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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 fractions: 2/5 ÷ 7/3

Dividing fractions is a breeze when you follow these simple steps! First, multiply the first fraction by the reciprocal of the second fraction. Then, multiply the numerators and denominators separately. Voila! You've successfully divided two fractions and found your answer. Keep practicing to master this essential math skill. Created by Sal Khan.

## Want to join the conversation?

- is there another method to do this(12 votes)
- (Prepare for a long answer) Srivish, To answer your question, there IS another way to solve it. Cross multiplication. Here are some steps to help solve it

1: First take your Equation, and if you've already written an answer. Erase it, then write a new set of brackets to have your fractions in.

2: Secondly, take your equation. Let's ignore that division sign for now. So you have your two pairs of fractions, Correct?

3: TO do this, you will have to multiply a bit. First, take the numerator of your first fraction, and multiply it with the denominator of the second Fraction. This will turn into your new Numerator. Now cross off the fractions you just used.

4: Following this, Take your remaining fractions and multiply. This will turn into your new denominator. And complete your answer.

However, if your Equation with variables, such as X, the whole question will change. In order to adapt to this, you will have to change the way you solve it. Here is a link detailing how to.

https://www.wikihow.com/Cross-Multiply

Hope this helps!(26 votes)

- at 0.29 i didn't understand why we flipped it(10 votes)
- Because dividing is the same thing as multiplying by the reciprocal of a number. A reciprocal is basically just a number flipped upside down. Example: 4 ÷ 2 is the same thing as 4 * 1/2.(11 votes)

- How the
*heck*does a reciprocal even work?! I'm mind blown. Can somebody tell me why?(10 votes)- A reciprocal is when you flip the numerator and the denominator to get it. So 2/4 would become 4/2, 5/6 would become 6/5, and so forth.(5 votes)

- Do you still have to do the extra math to the side to get the actual answer.(5 votes)
- not if you feel like torchuring yourself lol (no seriously, if you dont, it'll take forever to do it).(9 votes)

- When dividing two fractions how many methods are there and what are they?(5 votes)
- I think there is only one method, but it is shown or named in several ways. KCF (keep the first fraction, change the sign from / to *, and flip the second fraction) is a common mnemonic device to help remember what to do. The words are the same method of reciprocating the denominator and multiplying.(2 votes)

- I like and respect Khan Academy, but could they make the videos fast like this one? It gets boring when to rant.(6 votes)
- oh, my gosh, i was hoping Sal would show us on the number line as is the previous video. i have no problem with solving the problem, but i have no intuitive understanding! in the last video he worked on 8/3 divided by 1/3. it meant we were breaking up 8/3 into segments of 1/3 of a unit each. so we ended up with 8 segments of 1/3 unit, total. i have no idea how to follow that logic for 2/5 divided by 7/3... help, someone? thank you!(4 votes)
- Same idea except this time the segment is larger than the initial amount. If we have segments of 7/3 (2 1/3) how many of them make 2/5. In this case you need less than one of them. 6/35 of one in fact. This is because 6/35 of 7/3 equals 2/5.(5 votes)

- At0:28I do not understand why we flipped it.(4 votes)
- What if the fraction is improper(4 votes)
- Do we always have to flip the second fraction?(3 votes)
- It makes things much easier(2 votes)

## Video transcript

So let's calculate
what 2/5 divided by 7/3 is, and I encourage
you to pause this video and try to calculate
this on your own. Well we just have to
remind ourselves that this is going to be the exact
same thing as 2 over 5 times the reciprocal of 7/3,
which is 3 over 7. And then multiplying
two fractions is pretty straightforward. This is just going to
be equal to the product of the numerators. So 2 times 3 over the
product of the denominators, over 5 times 7-- I'm trying to
keep the colors consistent-- which of course is going
to be equal to 2 times 3 is equal to 6. And 5 times 7-- I'll do this
in a new color, let's see, I haven't used this shade of
blue yet-- 5 times 7 of course is equal to 35. So this is equal to 6/35.