Ratio and Proportion

A ratio is the relationship between one amount and another. Ratios occur whenever comparisons are being made. The ratio of a to b can be written a : b or as the fraction a/b. Ratios are usually reduced to lowest terms for simplicity. This can be done by dividing both terms by the greatest common factor. 

Example: 

Reduce the ratio 28:12 to lowest terms.

Solution:

In this case, the greatest common factor (the largest number both terms can be evenly divided by) is 4. 

28/4  :  12/4

        7 : 3

Example:

Determine the ratio of hydrogen to nitrogen in ammonia provided that when you have 18 hydrogen atoms you have 6 nitrogen atoms.

Solution:

If ammonia has 18 hydrogen atoms and 6 nitrogen atoms, then the ratio is 18:6. In simplest form, the ratio of hydrogen to nitrogen is 3:1.

SOLVING FOR AN UNKNOWN QUANTITY

When two ratios are set equal to each other, the resulting equation is called a proportion. If the ratio

A : B and the ration C : D are proportionate to one another they can be rewritten as the equation

\( \frac{A}{B}  =  \frac{C}{D}\)

An unknown variable in a proportion can be solved for using basic algebra.

Example: 

If 4 : 3 is proportionate to 20 : x, solve for x.

\( \begin{array}{c} \frac{3}{4} &=& \frac{x}{20} \\ \frac{3\cdot20}{4} &=& x \\ x &=& 15 \end{array} \)

 In chemical reactions, the amount of products produced is proportionate to the amount of reactants used.

Example: 

Given that 3 moles of carbon dioxide are produced for every mole of propane burned, determine the number of moles of propane required to produce 18 moles of carbon dioxide.

Solution:

\(1:3\) and \(x:18\)

\( \begin{array}{c} \frac{1}{3}&=&\frac{x}{18} \\ \frac{18}{3}&=&x \\ x&=&6 \end{array} \)

 

Ratio and Proportion Example 1:

Ratio and Proportion Example 2 - Similar Triangle:

Ratio and Proportion Example 3 - Concentration:

Ratio and Proportion Example 4 - Chemical Reaction: