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