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RATIO AND SCALE IN MATH

Updated on October 4, 2010

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.

 

 

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 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)

= 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

Comments

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    • profile image

      viswa 

      4 years ago

      Isn't a scale supposed to be in mm not in cm

    • profile image

      Alex su 

      4 years ago

      what is a scale for math?

    • t.elia profile imageAUTHOR

      t.elia 

      5 years ago from Northern Ireland

    • profile image

      danay 

      5 years ago

      thank you so much

    • profile image

      lol 33 

      6 years ago

      Thanks very much this really makes me understand what i have to do in the test.

    • profile image

      okoli gabriel 

      6 years ago

      I'm really impressed d way u tackle questn to a rare man's undrstnding. Keep it up

    • profile image

      Meghan 

      6 years ago

      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.

    • profile image

      Nadia 

      6 years ago

      Thanks you so much, it really helped me. Is it really that easy?

    • profile image

      ME 

      6 years ago

      oooooooooooooooooooooooooooo

    • profile image

      ME 

      6 years ago

      Well it could be writen in a simpiler form. I didn't get it that much stupid

    • profile image

      horst 

      6 years ago

      on a scale of i/500 what is .7

      on a scale of 1/400 what is .7

    • profile image

      Meeeeeeeee 

      6 years ago

      Thankkz for ur help im studying 4 an extention maths exam tomorrow and i heard that its really hard :S

    • profile image

      cookie 

      6 years ago

      Thanks a million this really helped.

    • profile image

      Juanita Johnson 

      7 years ago

      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

    • profile image

      zara 

      7 years ago

      this really helped me a lot but it could have been slightly more simple but thanks a mil anyway

    • profile image

      Sassafrass 

      7 years ago

      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

    • profile image

      edd 

      7 years ago

      thank you,for the definition and example,that may help for my homework.

    • profile image

      edd 

      7 years ago

      thank you for the defination..

    • profile image

      nbay 

      7 years ago

      ummmmmmmmm it's really help me in my work.

    • t.elia profile imageAUTHOR

      t.elia 

      7 years ago from Northern Ireland

      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.

    • profile image

      Alex 

      7 years ago

      Isn't a scale supposed to be in mm not cm

    • t.elia profile imageAUTHOR

      t.elia 

      8 years ago from Northern Ireland

      For further help follow the link in the hub "Let me solve your maths problems". Assistance can be found for

      Bodmas

      HCF

      LCM

      Prime and Composite numbers

      Square Root

      Cube Root

      Place Values

      Expanded Notation

      Rounding off Numbers

      Writing numbers as a product of their Prime Numbers

    • t.elia profile imageAUTHOR

      t.elia 

      8 years ago from Northern Ireland

      Thanks Taylor glad to help

    • t.elia profile imageAUTHOR

      t.elia 

      8 years ago from Northern Ireland

      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

    • profile image

      precious 

      8 years ago

      thanx very much.but why do you divide both sides by 20

    • profile image

      ndzu 

      8 years ago

      could you make them a little simpler

    • profile image

      CONFUSED 

      8 years ago

      WHAT ?

    • profile image

      Taylor 

      8 years ago

      Thanks that really helped me with my homework.

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