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### Course: Arithmetic > Unit 15

Lesson 5: Dividing fractions by fractions- Understanding division of fractions
- Dividing a fraction by a whole number
- Divide fractions by whole numbers
- Meaning of the reciprocal
- Dividing a whole number by a fraction
- Dividing a whole number by a fraction with reciprocal
- Divide whole numbers by fractions
- Dividing fractions: 2/5 ÷ 7/3
- Dividing fractions: 3/5 ÷ 1/2
- Dividing fractions

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# Dividing a fraction by a whole number

Dividing fractions by whole numbers can be done visually or using multiplication. To find the result of 2/3 divided by 5, divide 2/3 into 5 equal parts, each representing 2/15 of the whole. Alternatively, multiply 2/3 by 1/5, resulting in 2/15 as the final answer.

## Want to join the conversation?

- So... Denominator times whole number = New denominator...

And the numerator stays the same?

If this makes sense, please vote up!(170 votes)- If you look up " keep change flip" It is an awesome method. He is showing it here, but the visual made it kind of confusing for me. Hope this helps!(12 votes)

- If anyone is confused, think of it like this:

1. KEEP: the first number stays the same.

2. CHANGE: turn division into multiplication

3. FLIP: All whole numbers have an invisible one and a fraction bar over them. Flip it so the one is on the bottom and your original number is on the top. For fractions, the denominator and the numerator flip

You just multiply like normal.

I hope this was helpful.(28 votes) - So.. dividing and multiplying fractions are the same?(11 votes)
- Not quite. Dividing requires the extra step of inverting the second fraction, before multiplying the fractions.

Have a blessed, wonderful day!(11 votes)

- this is pretty easy for me those who dont understand you are basically multiplying all you have to do is put a 1 on top of the whole number and then multiply hope i helped(9 votes)
- Yes this very much helped me thanks 👍(2 votes)

- why overcomplicate it by making the whole number into a fraction when you can just flip the fraction allowing you to multiply? Or is that not how this works?(7 votes)
- This doesn’t work because the numerator and denominator would be reversed in the answer.

For example, 3/4 divided by 8 is 3/4 x 1/8 = 3/32. Note that 4/3 x 8 would instead give 32/3.

Have a blessed, wonderful day!(5 votes)

- Sorry sal, but dosent make sense to me! please help me understand this in an easier way :((5 votes)
- The idea comes from dividing fractions.

There are three possibilities, fraction divided by fraction such as (4/5)/(16/15) where you flip the denominator and multiply to get (4/5)(15/16) which will reduce to 3/4.

The other two have a whole number in numerator or denominator. In this case, you can change whole number to a fraction by dividing by 1.

Examples: (5)/(20/4) = (5/1)/(20/4) = (5/1)(4/20) = 1

(20/3)/5=(20/3)/(5/1)=(20/3)(1/5)=4/3.

Converting a whole number to a fraction by dividing by 1 is important in math in Algebra for slope and other applications.(10 votes)

- If Sal had not divided had not divided all the thirds into 5 equal sections at1:02would he have gotten the answer wrong ?(7 votes)
- No he wouldn’t(0 votes)

- Why would we have to flip the fraction, like the video Sal said that you would have to flip the fraction 5/1. Can someone please explain?(3 votes)
- Whats 2/5 divided by 4/1? Does it equal 2/5 times 1/4? Figure out the answer on a piece of paper(2 votes)

- This hurts my brain. Math is evil.(4 votes)
- Math is pretty easy once you know the basics. May be hard at first, but believe me, it's worth it!(2 votes)

- i have a final on thursday(3 votes)

## Video transcript

- [Instructor] Let's
see if we can figure out what 2/3 divided by five is equal to. Pause this video and see
if you can figure this out. Well, there is a couple of
ways that we can approach it. We can first do it in a conceptual way, think about it visually. To do that, let me represent 2/3, so let's say that what I'm drawing right over here is a whole. This is a square, and
it represents a whole. Now, I can divide into
three equal sections. I'm gonna try to hand-draw that. So, this is, that looks pretty good, three equal sections here. Each is 1/3, and we have 2/3, so we are really representing all of this stuff right over here. That is two of my thirds. Now, I wanna divide those 2/3 by five. Well, the way I could do this is I could divide it into
five equal sections. But, if I'm doing it, I might as well just divide everything, all the thirds, into five equal sections,
so let me do that. So, one, two, three, and then
four, and five equal sections. So, what is one of those
five equal sections of my original 2/3? Well, this right over here is one of those five equal
sections of my original 2/3. Notice I could draw that, I
could draw another one here, another one here, another one
there, and another one there, and I would have five equal
sections that make up those 2/3. But, what does just one of them represent? And if we figure out what
this represents of the whole, then we know what 2/3 divided by five is. Well, when I took my
thirds and I divided them into five equal sections, I
essentially constructed 15ths. How do I know that? Well, I had one, two, three thirds, and then I divided it into one, two, three, four, five sections, so each of these squares
right over here is a 15th. You have three times five, and you could count 'em if you like. And, what we have circled off
in red is two of these 15ths. We have 1/15 right over here, and then 2/15 right over there. So, this is going to be equal to 2/15. Now, another way that
you could think about, and over time this is the
way you will approach it, but it's nice to think
about it conceptually, when you divide by any number, it's the same thing as
multiplying by the reciprocal. So, five is the same thing
as five wholes, or 5/1. And so, 2/3 divided by
five is the same thing as 2/3 times the reciprocal of five, or the reciprocal of 5/1,
which is you just swap the numerator and the
denominator, which is 1/5. And so, another way of
thinking about this is this is 1/5 of 2/3, which
it once again will be this section right over here. The way you could compute this, conceptually, you see that this is 2/15, but you could also say well,
I could just multiply it. When I multiply fractions I can just multiply the numerators. Two times one is two. We do that same red color. Two times one is two, and then I could multiply
the denominators. Three times five is 15. And, hopefully, what we just drew out may help make sense of
why dividing by something is the same thing as
multiplying by the reciprocal. Then, when you multiply fractions, it's the same thing as
multiplying the numerators to get our new numerator,
and then multiplying the denominators to get
our new denominator.