Here we check out that the ratios of head size to body size are the same in both drawings.

You are watching: The product of the means equals the product of the extremes

So they room proportional.

Making the head too long or quick would look at bad!


Example: International file sizes (like A3, A4, A5, etc) all have actually the very same proportions:


So any kind of artwork or paper can be resized to fit on any sheet. Very neat.

Example: you desire to draw the dog"s head ... How long need to it be?


Let united state write the proportion through the aid of the 10/20 proportion from above:

?42 = 1020

Nowwe fix it using a unique method:


Multiply across the well-known corners,then divide by the 3rd number

And we gain this:

? = (42 × 10) / 20 = 420 / 20 = 21

So you should attract the head 21 long.

Using Proportions to resolve Percents

A percent is in reality a ratio! saying "25%" is actually saying "25 every 100":

25% = 25100

We can use proportions to solve questions involving percents.

The trick is to put what we know into this form:

PartWhole = Percent100

Example: what is 25% of 160 ?

The percent is 25, the whole is 160, and also we desire to discover the "part":

Part160 = 25100

Multiply throughout the known corners, then divide by the 3rd number:


Part = (160 × 25) / 100 = 4000 / 100 = 40

Answer: 25% the 160 is 40.

Note: we could have additionally solved this by law the divide first, choose this:

Part = 160 × (25 / 100) = 160 × 0.25 = 40

Either method works fine.

Example: what is $12 as a percent of $80 ?

Fill in what us know:

$12$80 = Percent100

Multiply across the known corners, then divide by the 3rd number. This time the known corners are peak left and bottom right:


Percent = ($12 × 100) / $80 = 1200 / 80 = 15%

Answer: $12 is 15% the $80

Example: The revenue price the a phone to be $150, i m sorry was only 80% of typical price. What was the common price?

Fill in what us know:

$150Whole = 80100

Multiply throughout the recognized corners, then division by the 3rd number:


Whole = ($150 × 100) / 80 = 15000 / 80 = 187.50

Answer: the phone"s regular price was $187.50

Example: just how tall is the Tree?

Sam tried utilizing a ladder, ice cream measure, ropes and various other things, however still couldn"t job-related out just how tall the tree was.


But climate Sam has actually a clever idea ... Comparable triangles!

Sam steps a stick and its shadow (in meters), and additionally the zero of the tree, and this is what that gets:

Now Sam makes a sketch of the triangles, and also writes under the "Height come Length" ratio for both triangles:

Height:Shadow Length: h2.9 m = 2.4 m1.3 m

Multiply throughout the known corners, then divide by the third number:

h = (2.9 × 2.4) / 1.3 = 6.96 / 1.3 = 5.4 m (to nearest 0.1)

Answer: the tree is 5.4 m tall.

And he didn"t also need a ladder!

The "Height" might have gone to the bottom, so long as it to be on the bottom for BOTH ratios, favor this:

Let us try the proportion of "Shadow size to Height":

Shadow Length:Height: 2.9 mh = 1.3 m2.4 m

Multiply throughout the recognized corners, then division by the 3rd number:

h = (2.9 × 2.4) / 1.3 = 6.96 / 1.3 = 5.4 m (to nearest 0.1)

It is the exact same calculation as before.

A "Concrete" Example

Ratios have the right to have more than 2 numbers!

For instance concrete is made by mixing cement, sand, stones and water.


A common mix the cement, sand and also stones is composed as a ratio, such together 1:2:6.

We deserve to multiply all worths by the same amount and also still have actually the very same ratio.

10:20:60 is the same as 1:2:6

So as soon as we usage 10 buckets of cement, we should use 20 of sand and also 60 the stones.

Example: you have actually just put 12 buckets the stones into a mixer, just how much cement and also how much sand have to you include to do a 1:2:6 mix?

Let us lay it the end in a table to make it clearer:

CementSandStonesRatio Needed:You Have:

You have 12 buckets of stones however the ratio says 6.

That is OK, you simply have twice as countless stones as the number in the proportion ... Therefore you need twice as lot of everything to keep the ratio.

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Here is the solution:

CementSandStonesRatio Needed:You Have:

And the ratio 2:4:12 is the same as 1:2:6 (because they display the same relative sizes)

So the prize is: include 2 buckets that Cement and 4 buckets of Sand. (You will also need water and a many stirring....)

Why are they the same ratio? Well, the 1:2:6 proportion says to have:

twice as much Sand as Cement (1:2:6)6 time as lot Stones together Cement (1:2:6)

In ours mix we have:

double as lot Sand together Cement (2:4:12)6 time as much Stones together Cement (2:4:12)

So it must be simply right!

That is the good thing about ratios. You have the right to make the quantities bigger or smaller and also so long as the relative sizes space the very same then the proportion is the same.

Ratios straight Proportional and Inversely Proportional Algebra Index