We’re asked, how many inches

are in 4 and 1/2 yards? And we’ll do it

a couple of ways. One, we could just say how

many inches are in 4 yards and how many inches

are in a 1/2 of a yard? And this really

4 plus 1/2 yards. Or we could convert this

into an improper fraction first and then convert. But before I even

do that, let’s just think about how many

inches there are in a yard. So if I have 1 yard,

we know that there are 3 feet for

every 1 yard, Right? And when you say, why am

I multiplying by 3 instead of saying there’s 1

yard for every 3 feet? And the easiest way to

think about it is you’re going to have a larger

value over here, and you’re also going to want

to have these units right over here cancel out. So yard is canceling

out with yard. So you have 1 yard is

equal to 3 feet, which is kind of what we already knew. I’m just showing you how

the dimensions cancel out. And how many inches

are there per foot? Well, we know that there are

12 inches for every 1 foot. And same logic over here,

inches is a smaller unit of measurement so it makes sense

that we’re multiplying by 12. 3 feet is going

to be more inches, so we’re multiplying by 12. And also these

units cancel out– foot in the numerator,

foot in the denominator. 3 times 12 divided by 1

is equal to 36 inches. So you might have

already known it. But this is nice to have

the dimensions cancel out like this. We know that 1 yard

is equal to 36 inches. Or there are 36 inches

for every 1 yard. And so we can now

either break this down, or we can turn this into

an improper fraction. First I’ll just break it down

into 4 yards plus 1/2 yards. So we could say that

this is 4 yards. So 4 yards is going

to be equal to– well, let’s just multiply

it times 36 inches, 36 inches for every 1 yard. The yards cancel out. 4 times 36 is 120,

plus 24, so that’s 144. So this is equal to 144 inches. That’s just the 4 yards. And then if we do the 1/2

yards, so 1/2 of a– I guess I say 1/2

yard, once again, times 36 inches per yard,

the yards cancel out. 1/2 times 36 is going to

be equal to 18 inches. So 4 and 1/2 yards

is the same thing as 4 yards plus 1/2 yards, which

is the same thing as 144 inches plus 18 inches, which is

going to give us– let’s just add it up over

here on the right, 144 plus 18. 4 plus 8 is 12. 4 plus 1 is 5. You have this 1 up here, so

it’s 6, and then we have a 1. So when you add them all

together, you get 162 inches. The other way to

do this would have been to convert this

into an improper fraction and then multiply by the unit. So let’s do it that way. If I have 4 and 1/2 of

anything, really– so let me write 4 and 1/2. I’m trying to find

a suitable color. So if I have 4 and 1/2,

this is the same thing– 4 is the same thing as 8/2. This is the same thing– so

let me write it this way. 4 and 1/2 is the same

thing as 4 plus 1/2, which is the same

thing as– if we want to have the same

denominator as this 2 over here or as

this 1/2 over here, this is the same thing as 8/2. Or you could say 4/1 is

the same thing as 8/2, if we want to have a common

denominator, so 8/2 plus 1/2. Actually, let me write it

that way, just so you really understand what we’re doing. 4 is the same thing as 4/1. So it’s 4/1 plus 1/2. If we want to find a

common denominator, it’s 2. So 4/1 is the same

thing as 8/2 plus 1/2, which is equal to 9/2. Now, I did it this way,

which takes longer, just so you really understand

how we converted it, why it makes– hopefully

conceptually why it just makes intuitive sense, why 4 and

1/2 is the same thing as 9/2. But if you want a

simple process for it, you could just say,

look, 4 times 2 is 8. 8 plus 1 is 9. And that gives you that 9

right over there, so 9/2. So we have 9/2 yards that we

want to convert to inches. Same process– times

36 inches per yard. Yard in the numerator,

yard in the denominator. We are left with 9/2 times 36. We could say times 36/1 if we

like, 36 Inches for every 1 yard. 36– or the number 36

really is the same as 36/1. And then we’re left with

just inches in our units. We’re just left with inches. And over here there’s several

ways that we can simplify it. Probably the easiest

way to simplify it is we can divide both our numerator

and our denominator by 2. So let me write it this way. I don’t want to skip steps. So we have 9 times 36 over

2 times 1, or over 2 inches. And we can divide the

numerator and the denominator by 2 to simplify it. They’re both divisible by 2. 36 divided by 2 is 18. 2 divided by 2 is 1. So we’re really just left

with 9 times 18 inches. We can just multiply 9 times 18. Let me do it over here. 18 times 9. 8 times 9 is 72. 1 times 9 is 9, plus 7 is

16, so we get 162 inches. So all of this simplifies to

162 inches, and we are done.

Metric system… make all of this SO much easier!

This just confuses me more :/

great

where does he get the 24 from in 2:04????

Why does he cancel out the yards

hehaw

I thinks this is the most confusing math video I have ever watched warning makes more confusing not easier😑😣😥

i love how you go into detail explaining how all the various ways you can go about finding the answer. like how 4 1/2 is actually 4 +1/2 which is actually 4 /1+1/2 which is 9/2. when i was a kid it was do it this way and your done. like all we were doing was learning how to pass a test.

Why are you using a improper fraction instead of using a number 🤔😑😣😥🤐🤢😓😨😖😩

This is the same as i do things in my head.