Scale Representation

What is Proportion?

A name that we give a statement that says two ratios are EQUAL

What is a RATIO?

A way to COMPARE two or more Quantities

Example

Lets compare 2x4s

And 2x6s

If we have (2) 2x4s and (3) 2x6s

we have (2) groups of lumber

One group containing (2) pieces and one containing (3) pieces

Lets compare 2x4s to 2x6s

(2) (3) Lets compare 2x4s to 2x6s

We can write this in different ways:

2 to 3

2 to 3 2:3

2 to 3 2:3 2 3

For the purpose of this Section we will use

2 3

So the Ratio of 2x4s to 2x6s is 2 3

If we compare 2x6s to 2x4s the ratio is 3 2

If we compare 2x6s to the total # of planks, the ratio is: 3 5

so what?

Let’s compare the length to the width of your houses

The ratio of length to width of your model house is 10:7

10 being the length in inches and 7 being the width in inches

If the full size house is 14’ wide, how long is it?

Set up the proportion like this:

10 = L 7 14

We cross multiply and divide by the lone soldier

10 = L 7 14

10 = L 7 14

10 x 14 7L

140 7L

20 7 140

Therefore, L=20

So, if the house is 14’ wide, it is 20’ long based on the ratio of 10:7

Are the two ratios equal? In other words are they proportionate?

Test by cross multiplying

10 = 20 7 14

7 x 20 = 140

10 = 20 7 14

Therefore 10:7 and 20:14 are equal which means they are in proportion

Let’s try shall we?