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# Dividing fractions by whole numbers: studying

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

Video transcript

Tommy is studying for
final exams this weekend. He will spend 1/5 of
the weekend studying. What fraction of
the weekend will he spend studying for
each of his 4 subjects if he spends the same amount of
time studying for each subject? So the total amount
of time he's going to spend studying this
weekend is 1/5 of the weekend. And he has to divide that
into 4 equal sections. And he's going to spend that
much time on each subject. So he's going to
divide this by 4. Now, we've already seen
that dividing by a number is the same thing as
multiplying by its reciprocal. You might say, hey, well,
what's the reciprocal of 4? You just have to
remind yourself that 4 is the same thing as 4/1. So 1/5 divided by 4/1 is the
same thing as 1/5 times 1/4. And you could also view
this as 1/4 of 1/5 or 1/5 of 1/4, either way. But here we multiply
our numerators to get 1. And then we multiply our
denominators, 4 times 5 is 20. So you get 1/20 of
the weekend will be spent studying
for each subject. Now, let's also try to
think about this visually. Let's imagine that this
is his entire weekend. And I've divided it
into 5 equal sections. And so we already know
that the total amount of his weekend spent
studying is 1/5. So that's the total
amount studying for the weekend is 1/5. Now, he has to divide this
into 4 equals section. So let's do that. He's got four subjects,
and he's going to spend the same amount of
time on each of the 4 subjects. So he's going to divide
this into 4 equal sections. So how much time does
he spend on one subject? Well, in each subject, that
would be this little area that I'm doing in
yellow right over here. And what is that? Well, that's 1 over-- how
many equal sections are there of that size in the weekend? Well, I've just
drawn out the grid. You had 5 rows, and
now you have 4 columns. So 5 rows times 4 columns,
you have 20 equal sections. So once again, looking
at it visually, he's spending 1/20
of his weekend on each of the 4 subjects. And then if you do this
for 4 subjects, that means that in this
whole weekend, 1/5 will be spent studying. But the question
that they're asking, he's spending 1/20 of the
weekend on each subject.