# Explain the difference between a ratio and a proportion

## Question:

Explain the difference between a ratio and a proportion

## Ratios and Proportions:

Ratios and Proportions are useful in many ways. Simply figuring out how much salt to add to a dish when the recipe was halved is an exercise in using ratios and proportions. Converting the units of measurement from miles to kilometers or euros to dollars are also opportunities to use ratio and proportion.

The biggest difference between ratio and proportion is in what they are used for and how they are written. They are often misused as one for the other. An illustrative example would bring this to light more.

A man wants to know if he has gained weight, when he saw a weighing scale in the gym. He weighed 189 lbs two weeks ago at home and weighed in at the gym at 78 kg. Did he lose weight?

In solving this, the relation of kilogram to pounds is a ratio:

{eq}\dfrac {2.2 lbs}{1 kg} {/eq}

A ratio is a description or mathematical expression of the relationship between quantities.

In converting the kilograms to pounds it is a proportion:

{eq}\begin{align} \dfrac {x lbs}{78 kg} &= \dfrac {2.2 lbs}{1 kg} \\ x &= \dfrac {(2.2 lbs)(78 kg)}{1 kg} \\ x &= 171.6 lbs \end{align} {/eq}

Equating one ratio to another is a proportion. Thus, aproportion is the mathematical equation between two ratios while ratios are mathematical expressions of the relationship between two quantities.