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### Course: MAP Recommended Practice > Unit 34

Lesson 32: Dividing fractions and whole numbers word problems# Dividing whole numbers by fractions: word problem

Learn to solve a word problem that involves dividing a whole number by a unit fraction. Created by Sal Khan.

## Want to join the conversation?

- Can't you just multiply 4 and 5 in the beginning?(112 votes)
- Yes you could have, but you will be more sure of your answer if you do it Sal's way (even though he
*is*basically doing that, but step by step).(85 votes)

- what is a potpurri?(65 votes)
- a mixture of dried petals and spices placed in a bowl to perfume a room.(11 votes)

- What is potpourri(14 votes)
- It seems to be there is two definitions of potpourri. The definition I know is "a little bit of everything" or "everything". Using context clues, I think potpourri is kind of like a trail mix of some kind of food. By trail mix, I mean, "a whole bunch of different types of foods". What kind of food, I don't know, but I hope I helped!(0 votes)

- Sal how do I make a fraction out of 5 and divide it by 1 half ( not a home work question) :)(5 votes)
- 5/1 and 5 divide by 1/2 equals 2 1/2 (i think)(1 vote)

- what is potpourri?(4 votes)
- A mixture of dried petals and spices placed in a bowl or small sack to perfume clothing or a room(3 votes)

- Ok, I'm confused, If I had 3 cups of something and only wanted a third of it would that equation not be 3 divided by 1/3. If so the answer is nine instead of one?(3 votes)
- Here is how I look at it. Words mean things. When you say "a third of it," the word "of" is the key: "of" means to multiply. So, "a third of it" which is "a third of 3 cups". Do a simple substitution of "times" for "of": "a third times 3 cups".

So 1/3 x 3 cups = 1 cup(5 votes)

- could you just say 4 times 5(3 votes)
- Yes, you could.. but some schools want you to show your work.(3 votes)

- do you get a different answer when you do 5/6divided by 2 or 2 dividded by 5/6(3 votes)
- Yes you do get different answers! The order in which you divide numbers makes a difference.

5/6 divided by 2 = 5/6 times 1/2 = 5/12.

2 divided by 5/6 = 2 times 6/5 = 2/1 times 6/5 = 12/5.

5/12 is not the same as 12/5. 5/12 is less than 1, but 12/5 is greater than 1.

Have a blessed, wonderful day!(3 votes)

- so its just the number divided by the denominator(3 votes)
- At2:18, what is the reciprocal?(1 vote)
- 2x 8/1

because reciprocol is the opposite of the numerator and the denominator. so, 8/1 is the same as 8 as a whole(2 votes)

## Video transcript

Tracy is putting out
decorative bowls of potpourri in each room of the
hotel where she works. She wants to fill each bowl
with 1/5 of a can of potpourri. If Tracy has 4 cans of
potpourri, in how many rooms can she place a
bowl of potpourri? So she has 4 cans, and
she wants to divide this 4 cans into groups
of 1/5 of a can. So if you have 4 of
something and you're trying to divide it into
groups of a certain amount, you would divide by
that amount per group. So you want to divide 4 by 1/5. You want to divide 4 cans of
potpourri into groups of 1/5. So let's visualize this. Let me draw one can of
potpourri right over here. So one can of potpourri can
clearly be cut up into 5/5. We have it right over here. 1, 2, 3, 4, 5. So 1 can of potpourri
can fill 5 bowls if you put 1/5 in each bowl. Now, we have 4 cans. So let me paste these. So 2, 3, and 4. So how many total bowls of
potpourri can Tracy fill? Well, she's got 4 cans. So this is going to
be equal to-- let me do this is the right
color-- this is going to be equal to, once
again, she has 4 cans. And then for each
of those cans, she can fill 5 bowls of potpourri
because each bowl only requires a 1/5 of those cans. So this is going to be the
same thing as 4 times 5. Or we can even write
this as 4 times 5 over 1. 5 is the same
thing as 5/1, which is the same thing
as 4 times 5, which, of course, is equal to 20. She can fill 20 cans-- or I
should say, with her 4 cans, she can fill 20
bowls of potpourri. Now, just as a
review here, we've already seen that
dividing by a number is equal to multiplying
by its reciprocal. And we see that right over here. Dividing by 1/5
is the same thing as multiplying by the
reciprocal of 1/5, which is 5/1. So she could fill up
20 bowls of potpourri.