Practice English Speaking&Listening with: Dividing Fraction Word Problems

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Hey, again, math class.

Okay, so now we're going to talk about dividing fraction word

problems.

Okay, and if you notice, this is a little bit different format

for our videos.

I'm trying something new.

This is called a Prezi.

I'd be curious for your feedback,

whether you liked it or not.

I was looking for a way to show you type easily, you know,

like have a word problem without having to write it on one of my

little white boards.

So, anyway, dividing fraction word problems.

Dividing fractions in a word problem can sometimes be tricky,

and the reason for that, obviously,

is that division is different than multiplication.

In multiplication, if I have 4 times 3, I get 12, right?

If I have 3 times 4, I get 12.

They equal the same thing.

But 12 divided by 3 is a completely different answer than

12 divided by 4, right?

So it's important, especially in dividing fractions,

to know which fraction is your first term, because otherwise,

if you don't do that, you're going to get a completely wrong

answer, and it gets really frustrating.

So to get around this, and to keep yourself from being

frustrated, when you're dividing,

you must ask yourself a question along the lines of,

What am I starting with, okay, or What did I go to the store

and buy?

Okay, let's look at some examples.

This is definitely one of those things that gets easier with an

example or two.

So let's look at this first example problem, number one,

Kendra uses 15 and 3/4 yards of wrapping paper to wrap 21

packages.

What was the average yardage she used per package?

So you want to ask yourself, What did Kendra start with, right?

Did she start with 21 packages or did she start with 15 and 3/4

yards of wrapping paper?

And so this problem -- maybe that's not the best question,

right, because if you're like me, I'm thinking to myself, oh,

she started with both things.

And, so then, you have to think a little beyond, okay,

what's being divided up?

Well, she's got this big, long roll of wrapping paper that

she's going to cut into 21 pieces for these these 21 packages.

So that's what's being divided up,

the 15 and 3/4 is going to be my first term, okay?

So see down here, I've got 15 and 3/4 as my first term.

I'm going to divide it into 21 pieces, okay?

So just like if it was a straight-up a division problem,

I still have to do all of the steps.

I have to convert 15 and 3/4 into an improper fraction, so 63/4.

And then I have to convert the 21 into a fraction,

so 21 over 1.

That's all I do.

Draw a line, put a 1 under it.

Then, I'm going to flip my second term, right,

so 21 over 1 becomes 1 over 21, and change to multiplication.

And then I can cross cancel.

I can do anything that I want.

In this problem, it's very nice.

21 is a factor of 30 -- or 63.

Who knew, right?

21 times 3 is 63.

And so, then, I can put the 3 right here.

21 divided by 21 is 1.

And, then, I multiply straight across.

So 3 -- this 3 times 1 is 3.

4 times 1 is 4.

So this tells me that she's going to end up using 3/4 yards

of wrapping paper for each package.

And so that answer makes sense, right,

because I have 21 packages.

21 is a larger number than 15, right?

So I'm thinking that it's going to be a number smaller than 1 as

my answer.

And it is.

3/4 is a number smaller than 1.

Okay, let's look at another example.

Example problem number 2.

How many 3/4-yard hair ribbons can be cut from a spool of

ribbon 12 yards long?

So this is a great one for that -- that second question that I

gave you, because we got to ask ourselves,

What did I start with?

And in this question, this is a great -- a great one for this.

What did I go to the store and buy?

Did I go to the store and buy a spool of ribbon,

or did I go and buy 3/4 yard hair ribbons?

No, I went and bought a whole spool of ribbon, right?

And then I came home and measured it out and cut them up.

Okay, so I know that this 12 yards is going to be my first term.

So you see how I put it down here in the first spot?

And then I'm going to divide it into 3/4-yard pieces.

So I have to convert that 12 into a fraction.

So I draw a line, put a 1 under it.

I'm going to divide it by 3/4, and then I'm going to change to

a multiplication problem and flip the second term.

So the 3/4 becomes 4 over 3, and then I'm going to cross cancel,

do whatever I need to do.

So 3 is a factor of 12.

So I can divide 3 out of both of these.

12 divided by 3 is 4.

3 divided by 3 is 1.

And so, then, I just multiply 4 times 4, which equals 16.

And I have a 1 on the bottom here,

so I don't have to -- I don't have to write that,

but I'm going to end up with 16 hair ribbons.

And if I hadn't have gotten these in the right spot,

let's say I put 3/4 in as my first term,

I would have ended up with a fraction down here,

and that would have felt like a really weird answer.

Hopefully, you would have been, like, well, wait a minute,

I have to at least have a few hair ribbons cut from this 12 yards.

It doesn't make sense to end up with a fraction.

So sometimes that's a good thing to sort of know,

to consider your answer and say, you know, gosh,

does this answer that I came up with makes sense?

Let's look at another practice problem here, number 3.

Wayne spent 11 and 1/4 hours on Saturday working on 5

complicated engineering problems.

What was the average amount of time spent on each problem?

Now this one, again, the -- the question that I told you to ask,

What did Wayne start with, maybe isn't the best question to ask,

because, again, he started with, like,

a whole Saturday or 11 and 1/4 hours of time on a Saturday,

and he started it with five complicated engineering problems.

So it doesn't really help us determine which is the first term.

But here's what I want you to think about,

time spent on each problem.

Okay, what they're really asking you,

and what I want you to kind of think of it as -- is time per

problem, because "per," this word, per,

right here means divide.

So I could read this as time-divided-by problem, right?

Which, as -- as you know, grammatically correct sentence

makes absolutely no sense whatsoever,

but time-divided-by problem makes sense in the context of

this word problem, right?

I'm going to come down here and write time divided by my number

of problems.

And that's how I know that time is 11 and 1/4 hours is my first

term, okay?

So 11 and 1/4.

I'm going to divide it by 5.

The first thing I have to do is convert that 11 and 1/4 into an

improper fraction.

11 times 4 is 44, plus 1, is 45.

My bottom number stays the same.

I'm going to make that 5, it's a whole number.

I'm going to make him a fraction,

simply by drawing line, putting a 1 under it, right?

And then I'm going to make it a multiplication problem by

flipping my second term.

So my problem becomes 45 over 4 times 1/5, right?

And I can cross cancel anything that I want.

Again, this is a nice -- nice, neat, little problem.

5 is a factor of 45.

So I can simply divide 5 out of both of them.

45 divided by 5 is 9.

5 divided by 5 is 1.

And then I can multiply straight across.

9 times 1 is 9.

4 times 1 is 4.

And then at this point, I got to ask myself my two questions, right?

Is this a proper fraction?

No, it's not, sadly.

So, I have to come down here and figure out my -- I have to do my work, right?

So here's -- here's my problem 4 divided into 9 goes twice,

which is 8, right?

4 times 2 is 8.

When I subtract, I have one left over,

and that leaves me with my mixed number of 2 and 1/4 hours.

So does this answer make sense?

He's got a chunk of time divided by five problems.

Yeah, it does make sense.

5 times 2 is 10, right?

10 is kind of close to 11 and 1/4 hours,

so I think that I'm -- I think I'm correct at 2 and 1/4 hours,

right here.

Again, if I had gotten these two terms switched,

I would have ended up with a weird answer down here,

and it wouldn't have made sense when I asked myself if -- if

that made -- if the answer I got makes sense.

So what will you ask yourself before answering a word problem

that requires dividing of fractions?

What did I start with?

What did I go to the store and buy?

And -- and, hopefully, these will help you to determine which

is your first term.

So, again, we're going to have some time to practice this.

I -- you know how I love to practice word problems,

and we'll see you in class tomorrow.

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