Given:
The given ratio is [tex]16 : 12[/tex]
We need to determine three ratios that are equivalent to the given ratio.
Option A: [tex]8:6[/tex]
The given ratio is [tex]16 : 12[/tex]
Let us divide the given ratio [tex]16 : 12[/tex] by 2.
Thus, we have;
[tex]8:6[/tex]
Hence, the expression [tex]8:6[/tex] is equivalent to [tex]16 : 12[/tex]
Thus, Option A is the correct answer.
Option B: [tex]32:24[/tex]
The number 32 goes by 16 in 2 times and the number 24 goes by 12 in 2 times.
Thus, multiplying the ratio [tex]16 : 12[/tex] by 2, we get;
[tex]32:24[/tex]
Thus, the expression [tex]32:24[/tex] is equivalent to [tex]16 : 12[/tex]
Hence, Option B is the correct answer.
Option C: [tex]4:3[/tex]
Let us divide the given ratio [tex]16 : 12[/tex] by 4.
Thus, we have;
[tex]4:3[/tex]
Thus, the expression [tex]4:3[/tex] is equivalent to [tex]16 : 12[/tex]
Hence, Option C is the correct answer.
Option D: [tex]12:8[/tex]
The number 12 goes by 16 in [tex]\frac{3}{4}[/tex] times and the number 8 goes by 12 in [tex]\frac{2}{3}[/tex] times.
The ratios are multiplied by different numbers.
Thus, the expression [tex]12:8[/tex] is not equivalent to [tex]16 : 12[/tex]
Hence, Option D is not the correct answer.
Option E: [tex]24:16[/tex]
The number 24 goes by 16 in 1.5 times and the number 16 goes by 12 in 0.75 times.
The ratios are multiplied by different numbers.
Thus, the expression [tex]24:16[/tex] is not equivalent to [tex]16 : 12[/tex]
Hence, Option E is not the correct answer.
Therefore, the equivalent ratios are Option A, B and C
