Ratio and Proportion

a : b = a/b

6 : 8 = (6 ÷ 2) : (8 ÷ 2) = 3 : 4

3 : 4 = 3/4

If each term of a ratio is multiplied or divided by the same non-zero number, the ratio remains the same.

Share = (part of ratio / total parts) × total quantity

2 : 3 => total parts = 2 + 3 = 5

When four quantities are so related that the ratio between the first and the second quantities is equal to the ratio between the third and the fourth

Product of extremes = Product of means

3 : 4 = 18 : x => 3 × x = 4 × 18

3 : 4 = 18 : x

12 : 30 = 30 : x => 12 × x = 30 × 30

a : b = b : c

b^2 = ac

b = sqrt(ac)

a : b and b : c to a : c = (a/b) × (b/c) = a/c