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### Course: Numbers & Operations - The Real & Complex Number Systems 211-217 > Unit 7

Lesson 5: Dividing fractions and whole numbers word problems# 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.

## Want to join the conversation?

- So Basically An Reciprocal Is The Opposite?(4 votes)
- Kind of, yes.

You just have to exchange the numerator and denominator for each other to get the reciprocal

For example the reciprocal of 4 would be 1/4, the reciprocal of 1/4 would be 4, and the reciprocal of 2/3 would be 3/2(2 votes)

- When Im dividing fractions and whole numbers (word problems) I always get stumped up on whether or not to keep my answer as a whole number or to add the "1" on top as my numerator. For example- Sally has 1/4 of a tray of brownies. She splits it up between 4 of her friends. How many brownies does each person get? Would my answer be 1/16 or 16? Sorry if this was confusing I'm not that good at explaining things.(3 votes)
- 1/4÷4 would be equal to 1/4×1/4 (flip the second number over). So 1/16 would be the answer. 16 wouldn't be possible because sally only has 1/4 of a tray of brownies; 16 is bigger than 1/4 so 16 is impossible to get(5 votes)

- Kwambok had 30kg of sugar . She put the sugar into packes wagging 3/4 kg each .how many packets did she full?(3 votes)
- Each packet contains 3 ∕ 4 kg, so 10 packets then contains 30 ∕ 4 kg, so in order to get to 30 kg we need 4 ∙ 10 = 40 packets.

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Also, the total weight ∕ the weight of each packet = the number of packets

This gives us 30 ∕ (3 ∕ 4) = 30 ∙ 4 ∕ 3 = 10 ∙ 4 = 40(4 votes)

- at2:34i loved it so much(4 votes)
- I don't get this quite yet could any one help me with this?(2 votes)
- :^| i could help!

the reciprocal is the number flipped. so if you divide lets say, 1/2 by 5, it would be the same thing as multiplying 1/2 by 1/5, which is the reciprocal of 5. then you multiply, giving you 1/10. So, 1/2 divided by 5 is equal to 1/10.

I hope this helped!

Also here's a less math-y way of doing this:

1/2/5

multiply the right two numbers.

1/10

easy right?(2 votes)

- Why does multiplying by a reciprocal is the same than divining fractions? I have not find a video that explains why it works.(2 votes)
- If division is the reverse of multiplication, does this mean that 1/5 x 1/20 = 4?

It is really confusing!'(2 votes)- 1/5 * 1/20 = (1*1) / (5*20) = 1/100, not 4.

Division is the reverse of multiplication in the sense that: 9*5 = 45. So, then 45/5 = 9 or 45/9 = 5. The division reverses or undos the multiplication.(1 vote)

- So do you just multiply the denominator of the first fraction and the numerator of the second fraction(4 votes)
- Unlike adding you multiply the denominator and the numerator and same with division.(0 votes)

- Why divide 1/5 of 4 when you can multiply?(2 votes)
- what is reciprocal?

tell me in easy word(1 vote)- Reciprocal is just flipping the integer or fraction over. For example, the reciprocal of 5 is 1/5 since we can view 5 as 5/1.(2 votes)

## 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.