For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Dividing Fractions and Mixed Numbers

#### Related Links

- Change mixed numbers to improper fractions
- Flip the second fraction by switching the top and bottom numbers (that is, switch the numerator with the denominator)
- Multiply the fractions
- If the quotient is an improper fraction, convert it to a mixed number

### Dividing Fractions and Mixed Numbers

[2/5] ÷[3/4]

- [2/4] ×[4/3]

[3/7] ÷[4/5]

- [3/7] ×[5/4]

3[2/5] ÷4[1/4]

- [17/5] ÷[17/4]
- [17/5] ×[4/17]

5[1/5] ÷4[5/6]

- [26/5] ÷[29/6]
- [26/5] ×[6/29]

1[7/8] ÷3[6/11]

- [15/8] ÷[39/11]
- [15/8] ×[11/39]

[1/2] ÷3[3/4]

- [1/2] ÷[15/4]
- [1/2] ×[4/15]

[3/4] ÷5[1/2]

- [3/4] ÷[11/2]
- [3/4] ×[2/11]

[4/5] ÷4[4/6]

- [4/5] ÷[28/6]
- [4/5] ×[6/28]

6[1/2] ÷9[1/2]

- [13/2] ÷[28/2]
- [13/2] ×[2/28]

4[3/5] ÷8[4/5]

- [23/5] ÷[44/5]
- [23/5] ×[5/44]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Dividing Fractions and Mixed Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Dividing Fractions 0:09
- Step 1: Change Mixed Numbers to Improper Fractions
- Step 2: Flip the Second Fraction
- Step 3: Multiply the Fractions
- Extra Example 1: Dividing Fractions 1:23
- Extra Example 2: Dividing Fractions 5:06
- Extra Example 3: Dividing Fractions 9:34
- Extra Example 4: Dividing Fractions 12:06

### Basic Math Online Course

### Transcription: Dividing Fractions and Mixed Numbers

*Welcome back to Educator.com.*0000

*The next lesson is on dividing fractions including fractions that are mixed numbers.*0002

*In the same way that we multiply fractions,*0013

*when we divide fractions, we have to make sure that we have no mixed numbers.*0015

*If you do have mixed numbers, make sure to change them to an improper fraction.*0020

*When you have a fraction A/B and you are dividing it by another fraction C/D,*0028

*what you are going to do is take the second fraction and you are going to flip it.*0035

*You are just going to make this number, the top number, the bottom number.*0044

*Then the bottom number becomes your top number.*0049

*When you do that, you are going to change the division to a multiplication sign.*0052

*Now your problem becomes A/B times D/C.*0058

*You are going to multiply the fractions the same way.*0065

*Again take the second fraction and flip it.*0069

*When you flip it, it is going to go from dividing to multiplying.*0074

*Let's do a few examples; 2/3 divided by 3/4; I have no mixed numbers.*0083

*I can go ahead and work with these fractions right here, 2/3.*0094

*I am going to switch this sign to a multiplication sign because I am going to take this fraction right here.*0101

*My 4, my denominator, becomes my numerator; my numerator becomes my denominator.*0110

*Don't forget; if you flip the first fraction, you are going to get it wrong.*0119

*Make it is not the first fraction; it is the second fraction that you flip.*0124

*From here, I am going to multiply my numerators.*0129

*2 times 4 is 8; 3 times 3 is 9.*0135

*2/3 divided by 3/4 is 8/9.*0143

*The next example, 1 and 2/5 divided by 2 and 3/5.*0151

*Both of my fractions are mixed numbers.*0156

*I have to make sure to change them to improper fractions before I go ahead and divide them.*0159

*When you change it from a mixed number to an improper fraction, you take the bottom number 5.*0167

*Multiply it to your whole number and add the top number.*0172

*You are going to go 5 times 1 is 5; plus 2 is 7.*0177

*It is 7/5 divided by... 5 times 2 is 10, plus 3 is 13; 13/5.*0182

*Look at how I kept the division sign.*0199

*I can only switch it to multiplication when I flip my top and bottom numbers.*0201

*For now, I didn't flip it yet.*0209

*All I did was just convert this mixed number to an improper fraction.*0210

*I had to keep this sign.*0214

*My next step, I am going to make it a multiplication problem by flipping these.*0219

*My 5 now goes on the top.*0226

*My 13 is going to go on the bottom.*0228

*Remember from last lesson, if I have this problem right here, I can see if a number from the top*0233

*and a number from the bottom can reduce, can simplify if they have common factors.*0242

*7 and 13 have no common factors because they are both prime.*0249

*7 is a prime number; 13 is a prime number.*0253

*The only common factor between them would be 1.*0256

*This 5 and the 5 up here, they have a common factor of 5.*0260

*They are the same numbers so their common factor would be itself.*0267

*I can simplify these numbers by dividing their common factor of 5.*0272

*I am going to take this 5; divide it by 5 which is 1.*0277

*Then this number divided by 5; that also becomes 1.*0282

*Now I can multiply the top numbers together and then multiply my bottom numbers together.*0289

*7 times 1 is 7; 1 times 13 is 13; that is my answer.*0295

*Some more examples, 6/5 divided by 3/4.*0307

*Since none of these are mixed numbers, I can go ahead and just work with those.*0315

*Since I am dividing, I can now multiply after switching these.*0324

*It becomes 4/3; again you can just multiply them.*0329

*Just do 6 times 4, 24, over 5 times 3 which is 15; then simplify that fraction.*0338

*Or you can simplify the problem--this is the problem--by seeing if any numbers have common factors.*0346

*Again 6 and 4, this number 6 and this number 4 have a common factor of 2 because they are both even numbers.*0356

*But I can't cancel those out because they are both on the top.*0362

*Whenever you cancel numbers out, make sure that one of them is on the top and one of them is on the bottom.*0368

*I can only do maybe 5 and 4.*0374

*But they don't have any common factors besides 1.*0377

*6 and 3 have a common factor of 3.*0381

*3 divided by 3 is 1; 6 divided by 3 is 2.*0388

*Make sure you divide both numbers by that same factor.*0394

*Now I am going to multiply; 2 times 4 is 8.*0401

*5 times 1 is 5; that is an improper fraction.*0407

*But I can leave it like; that is my answer.*0412

*The next example, 4 and 1/4 divided by 5/3.*0417

*I have a mixed number; I need to convert that.*0423

*4 times 4 is 16; plus 1 is 17; 17/4 divided by 5/3.*0427

*I didn't change it yet because I didn't flip this fraction.*0443

*17/4 times 3/5; make sure it is the second fraction that you flip.*0448

*From here, let's see, 17 with 5; no, they don't have any common factors.*0461

*4 with 3?--nope, no common factors besides 1.*0469

*I have to just solve it out; 17 times 3; and then 4 times 5.*0474

*17 times 3; let's do that problem.*0481

*7 times 3 is 21; the 2 up here; 1 down here.*0485

*Multiply these two and then add that number.*0492

*3, 5; 51 over... 4 times 5 is 20; this is my answer.*0494

*You can change it to a mixed number if you would like.*0509

*All you are going to do is see how many times 20 is going to fit into 51.*0512

*That is going to be your whole number.*0518

*How many you have left over is your numerator; keep the same denominator of 20.*0521

*Let's just do that; 20 is going to fit into 51 two times.*0527

*If you do it two times, it is 51 divided by 20.*0534

*It is going to fit in there two times; that becomes 40.*0541

*I have 11 left over; I can write it like this.*0545

*Or I can write it like... 2 is my whole number; I have 11 left over... over 20.*0551

*Either fraction, improper or mixed number, is going to be your answer.*0564

*You can leave it this way; or you can write it this way.*0568

*Few more examples, 7/8; you can divide and then change this fraction.*0575

*9 times 3 is 27; add the 2; that is 29/9.*0586

*I am going to do 7/8 times 9/29.*0595

*8 and 9 have no common factors; 7/9 have no common factors.*0606

*I can go 9 with 29; I can compare those two.*0611

*But nothing has any common factors for me to simplify or to reduce.*0617

*I am going to multiply; 9 times 7 is 63; 29 times 8.*0623

*29 times 8; 9 times 8 is 72; 8 times 2 is 16.*0632

*Plus 7 is 23; that is 232.*0641

*I know they have no common factors because none of these were able to reduce.*0653

*This will be my final answer.*0658

*The next example, 5/4 divided by 9/11; that is my problem.*0663

*Before I start cancelling numbers out, I have to make sure I change this to a multiplication problem first.*0674

*5/4 times 11/9; don't forget to flip this one.*0683

*Let's see; 11 with 9--no; 11 with 4--no; 5 with 9--no.*0692

*None of these have any common factors for me to cross cancel numbers out.*0700

*5 times 11 is 55; 4 times 9 is 36; that is my answer.*0710

*The next couple of examples, I have 3 and 3/7 divided by 6 and 1/4.*0726

*These are both mixed numbers; I have to convert them to improper fractions.*0734

*I take my denominator of 7, multiply it to my whole number, and then add the numerator.*0743

*7 times 3 is 21; plus 3 is 24;*0749

*Then 4 times 6 is 24; plus 1 is 25.*0758

*Make sure you keep the same denominator.*0767

*Now I can go ahead and divide these fractions.*0772

*For me to divide fractions, I have to take my second fraction and flip it.*0774

*My top number is going to become my bottom number.*0780

*My bottom number will become the top number; let's write it right here.*0782

*Once I flip it, I am going to change my sign to multiplication.*0790

*It is going to be 24/7 times 4/25.*0797

*Make sure you flip the second one and not the first one.*0804

*If you flip the first one, you are going to get the wrong answer.*0806

*It is 24/7 times 4/25.*0809

*You are going to see if you can cancel any of these numbers out.*0816

*Make sure that one number is the numerator and another number is in the denominator position.*0820

*7 with 4, they have no common factors because 7 is a prime number.*0826

*24 and 25 also have no common factors.*0834

*You are going to have to multiply the top numbers and then multiply the bottom numbers together to get your answer.*0839

*24 times 4; 24 times 4; 4 times 4 is 16.*0845

*I put the 1 right here; 6 down there.*0853

*4 times 2 is 8; add the 1; 9; this becomes 96 over... 25 times 7.*0856

*5 times 7 is 35; I put the 3 up here; 5 right there.*0869

*7 times 2 is 14; plus 3 is 17; this is 175.*0875

*Since none of these were able to reduce or cross cancel, I know that this is my answer.*0887

*The next example, 2 and 4/5 divided by 10/3.*0898

*10/3 is an improper fraction; I can leave that as it is.*0903

*This one I have to convert; 5 times 2 is 10.*0908

*Plus the 4 is 14; 14/5 divided by 10/3.*0915

*I am going to flip the second fraction so that the top number and my bottom number switch positions.*0930

*That changes this division to multiplication; 14/5 times 3/10.*0938

*From here, now that it is a multiplication problem, I can see if any numbers will cross cancel.*0953

*5 and 3 have no common factors because they are both prime numbers.*0960

*14 and 10 have a common factor.*0965

*Before we do that, let me just point out... 5 and 10, I have a common factor of 5.*0969

*5 goes into both of these numbers.*0977

*But remember you can't cancel those out because they are both denominators.*0979

*They are both on the bottom.*0985

*When you cancel numbers out, you have to make sure that*0987

*one of them is on the top and another one is on the bottom.*0990

*Since 14 is on the top and 10 is on the bottom, I can cross cancel those numbers out.*0996

*A common factor between 14 and 10 is 2 because they are both even numbers.*1003

*I am going to take both numbers and divide it by that common factor.*1011

*Since the common factor is 2, I am going to divide this number by 2.*1017

*That is 5; then take the 14, divide it by 2; that becomes 7.*1021

*You have to make sure that you are going to divide by the same factor.*1028

*There are no more; 7 and 5, they have no common factors.*1036

*I can go ahead and multiply them.*1041

*7 times 3 is 21; 5 times 5 is 25; that is your answer.*1042

*Make sure when you divide fractions, number one, convert all mixed numbers to improper fractions.*1058

*Then you are going to switch the second fraction.*1065

*The top number becomes the bottom number; the bottom number becomes the top number.*1069

*Then you are going to multiply those fractions together.*1073

*That is it for this lesson; thank you for watching Educator.com.*1077

0 answers

Post by Mohamed Loirraqi on January 7 at 10:47:00 PM

Why we flip when we multiply?

0 answers

Post by Mohamed Loirraqi on January 7 at 10:45:16 PM

Why we flip when we multiply?

0 answers

Post by EN N on November 8, 2015

Hello,

In practice question number 9, the answer and steps are wrong. The question is 6 1/2 divided by 9 1/2. For step one it says 13/2 divided by 28/2.

0 answers

Post by Oscar Prado on September 15, 2015

How can you simplify the answer instead of the problem?

1 answer

Last reply by: Professor Pyo

Thu Jan 2, 2014 5:05 PM

Post by Dmitry Kischukov on December 26, 2013

can i multiplay like a g

_ . _ =y

r t

1 answer

Last reply by: Professor Pyo

Thu Jan 2, 2014 4:59 PM

Post by Mashrur Elahi on April 25, 2013

Can you use parentheses for fractions?

1 answer

Last reply by: Mashrur Elahi

Thu Apr 25, 2013 7:15 PM

Post by Anwar Alasmari on January 2, 2013

Yes, you can, but you may face some difficults to simplify them that you have to take into consideration the position of numbers. I think you can follow an easy way (as showed on this lecture) to solve any problems.

1 answer

Last reply by: Mary Pyo

Fri Aug 19, 2011 11:46 PM

Post by Carlos Garcia on July 19, 2011

Hello,

I have a question. Can I simplify the fractions when they are dividing before coverting it into a multiplication?