Answer:
Option (3)
Step-by-step explanation:
If the two ratios are equivalent then the value of the ratios will be equal.
[tex]\frac{x_1}{y_1}=\frac{x_2}{y_2}[/tex]
Option (1)
[tex]\frac{11}{12}=\frac{44}{46}[/tex]
Simplified form of the fraction [tex]\frac{44}{46}[/tex] is,
[tex]\frac{44}{46}=\frac{22}{23}\times \frac{2}{2}=\frac{22}{23}[/tex]
Therefore, [tex]\frac{11}{12}=\frac{22}{23}[/tex]
Which is not true,
Therefore, option (1) doesn't show the equivalent ratio.
Option (2)
[tex]\frac{36}{40}=\frac{4}{9}[/tex]
Simplified form of [tex]\frac{36}{40}[/tex] is,
[tex]\frac{36}{40}=\frac{9}{10}\times \frac{4}{4}=\frac{9}{10}[/tex]
Therefore, [tex]\frac{4}{9}= \frac{9}{10}[/tex]
Which is not true.
Therefore, option (2) doesn't show the equivalent ratio.
Option (3)
[tex]\frac{1.5}{3}=\frac{12}{24}[/tex]
Since simplified form of [tex]\frac{1.5}{3}[/tex] is,
[tex]\frac{1.5}{3}=0.5[/tex]
And simplified form of [tex]\frac{12}{24}[/tex] is,
[tex]\frac{12}{24}=0.5[/tex]
Therefore, [tex]\frac{1.5}{3}=\frac{12}{24}=0.5[/tex]
Option (3) shows the equivalent ratios.
Option (4)
[tex]\frac{8}{12}=\frac{4}{24}[/tex]
Since, [tex]\frac{8}{12}=\frac{2}{3}\times \frac{4}{4}=\frac{2}{3}[/tex]
And [tex]\frac{4}{24}=\frac{1}{6}\times \frac{4}{4}=\frac{1}{6}[/tex]
But [tex]\frac{2}{3}\neq \frac{1}{6}[/tex]
Therefore, equation in this option doesn't show the equivalent ratios.
