# 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.

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

## More by this Author

Taylor 6 years ago

Thanks that really helped me with my homework.

CONFUSED 6 years ago

WHAT ?

ndzu 6 years ago

could you make them a little simpler

precious 6 years ago

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

t.elia 6 years ago from Northern Ireland Author

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)

1 : 200

t.elia 6 years ago from Northern Ireland Author

t.elia 6 years ago from Northern Ireland Author

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

Alex 5 years ago

Isnt a scale supposed to be in mm not cm

t.elia 5 years ago from Northern Ireland Author

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.

nbay 5 years ago

ummmmmmmmm it's really help me in my work.

edd 5 years ago

thank you for the defination..

edd 5 years ago

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

Sassafrass 5 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

zara 5 years ago

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

Juanita Johnson 5 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

Thanks a million this really helped.

Meeeeeeeee 4 years ago

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

horst 4 years ago

on a scale of i/500 what is .7

on a scale of 1/400 what is .7

ME 4 years ago

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

ME 4 years ago

oooooooooooooooooooooooooooo

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

Meghan 4 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.

okoli gabriel 4 years ago

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

lol 33 4 years ago

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

danay 3 years ago

thank you so much

t.elia 3 years ago from Northern Ireland Author

Alex su 2 years ago

what is a scale for math?

viswa 2 years ago

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