RATIO AND SCALE IN MATH
73Using 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.
Examples;
( 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 Aircrafts 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)
= 33mm
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.
Therefore;
DL : TL
20mm : 4000mm ( ÷ by 20 )
= 1mm : 200mm
So the Scale used was 1 : 200
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CommentsLoading...
WHAT ?
could you make them a little simpler
thanx very much.but why do you divide both sides by 20
Hi precious,
This is done to simplify the terms as they have to be written in their simplist form.
20mm : 4000mm (well 20 goes into both and takes the ratio down to its simplist form)
Therefore the answer is
1 : 200
Thanks Taylor glad to help
For further help follow the link in the hub "Let me solve your maths problems". Assistance can be found for
Bodmas
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Prime and Composite numbers
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Isnt a scale supposed to be in mm not cm
Alex,
A scale can be given to you in any measurement and it is up to you to convert the measurements to come up with the measurement required for the answer. If it was as you say wouldn't life be a breeze.
ummmmmmmmm it's really help me in my work.
thank you for the defination..
thank you,for the definition and example,that may help for my homework.
Wow, this has really helped me. I have a maths test tomorrow and i know it has some scale questions in it. Thank you so much for these examples, i think i'll do better in the test now because of your help. Thanks heaps :D
this really helped me alot but it could have been slightly more simple but thanks a mil anyway
Hi t.elia,
I'm a parent to twin six graders. I, personally, have been out of school for over twenty-five years. Anyhow, my kids came home with the following math problem, which I had no clue of how to figure it out. Please help!
Challenge Problem: The Port Austin Reef Lighthouse is 60 feet tall. Use the height of the model given to complete the scale. How many times taller than the model is the actual lighthouse?
15. Height: 10 inches 16. height: 6 inches
scale: 20 in.:?ft scale: 2 in.:? ft
Your help means a lot to me and my family, and we thank you in advance for your expertise. God bless
Respectfully,
Mrs. Johnson
Thanks a million this really helped.
Thankkz for ur help im studying 4 an extention maths exam tomorrow and i heard that its really hard :S
on a scale of i/500 what is .7
on a scale of 1/400 waht is .7
Well it could be writen in a simpiler form. I didn't get it that much stupid
oooooooooooooooooooooooooooo
Thanks you so much, it really helped me. Is it really that easy?
Hi I was confused and didn't want to look stupid asking my teacher for help this really made it more clear for me, thank you.
I'm really impressed d way u tackle questn to a rare man's undrstnding. Keep it up
Thanks very much this really makes me understand what i have to do in the test.
dear, can you simply provide me with the length, width and height in cms of scale 1:500?
Taylor 2 years ago
Thanks that really helped me with my homework.