Solution ratio: 1 / 2: 1 / 4: X

Solution ratio: 1 / 2: 1 / 4: X

1 / 2:1 / 5 = 1 / 4: X
1 / 2 × x = 1 / 4 × 1 / 5
1 / 2 × x = 1 / 20
X = 1 / 20 ／ 1 / 2
X = 1 / 10

What's the basis for solving the scale? The following scale X / 4 equals 6 / 5, X ratio 2 / 1 equals 3 / 2 ratio 4

Basis:
a:x=y:b
AB = XY (the product of two external terms ab of proportion = the product of two internal terms XY)
Here's the solution:
x/4=6/5
5x=4x6
5x=24
x=24/5
x:(2/1)=(3/2):4
4x=(2/1) x (3/2)
4x=3
x=3/4

0.5:3 / 4 = 6: X

5 (external): 3 / 4 (internal) = 6 (internal): X (external) internal × internal = external × external 0.5x = 3 / 4 × 60.5x = 9 / 2 x = 9 / 2