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RATIO AND SCALE IN MATH
Using Scale and Ratio
To begin with lets consider the scale 1 : 500
What does this actually mean ?
It means that 1cm on the drawing actually represents 500cms in actual length
In ratio format this will be written as;
D : AL
1 : 500
This can also be written as 1cm : 5m (WHY?)
There are 100cm in 1m
Therefore if we divide the 500cms by 100 we end up with 5m
Next if we consider the scale 5cm : 1km
The " : " means "is to"
Now we will change the km to cm
1km = 1000m = 100 000cm
There is 1000m in a km and to change the m to cm we multiply by 100
So 5cm : 1km can also be written as 5cm : 100 000cm (can be simplified)
To simplify we divide by 5 which equals 1cm : 20 000cm
Therefore 5cm : 1km is equivalent to 1cm : 20 000cm
They are equivalent scales.
( i ) The distance between two towns measures 6cm on a map. What is the true distance if the scale is 1 : 50 000
The True Distance = 6cm x 50 000
= 300 000cm
We can simplify this by dividing the 300 000 by 100 which gives us 3000m
and by further dividing the 3000m by 1000 we can simplify this to 3km
Therefore the True Distance betweeen the two towns is 3km.
( ii ) This next example is the opposite working of the above, this time we are looking the Measurement on the map as we have been given the True Distance.
The drawing of an Aircraft uses a scale of 1 : 900
If the Aircraft wingspan is 30m what length on the drawing actually represents this?
Drawing Length = 30m ÷ 900
= 0.033 m ( to change 0.033 to mm X 1000)
Therefore the length on the drawing that represents the wingspan is 33mm.
The next example shows how to work out a Scale:-
( iii ) The plans of a house show a room to be 4.0m X 3.6m. The dimensions of the room on the plans measure 20mm X 18mm.
What was the scale used?
True Lengths = 4.0m X 3.6m
Drawing Lengths = 20mm X 18mm
To find out the scale we will use the first part of each of the above;
DL : TL
20mm : 4.0m ( x by 1000 to change to mm)
20mm : 4000mm
As you can see both parts of the equation are now in mm, so how can we break this down and simplify it.
Well we can divide both sides by 20.
DL : TL
20mm : 4000mm ( ÷ by 20 )
= 1mm : 200mm
So the Scale used was 1 : 200