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Here are a few recommended readings before getting started with this lesson.
When modeling a reallife situation, it is sometimes impossible to represent an object or scenario using the original dimensions. In these situations, it is more convenient to work with manageable units while still being able to maintain the same properties as the original. This can be done by making a scale drawing.
A scale drawing is a drawing that is similar to an actual object or place. In a scale drawing, the ratio of any length on the drawing to the actual length is always the same. Possible examples of scale drawing are floor plans, blueprints, and maps.
In the case of the original reallife situation involving a threedimensional object, making a $3D$ model is more useful than a drawing. The idea behind a $3D$ model is the same as a scale drawing, but the model has three dimensions instead of two.
A scale model is a threedimensional model that is similar to a threedimensional object. The ratio of a linear measurement of a model to the corresponding linear measurement of the actual object is always the same. Here is an example scale model of a building.
The scale of a model or drawing is the ratio between any length on the model or drawing and its corresponding length on the actual object or place.
Suppose a drawing has a scale of $1in:100ft.$ This means that $1$ inch on the drawing represents $100$ feet on the actual object. Therefore, a scale can also be expressed using an equals sign. Moreover, a scale can also be written as a fraction, as it is a ratio.
Denoting a Scale  

Ratio  $1in:100ft$ 
Equals Sign  $1in=100ft$ 
Fraction  $100ft1in $ 
When a scale is written without specifying the units, it is understood that both numbers have the same units of measure. For example, a scale of $1:2$ means that the actual object is twice the size of the model. A scale of $1:0.5$ means that the actual object is half the size of the model.
Multiply $1300000000cm$ by $100cm1m ⋅1000m1km $
Cross out common factors
Cancel out common factors
Multiply fractions
Calculate quotient
The United States of America has an area of $9147420$ square kilometers. In mid$2020,$ the total population was $331923317$ people.
In the United States of America, the population density is $94$ people per square mile. The population density measures the number of people per unit of area.
People per square mile can be written as $mi_{2}people .$ This implies that the population density is expressed as a ratio. Remember that $1$ square kilometer is equal to $0.386102$ square mile.
Multiply $9147420km_{2}$ by $1km_{2}0.386102mi_{2} $
Cross out common factors
Multiply fractions
The population density of the United States of America is approximately $94$ $people$ per $square mile.$
This statement assumes that the total population is spread out evenly across the United States.
Mark wants to paint all of the walls of his bedroom except for the wall that contains the door. Each rectangular wall is $2.8$ meters high. The paint he will use is sold in $5$liter cans — the price per liter is $$25.$
After painting for a few minutes, Mark noticed that $5$ square meters can be covered with one liter of paint.
Dimensions  

Wall $1$  $ℓ_{1}h =4.75m=2.8m $

Wall $2$  $ℓ_{2}h =4.75m=2.8m $

Wall $3$  $ℓ_{3}h =3m=2.8m $

$ℓ_{1}=4.75m$, $h=2.8m$
Multiply
On the applet, the model and the actual object are shown. Using the given information, find the scale or the size of either the model or the actual object.
Tadeo wants to buy a cheap phone plan for calling his friends and family. He asked Ali and Ramsha how much they pay per call.
Initially, Tadeo decided to take Ramsha's plan since she paid less. Later, he realized that this information is not helpful since he does not know the duration of each of the calls made by Ali and Ramsha.
Price per call is not an appropriate unit.
Therefore, Tadeo decided to ask Ali and Ramsha how long each phone call lasted.
Person  Scale of the Plan 

Ali  $40min$10 =$0.25$ per minute 
Ramsha  $30min$8 ≈$0.27$ per minute 