In the last video, we made

a visual argument as to why this expression has

to be less than 1/3, and this expression

we already figured out is the fraction that are bears. Now we will make an

algebraic argument, or I could call it

an analytic argument. And to make this

argument, I’m going to leave this expression– we

know this is the fraction that are bears– and I’m going to

write this 1/3 in a form that looks a lot like

this, and then based on the information we have,

we can directly compare them. So how can I write 1/3? Maybe with the b as a numerator. Well, 1/3 is the same

thing as b over 3b, which is the exact same thing

as b over b plus b plus b. So now, this is

looking pretty similar. The only difference between this

expression right over here, b over c plus d plus

b and b over b plus b plus b is that our

denominators are different. And the only difference in our

denominators, this denominator has a c plus d here, while

this has a b plus b over here. Now, we have to ask

ourselves a question. What is larger? Is c plus d larger

than b plus b? And I encourage you to

pause that and think about that for a second. Well, yes. We already see right over here. It was given to us

that c is greater than d that is greater

than b, so both c and d are greater than b. So c plus d is definitely going

to be greater than b plus b. So this denominator right

over here is greater, so this has a

larger denominator. This right over here has

a smaller denominator. And since we know this

has a larger denominator, this has a smaller

denominator, they have the exact same

numerator– they both have b as a numerator– we know

that this whole thing must be a smaller quantity. If you have the same numerator

but one expression has a larger denominator, it must be smaller. Wait, so how does that work? Well, just remember. I mean, just imagine. You have the same numerator,

what’s going to be bigger, a over 7 or a over 5? Well here, you’re

dividing a by 7. You’re dividing into many

more chunks than over here, so this right over

here is smaller. This right over here is larger. So this is the larger. This right over here is smaller. So the same numerator, the

larger the denominator, the smaller the

quantity is going to be. So going back to the

original question, this is the smaller quantity,

and this right over here, 1/3, is the larger quantity.

1nd?

2rd

3th

4nd

Ford 😀 get it? For-d? No? Okay 🙁

4st

Even though I'm a second year maths student and these videos are not teaching me anything new, they are just amazing to watch.

5nd!

Really like the way you explain things… Simple, clear and to the point. Hope every math/physics teacher would be able to do it in such way)

Thank you very much!

6rd

Komander