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### Course: 5th grade > Unit 7

Lesson 2: Relate fraction division to fraction multiplication# Multiplication and division relationship for fractions

We learn how multiplication and division are related, even when we're dealing with fractions. Watch how dividing by a number is the same as multiplying by its reciprocal. Then watch Sal practice expressing these relationships using both division and multiplication.

## Want to join the conversation?

- So couldn't
be written as**42 = 7 / 1/6**instead of**42 x 7 = 1/6**?**42 x 1/6 = 7**(24 votes)- There is this to consider.

"Example one":

2x3 = 6 and 3x2 = 6

This is not true for the order in division.

15/3 = 5 however 3/15 = 1/5 or 0.2 they both yield a smaller number however the one with a larger number for its denominator yields a significantly smaller number when compared to the one with a larger numerator.

When dividing fractions this has to be taken into consideration.

"Example two":

4 x 1/16 = 1/4 or 0.25

1/16 x 4 = 1/4 or 0.25

4 divided by 1/16 = 64

1/16 divided by 4 = 1/64 or 0.015625

"Example three":

A whole number divided by a fraction yields a larger "whole" number.

A fraction divided by a whole number yields an even "smaller fraction."

Example three simplified:

number/fraction = number or "n/f=n"

fraction/number = fraction or "f/n=f"

There needs to be a video called "The differences between multiplying and dividing fractions".

After wracking my brain on this for six hours I had to break this apart and figure out the underlying system so that it's possible to get the right answer every time.(25 votes)

- What's the reason of doing 42*1/6=7? Can't I write as 42*7=1/6? Unfortunately, This is very common in Khan Academy videos. There isn't enough explanation in details.(14 votes)
- So is your question 42*1/6=7 = 42*1/6=7?

because 42*1/6=42/6 and fraction is basically division so 42÷6=7 that makes sense and 42*7=294 so did I answer your question?(15 votes)

- I don't understand this video(17 votes)
- Sal is trying to explain that like whole numbers, you have a "family" of numbers, or that the numbers should equal each other like as an example 5*6=30,so 30/6=5. Hope that helped!(* times. / divide)(2 votes)

- Bro why show the hard way then the easier way?(9 votes)
- I am trying to understand this for 6 hours now , i give up, i think i am retarded. I just cannot figure out which by which you have to multiply to get the right answer. It seems like every time its a different component that has to be divaded or multiplied.(10 votes)
- You have to multiply the bottom number/denominator with the whole number and then just stick a 1/ before product. Let’s say, 1/3 divided by 4. The bottom number would be 3, and 4 is a whole number. 4x3=12 So now we put 1/ before 12, which means the answer is 1/12(0 votes)

- This is so confusing(6 votes)
- they show too much divison and fration(6 votes)
- I need more explanation . I don't understand which number I should use to divide. 5.NF.B7(5 votes)
- You have to multiply the bottom number/denominator with the whole number and then just stick a 1/ before product. Let’s say, 1/3 divided by 4. The bottom number would be 3, and 4 is a whole number. 4x3=12 So now we put 1/ before 12, which means the answer is 1/12(0 votes)

- me to I need help to understand it's kind of confusing to me(4 votes)
- Let me try to explain this,
`1/4 ÷ 2 = 1/8`

If you now think of these numbers as,

1/4 - Total of a chocolate bar left

2 - number of groups/breaks you want to make

1/8 - Fraction of chocolate that goes into the each group

Now you can re-write this in any meaningful order,

1.`Fraction of chocolate bar in each group = Total of chocolate bar ÷ number of group`

This is,

1/8 = 1/4 ÷ 2

2.`Total of chocolate bar = Fraction of chocolate bar in each group × number of groups`

This is,

1/4 = 1/8 × 2

3.`number of groups = Total of chocolate bar ÷ Fraction of chocolate bar in each group`

This is,

2 = 1/4 ÷ 1/8(4 votes)

## Video transcript

- [Instructor] You are
likely already familiar with the relationship between
multiplication and division. For example, we know that three times six is equal to 18. But another way to express
that same relationship is to say, all right, if
three times six is 18, then if I were to start with
18 and divide it by three, that would be equal to six. Or you could say something like this, that 18 divided by, divided by six is equal to three. Now we're just going to
extend this same relationship between multiplication and division to expressions that deal with fractions. So for example, if I were to tell you that 1/4 divided by, and I'm going to color-code
it, divided by two is equal to 1/8, is equal to 1/8, how could we express this relationship, but using multiplication? Well, if 1/4 divided
by two is equal to 1/8, that means that 1/8 times
two is equal to 1/4. Let me write this down, or
I could write it like this. I could write that 1/4
is going to be equal to, is going to be equal to 1/8 times two, times two. And we could do another example. Let's say that I were to
walk up to you on the street and I were to tell you that, hey, you, 42 is equal to seven, seven divided by 1/6. In the future, we will learn
to compute things like this. But just based on what you see here, how could we express
this same relationship between 42, seven, and 1/6, but express it with multiplication? Pause this video, and think about that. Well, if 42 is equal to
seven divided by 1/6, that means that 42 times 1/6 is equal to seven. Let me write that down. This is the same relationship
as saying that 42 times 1/6, 1/6 is equal to seven. Now let's say I walk
up to you on the street and I were to say, all right, you, I'm telling you that 1/4 divided by, divided by six is equal to some number that we will express as t. So can we rewrite this relationship
between 1/4, six, and t, but instead of using
division, use multiplication? Pause this video, and
try to think about it. So if 1/4 divided by six is equal to t, based on all of the
examples we've just seen, that means that if we
were to take t times six, we would get 1/4. So we could write it
this way, t times six, times six is going to be equal to 1/4. If this isn't making sense, I really want you to think
about how this relationship is really just the same
relationship we saw up here. The only new thing here is instead of always having whole numbers, we're having fractions and representing some of
the numbers with letters.