Use diagrams or description of equivalent ratios to show that the ratios 2: 3,4: 6,and 8: 12 are equivalent

Start with ratio 2 : 3

    2    :    3
[2×2] : [3×2]
    4   :    6

The ratio 2 : 3 is equivalent to  4 : 6 because we multiply both '2' and '3' by the same multiplier '2' to get 4 : 6

   4    :   6
[4×2] : [6×2]
   8    :   12

The ratio 4 : 6 is equivalent to 8 : 12 because we multiply both '4' and '6' by the same multiplier '2'

We worked out earlier that 2 : 3 = 4 : 6, and since 4 : 6 =  8 : 12, we can conclude that 2 : 3 = 4 : 6 = 8 : 12