Ratio, Proportion and Variation

Ratio of a, b = a: b = l*a: l*b = k*a: k*b = a*a: a*b = a/x: b/x = a/s: b/s….

(a/b)*(c/d)*(e/f) = k/l is the compounded ratio of a/b, c/d, e/f.

a/b = c/d = ( c + a*m )/( d + b*m ).

For k>0 and a/b>1, ( a + k )/( b + k ) < a/b, and ( a - k )/( b - k ) > a/b.

For k>0 and a/b<1, ( a + k )/( b + k ) > a/b, and ( a - k )/( b - k ) < a/b.

a/b = c/d => ( a + b )/b = ( c + d )/d, and, ( a – b )/b = ( c – d )/d.

Thus, we have a/b = c/d => ( a + b )/( a – b ) = ( c + d )/( c – d ).