>> Welcome to a video on proportions.
The goals of this video are to determine whether two pairs
of numbers form a proportion and also to solve proportions.
A proportion states that two ratios or rates are equal.
If A to B and C to D are two equal ratios, then we can say they are equal and form a proportion.
And A over B is C over D, if any only if A times D equals B times C.
And these are called the cross products of the proportion.
A and D are sometimes called the extremes and B and C are sometimes called the means.
But the key concept here is if we have a proportion, A times D must equal B times C
and if A times D equals B times C, we must have a proportion.
So saying that one more time.
If two fractions are equal, then their cross products are equal
and if the cross products are equal, then the fractions are equal or form a proportion.
Let's take a look at an example of this.
We want to write ratios for the pairs of numbers and determine if they form a proportion.
So for number one, the first ratio would be 24 to 36 and the second ratio would be 1.8 to 2.7.
If these are equal and form a proportion, then their cross products must be equal.
So to see if this is true, we cross multiply.
24 times 2.7 must equal 36 times 1.8 if this forms a proportion.
Let's go ahead and see if it does.
24 times 2.7 and 36 times 1.8.
They're either equal or not.
And we can see they are both equal to 64.8.
Therefore this is a proportion.
For number two, the first ratio would be 10 to 8 and the second ratio would be 14 to 11.
And we want to know if this would form a proportion.
And we can determine this by finding the cross products and seeing if they're equal.
So 10 times 11 must equal 8 times 14 if we have a proportion.
10 times 11 will be 110.
8 times 14 would be 80 plus 32 over 112.
Well these aren't equal.
Therefore these ratios do not form a proportion.
Now we're going to talk about how we can solve a proportion
if one of the four numbers is missing.
And here's the procedure.
We'll first find the cross products to form an equation,
then we'll solve the equation and then we'll check our answer.
So since we know these are equal to each other, the cross products must be equal.
I always like to do the cross product that involves the variable first.
So 2 times X would be 2x must equal 5 times 8 which is 40.
So now we'll solve this equation by dividing both sides by 2 and we have X equals 20.
To check this, we have 5 is to 2 as 20 is to 8.
5 times 8 is 40, 2 times 20 is also 40.
So it checks.
Let's go and do a couple more of these.
We have a proportion, therefore, the cross products must be equal
which means 8 times N or 8N must equal 2.4 times 18.
So we'd have 8N equals 43.2.
Now dividing both sides of the equation by 8, we can determine the value of N.
And it looks like N is equal to 5.4.
So 8 times 5.4 would equal 4.2 times 18.
If you want you can go ahead and check that.
Let's go and take a look at one more.
This one looks a little more confusing because the denominator
of this first fraction is a fraction in itself.
So it's going to helpful to rewrite this to make it look a little nicer.
Meaning we have Y over one third must equal 6 over 5.
Now we'll go ahead and cross multiply.
So we have 5 times Y or 5Y must equal one third times 6.
Well one third times 6, this would be six thirds or 2.
So we have 5Y equals 2.
So dividing both sides by 5, we have Y equals two fifths.
Let's go ahead and check this one.
We already determined that one third times 6 is equal to 2.
So if Y is equal to two fifths, two fifths times 5 or 5 over 1 would also give us 2.
So it checks.
That will do it for proportions.
Thank you for watching.
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