# 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 **

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## Comments 28 comments

Thanks that really helped me with my homework.

WHAT ?

could you make them a little simpler

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

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

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 a lot 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 what 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.

thank you so much

what is a scale for math?

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

28