Multiplying fractions

Multiplying fractions

Welcome to the presentation on multiplying fractions.

Well, I think today you'll be very happy because you'll find

out that this is one of the few times where multiplying

something is easier than adding it, I think, or subtracting

it for that matter.

And if you don't believe me, let's do some problems.

Okay, let's get started.

Let's start with one half times one half.

So when you multiply fractions it's very straightforward.

It's essentially just two separate multiplication

problems.

You multiply the numerators, so you get one times one.

And you multiply the denominators, two times two.

one times one is one.

two times two is four.

So one half times one half is equal to one fourth.

That makes sense.

That's like saying one half of one half is one fourth, which makes sense.

What if we had negative numbers?

Well, if I had one half times negative one half -- and when you

have a negative fraction it's good ascribe the

negative number.

I tend to ascribe the negative number to the numerator

-- negative one over two.

You realize that negative one half is the same thing

as negative one over two.

Hopefully that make sense.

So one half times negative one half, that's just the same thing as one

times negative one over two times two, which equals negative one

over four, which is the same thing as negative one fourth.

What if I had different denominators, and when you're

adding and subtracting fractions that tends to

make things difficult.

Well, it's not necessarily the case here.

If I had two thirds times one half, just multiply the numerators, two

times one, and you multiply that denominators three times two.

So you get two times one is two, three times two is six.

And two over six we know from equivalent fractions is

the same thing as one third.

That was an interesting problem.

Let's do it again and I want to show you a little trick here.

So, two over three times one half -- as we said, any multiplication

problem you just multiply the numerators, multiply the

denominators and you have your answer.

But sometimes there's a little trick here where you can divide

the numerators and the denominators by a number,

because you know that this is going to be the same thing as two

times one over three times two.

Which is the same thing -- I'm just switching the order on top

-- as one times two over three times two.

All I did is I switched the order on top, because you can

multiply in either direction.

And that's the same thing as one third times two over two.

Well that's just is one third times one, which is equal to one third.

And why did I do that?

Well I want to show you that these twos, these twos, all I did

is switch the order, but at all times we had one, two in the

numerator, and I had one, two in the denominator.

If I wanted to, and this is kind of a trick for doing

multiplication really fast so you don't have to reduce the

final fraction too much, you get two thirds times one third --

two thirds times one half, sorry.

You say I have a two in the numerator, two in the

denominator, let me divide them both by two, that equals one third.

Just a fast trick.

I hope I didn't confuse you.

Let's do a couple of more problems, and I'll do

it both with the trick and without the trick.

What if I had three sevenths times two over five.

Well, multiply the numerators, three times two is six.

seven times five is thirty-five.

That's it.

Let's do some negative numbers.

If I had negative three over four times two over eleven, well, that's

negative six over forty-four, which is the same thing as

negative three over twenty-two.

And we could have done that cross-dividing trick here.

Let's do it again with the cross--.

Times two over eleven.

We say oh, well two and four, they're both divisible by two, so

let's divide them both by two.

So two becomes one, four becomes two, and then our answer

becomes minus three over twenty-two.

Negative three times one is minus three.

two times eleven is twenty-two.

Do another one right here.

If I had negative two fifths times minus two fifths, well, that just is

equal to negative two times negative two is positive four.

It's five times five is twenty-five.

four over twenty-five.

And that's, just remember, a negative times a negative is a

positive, which makes sense.

Let's just do a couple more problems since we

have a lot of time.

But I think you probably got this by now.

You're probably realizing that multiplying fractions is a

lot easier than adding or subtracting them, hopefully.

I guess it's not a bad thing if you find adding or subtracting

fractions easy as well.

Let's do -- I'm just making up numbers now

-- two ninths times eighteen over two.

Well here we could, well, we have a two in the numerator

and a two in the denominator.

Let's divide them both by two, so they both become one.

And we have an eighteen in the numerator and a nine

in the denominator.

Well they both are divisible by nine, so let's divide

them both by nine.

So nine becomes a one, and the eighteen becomes a two.

So you have one times two over one times one, well, that just equals

two over one which equals two.

That was pretty straightforward.

We could have done it, I guess you could call it the hard

way, if we said two over nine times eighteen over two.

two times eighteen is thirty-six.

nine times two is eighteen.

And thirty-six divided by eighteen, and we can see eighteen goes into thirty-six two

times, that also equals two.

Either way is fine.

If you don't feel comfortable doing this trick right

now, you don't have to.

All that does is it makes it easier--you won't end up with huge numbers in your

product that you'll have to figure out if they can

be reduced further.

Let's do two more problems.

Minus five over seven times one over three.

Minus five times one is minus five.

seven over three is twenty-one.

That's it.

Let me do one with the little trick I showed you.

Say I had fifteen, and here I think you'll see why that trick

is useful, over twenty-one times fourteen over five.

Well clearly, if we multiply this out we end up with

pretty big numbers.

I think two hundred and twenty over one hundred and five and you have to reduce those.

It becomes a big mess.

But we can see that fifteen and five are both divisible by five.

So let's divide them both by five.

So fifteen divided by five is three.

five divided by five is one.

fourteen and twenty-one, they're both divisible by seven.

fourteen divided by seven is two.

twenty-one divided by seven is three.

So we get three times two is six over three times one is three, which equals two.

That's the same thing as what I said before.

If we had multiplied fifteen times fourteen that would

have been two hundred and ten I think.

Yeah, fifteen times fourteen is two hundred and ten.

And twenty-one times five would have been one hundred and five, and you would have to say,

I guess in this case it's kind of obvious, that two hundred and ten is two times

one hundred and five and you would have gotten two as well.

So hopefully I didn't confuse you too much

with that last problem.

But I hope you realize multiplication's pretty straightforward.

You just multiply the numerators, you multiply the

denominators, and then if you have to reduce you reduce, but

you're pretty much done.

I think you're ready now to try the multiplication module,

and I hope you have fun.