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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 whole number by a fraction

Dividing a whole number by a fraction involves multiplying the whole number by the fraction's reciprocal. For example, when dividing 4 by 2/3, multiply 4 by 3/2, resulting in 12/2, which equals 6. This method demonstrates how many sections of the fraction fit into the whole number.

## Want to join the conversation?

- What's a reciprocal? (0:15)(45 votes)
- But, why does it work by using the reciprocal? How did he come to the conclusion he needs to use the reciprocal to find the correct answer?(21 votes)

- So reciprocal means to flip(17 votes)
- yes,a reciprocal means u flip.(in fractions)(11 votes)

- Am I supposed to multiply the numerators with the 4/1 (0:50)?

I'm*VERY*confused. How do I do this but in an**easier way**`?`

(note: I am very new to this)(12 votes)- Hey Neika!!

What do you mean by an easier way?

If you had a fraction like 5/6, you would multiply the "5" (as it is in the numerator) by the "4" in the fraction 4/1, as the 4, in this case, is in the numerator. Multiplying both numerators would give you 20/6, which cannot be simplified further. Did this help at all? Tell me if not.

P.S Just thought I'd like to mention that your grammar is better than almost any 10th grader I know, and education is definitely the key to freedom! Wise words from a wise person!(17 votes)

- how do you divide two whole numbers with fractions?(9 votes)
- You do the reciprocal of the second fraction but instead of dividing, you multiply.(7 votes)

- Ok I'm a bit confused about how to know what fraction to flip. In the video before this on Sal used the example of 2/3 divided by 5. he flipped the 5 to make it 1/5. So it was 2/3 X 5/1= 2/15's. In this video he flips the 2/3, which isn't the whole number. I'm a bit confused about why he didn't flip the whole number. Any help would be great thanks!(7 votes)
- You always flip the number that follows the division symbol. Some people use the phrase "keep change flip" to help them remember what to do.

"keep" means "keep the first number as is"

"change" means "change division to multiplication"

"flip" means "flip the next number".

Hope this helps.(9 votes)

- Whats a reciprocal?(3 votes)
- a rciprocal is like 1/3 is the reciprocal of 3 because 3*1/3=1 p.s might be confusing to you chase sorry if it is(10 votes)

- You explained by 2/3 fits into 4, 6 times but you never explained why it makes sense that 4 divided by 2/3 is the same thing as dividing 4 by the reciprocal. Can you please send me a video where I might have missed this explanation? Why does it make sense to multiply 4 by the reciprocal of 3/2, to solve 4 divided by 2/3?(6 votes)
- We multiply by the reciprocal while dividing because the division is basically inverse multiplication. For example, dividing by 4 is basically multiplying by 1/4. And it is the same for fractions. Dividing by 1/2 is the same thing as multiplying by 2. If you still feel confused, ask! I'll try explaining further and I bet some people on Khan might have a clearer answer.(5 votes)

- While I learned this in 5th grade, I wondered, "How come when you divide a whole number by a fraction, the answer is always bigger than either number?". Well this answers all my questions about that, thank you so much!(7 votes)
- I need help with dividing a whole number by a fraction(5 votes)
- if you have the equation 3*1/3 then you can take the three, and turn it into a fraction. 3=3/1 right? so since 3 = 3/1 then 3*1/3 = 3/1*1/3 which equals 3/3 which equals 1(5 votes)

- This is all very simple so far.(6 votes)

## Video transcript

- Let's see if we can figure
out what 4 divided by 2/3 is, and like always, pause this video, and see if you can figure
it out on your own. Well, one way to approach it is to realize that this is the same thing as 4 times the reciprocal of 2/3. So it'd be 4 times 3 over 2, and what is this
going to be equal to? You could pause the video
again if you're so inspired. Well, what you need to realize
is this is the same thing. 4 could be written as
a fraction as 4 over 1. So 4 over 1 times 3/2, and we've multiplied fractions before. To do that, you just
multiply the numerators. 4 times 3 is equal to 12, and you multiply the denominators. 1 times 2 is equal to 2. 12/2, well that's the same thing as 6. This is the same thing as 12 divided by 2, but a key question is
why does this make sense. You know, I said dividing by something is the same thing as multiplying
by the reciprocal. And to think about that,
let's draw four wholes. So let me draw it in the same red color. So let's say that this is
one whole right over here. This is two wholes. This is three wholes. And then this is four wholes. So I have four wholes there. And imagine splitting it up into groups that are each 2/3 of a whole. So actually, let me just divide everything into 1/3s real fast. So I'm gonna divide everything
into 1/3s, into 1/3s. So I'm gonna make each
group a different color. So here's one group that is 2/3. Here's another group that is 2/3. Here is another group that
is, or another section, that I could say, that represents 2/3. Here is another section
that represents 2/3. Here is another section. Folks, let me do that
in a different color. Here is, here is another section that can represent 2/3 if I take those two blue 1/3s together. That's 2/3, and then last but
not least, I have another 2/3. So how many sections that
are each 2/3 large do I have? Well, I have one, and then these is two, and then I have three,
and then I have four, and then these two combined make a, make my fifth section that is 2/3 large, and then finally, I have six. So I have six. I can take four wholes and split it into six equal sections that
are each 2/3 of a whole. So 4 divided into sections
that are 2/3 of a whole, you will get 6 sections.