# 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

A/B = 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.

^{ 3}/_{4}= ^{x}/_{20}

^{3x20}/_{4} = x

x = 15

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

^{1}/_{3} = ^{x}/_{18}

^{18}/_{3 }= x

x = 6

**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:**