5}\][/tex]
From these comparisons, the three ratios that are equivalent to [tex]\(8:20\)[/tex] are:
B [tex]\(4:10\)[/tex]
C [tex]\(24:60\)[/tex]
D [tex]\(2:5\)[/tex]
