Solving proportions by means of cross-multiplication relies on equating the products of the means and the extremes of the proportions to solve for an unknown component. The means are the denominator of the first ratio and the numerator of the second while the extremes are the numerator of the first ratio and the denominator of the second. An example from the proportion a/b=x/y would be a*y=b*x after cross multiplying.
Illustration
For 6/10=x/5
6*5=x*10
30=10x
Therefore
X = 3
Vertical relations help to solve unknowns by determining the numerical relationship between the numerator and denominator of one ratio and equating it to the numerical relationship of the other. For proportions, both ratios have the same value for the relationship, which you may use to solve for the unknown variable.
Example:
6/10=x/5
Divide the numerator of the first fraction by its denominator: 6/10=0.6, then equate the answer obtained to x/5: x/5 = 0.6 which is
simplified to x = 3.
Use horizontal relations to derive the unknown in a proportion by equating the numerical relation between the numerators of both ratios to the relation of the denominators. The two numerators or denominators are related by either multiplying or dividing one of
each with a number to obtain the other. Multiply or divide the respective number by the same relationship established to obtain the unknown in the proportion.
Illustration
6/10=x/5
From the denominators; 10/2 = 5. Therefore, dividing by 2 is the relationship between the two denominators. For the numerator therefore, 6/2 = 3. From this, you find that x=3
You may also choose to solve for proportions using online applications such as Algebra.help. Such sites provide proportion calculators to solve for unknowns. You need to analyze the problem at hand, determine the missing variable and feed it into the calculator to obtain its value.