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## Arithmetic

### Course: Arithmetic > Unit 15

Lesson 4: Dividing fractions and whole numbers word problems# Dividing fractions and whole number word problems

Sal uses tape diagrams to solve word problems involving fraction and whole number division.

## Want to join the conversation?

- Pls im new pls like my commets(21 votes)
- thats cap my friend(17 votes)

- Could you just do 1/4 divided by 2 much simpler? I think you can(20 votes)
- yes you can i agree sertantly(14 votes)

- Also, why are they called "
*tape diagrams*"?(6 votes)- Hi there! tape diagram is called like that, because they look like tape. Hope this helped, (this is from grammar but I will do this here X-D) you can learn anything, Joy out!(18 votes)

- Spooder man is coming to stop the Waffle House upvote this comment to stop him(14 votes)
- I am Spooder Man(0 votes)

- There is no single division problem that is the hardest one in the world. When working division problems by hand, some people find one kind of problem harder than others, but everyone would not agree on which problem is hardest. When using a computer or calculator, all division problem have essentially equal difficulty.

There is no definitive answer to that, as difficulty will differ from person to person. One could argue that there are degrees of difficulty in different types of division problems. For instance:

1 / 1 might be one of the easiest possible ones.

2 / 1 could arguably be a little more difficult

4 / 2 may perhaps be a little more difficult than that

7 / 2 a bit harder

3 / 7 harder still

pi / 7 again perhaps harder

pi / √2 may be even more so

These are very subjective statements. This order may make sense some, but to others, it may be easier to divide seven by two than four by two. This is akin to asking whose face is the prettiest. You could get a billion different answers and all of them correct from the point of view of those giving the answer.

Another point to made here is that it may not be possible to define a "hardest" division problem, as one could argue that it's always possible to take an existing problem and make it more difficult. This would be comparable to asking what the highest number is.(6 votes) - what do the upvotes do? Does it give you money or something?(3 votes)
- It makes it so more people see your comment(3 votes)

- no your not bro chill(4 votes)
- it's 4 x 2 = 8 then make it a fraction make 8 denominators and make 1 numerator(3 votes)
- wait.. Why do we have to divide the fourth Square by 2.?(3 votes)
- how are you today?(1 vote)

## Video transcript

- [Instructor] We are told that Billy has 1/4 of
a pound of trail mix. He wants to share it equally between himself and his brother. How much trail mix would they each get? So pause this video and
try to figure that out. All right, now let's work
through this together. So Billy starts with 1/4
of a pound of trail mix. So how can we represent 1/4? Well, if this is a whole pound, let's just imagine this
rectangle is a whole pound, I could divide it into
four equal sections. So let's see, this would be
roughly two equal sections, and then if I were to divide
each of those into two, now I have four equal sections. So Billy is starting with 1/4 of a pound. Draw a little bit, try to make
it a little bit more equal. Billy is starting with 1/4 of a pound, so let's say that is that 1/4 of a pound that he starts with. He's starting with 1/4 of a pound, and he wants to share it equally between himself and his brother. So he wants to share it equally between two people right over here. So what we wanna do is essentially say, let's start with our
total amount of trail mix, and then we're going to divide
it into two equal shares. So when they ask us how much
trail mix would they each get, we're really trying to figure out what is this 1/4 divided by two? So what would that be? Well, what if we were to take all of these four equal sections
and divide them into two? So I'll divide that one into two. I will divide this one into two. I will divide this one into two, and then I would divide this one into two. And now what are each of these sections? Well, each of these are now 1/8. That's a 1/8 right over there, the whole is divided into
eight equal sections. And so you can see, that
when you start with that 1/4, and you divide it into two equal sections, so one section and two equal
sections right over there, each of these is equal to 1/8. So 1/4 divided by two is equal to 1/8. Let's do another example. So we are told Matt is
filling containers of rice. Each container holds 1/4
of a kilogram of rice. And then they tell us if Matt
has three kilograms of rice, how many containers can he fill? So like always, pause this video, and see if you can figure that out. All right, so let's think
about what's going on. We're starting with a total
amount, three kilograms of rice, and we're trying to divide
it into equal sections. In this case we're trying to
divide it into equal sections of 1/4 of a kilogram. So we are trying to figure out what three divided by 1/4
is going to be equal to. Now to imagine that, let's
imagine three wholes, this would be three whole kilograms. So that is one whole, this is two wholes, trying to make them all the
same, but it's hand-drawn, so it's not as exact as I would like. So that's three whole kilograms here. And he wants to divide
it into sections of 1/4. So if you divide it into fourths, how many fourths are you going to have? Well, let's do that. So let's see, if we were
to divide it into halves, it would look like this. If you divide these
three wholes into halves. But then if you want to
divide it into fourths, it would look like this, I'm trying to get it as
close to equal sections. They should be exactly equal sections. So I am almost there. So there you have it. So I've just taken three wholes and I've divided it into fourths. So how many fourths are there? Well, there are one, two,
three, four, five, six, seven, eight, nine, 10, 11, 12 fourths. So three divided by 1/4 is equal to 12. And I encourage you to really think about why this is the case, that if we take a whole number like three and you divide it by 1/4, we're getting a value larger than three. And we're getting a value
that is four times three. Think about why that is the case.