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

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

### Multiplying Fractions and Mixed Numbers

#### Related Links

- Change mixed numbers to improper fractions
- Multiply the numerators together
- Multiply the denominators together
- If the product is an improper fraction, convert it to a mixed number

### Multiplying Fractions and Mixed Numbers

[1/2] ×[5/6]

[3/4] ×[1/9]

[6/11] ×[7/11]

2[1/7] ×3[3/4]

- [15/7] ×[15/4]

3[5/6] ×4[1/2]

- [23/6] ×[9/2]

4[3/4] ×6[1/6]

- [19/4] ×[37/6]

2[7/8] ×3[1/3]

- [23/8] ×[10/3]

3[5/8] ×[2/3]

- [29/8] ×[2/3]

6[1/2] ×[4/5]

- [13/2] ×[4/5]

[5/6] ×4[1/3]

- [5/6] ×[13/3]

*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

### Multiplying 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
- Multiplying Fractions
- Step 1: Change Mixed Numbers to Improper Fractions
- Step2: Multiply the Numerators Together
- Step3: Multiply the Denominators Together
- Extra Example 1: Multiplying Fractions
- Extra Example 2: Multiplying Fractions
- Extra Example 3: Multiplying Fractions
- Extra Example 4: Multiplying Fractions

- Intro 0:00
- Multiplying Fractions 0:07
- Step 1: Change Mixed Numbers to Improper Fractions
- Step2: Multiply the Numerators Together
- Step3: Multiply the Denominators Together
- Extra Example 1: Multiplying Fractions 1:37
- Extra Example 2: Multiplying Fractions 6:39
- Extra Example 3: Multiplying Fractions 10:20
- Extra Example 4: Multiplying Fractions 13:47

### Basic Math Online Course

### Transcription: Multiplying Fractions and Mixed Numbers

*Welcome back to Educator.com.*0000

*This lesson is on multiplying fractions; that includes mixed numbers.*0002

*If you are multiplying fractions and you do have mixed numbers,*0009

*then make sure to change them to improper fractions first.*0013

*I am going to do a few examples here.*0018

*But if you don't remember how to do that, just go back*0020

*to the previous lesson on switching between mixed numbers and improper fractions.*0023

*Once all of your fractions are either proper fractions or improper fractions,*0029

*then you are going to take the numerators which are the top numbers, multiply them together.*0034

*If we have A/B, A/B which are variables, they are going to represent numbers.*0042

*If this is a fraction, a number over number, times another fraction, C/D,*0050

*then you are going to take this top number, multiply it to this top number.*0057

*You get AC.*0062

*Then you are going to take your denominator, B, and multiply it to the other denominator, D.*0064

*It becomes AC/BD.*0069

*Don't get confused between multiplying and adding and subtracting fractions.*0073

*Remember when we add or subtract fractions, you have to make sure that these denominators are the same.*0078

*For your answer, your denominator is going to be the same as well.*0086

*But in this case when you are multiplying fractions, you are just going to multiply the denominators together.*0090

*Here are some examples, 2/3 times 3/4.*0099

*2/3, that is not a mixed number; 3/4 is not a mixed number.*0107

*I can go ahead and multiply them.*0112

*2/3... I am just going to write it out again... 3/4.*0116

*You can do 2 times 3 which is 6 over... 3 times 4 which is 12.*0123

*6/12, they have a common factor; they have a common factor of 2.*0132

*Or the greatest common factor, the biggest factor that they have in common, is 6.*0141

*I can just divide the top number by 6 and then divide the bottom number by 6.*0146

*This is going to become 1/2; 1/2 is going to be the answer.*0153

*Another way when you have the problem like this,*0160

*I can go ahead and simplify straight from here and get my answer as 1/2.*0163

*I can do what is called cross cancelling.*0172

*If I have a 3 down here and a 3 up there, then I can cross this out because they are the same.*0175

*They can cancel each other out.*0186

*2/4, there is a common factor between 2/4 which is 2.*0187

*I can just divide this by 2; that becomes a 1.*0193

*4 divided by 2 becomes a 2; I can simplify it that way.*0199

*Make sure if you are going to simplify two numbers,*0204

*one of the numbers has to be on the top, one of the numerators.*0206

*Another one has to be on the denominator.*0211

*It doesn't matter if one is on the top up here and the other one is a denominator here*0213

*or one is numerator up here and then the other one is a denominator here.*0217

*As long as one number is the numerator and the other number is the denominator, you can cross cancel them.*0222

*If you multiply 1 times... this is just a 1.*0231

*Then 3 cancels out to make a 1; 1 times 1 is 1.*0234

*1 times 2 is 2; either way you get the same answer.*0240

*In the other example here, I have 1 and 2/5 times 2 and 3/5.*0246

*These numbers, these fractions, are mixed numbers; I have a whole number in the front.*0253

*I have to change this fraction from a mixed number to an improper fraction, 1 and 2/5.*0259

*If I want to change this to an improper fraction, I take my bottom number, my denominator.*0275

*Multiply it to my whole number; it is going to be 5 times 1.*0281

*Then add the numerator; 5 times 1 is 5; plus 2 is 7.*0285

*This becomes 7/5; I have another mixed number here, 2 and 3/5.*0291

*I multiply my denominator to my whole number and then add my numerator.*0304

*5 times 2 is 10; I add the 3; that is 13; 13/5.*0308

*Instead of multiplying this number, the mixed number, I am going to multiply 7/5 times 13/5.*0321

*This is a 5 right here; this is a 5 right here.*0337

*I can't cancel those out because those are both numerators.*0340

*Remember if I want to cancel or simplify numbers, one of them has to be the denominator.*0343

*Another one has to be a numerator; in this case, they are both denominators.*0349

*5 to 13, nothing can simplify; I can't cancel anything out.*0358

*I am just going to go ahead and multiply my numerators.*0364

*7 times 13 is... you can use your calculator if you want.*0367

*7 times 13 is 91 over... 5 times 5 is 25.*0376

*If you look at this, they are not going to have any common factors, 91/25.*0383

*That is an improper fraction, but you can just leave it like that.*0390

*This will be my answer, 91/25.*0393

*Another example, we have 6/5 times 3/4.*0400

*6/5... let me rewrite this problem.*0406

*6/5 is an improper fraction because we know that 6 is bigger than the denominator.*0413

*This is an improper fraction.*0422

*This is a proper fraction because the numerator is smaller than the denominator.*0423

*It doesn't matter; we can still multiply it the same way.*0429

*From here, I can either just multiply it out.*0434

*If you don't feel like checking to see if numbers can cancel or can reduce,*0439

*you can just multiply and then simplify your answer.*0447

*Or you can see if you can simplify any of these numbers.*0451

*5 and 3, they have no common factors; the greatest factor is 1.*0458

*We have to leave those numbers.*0463

*But 4 and 6; 4 and 6 have the common factor of 2.*0466

*I can divide each number by 2 and just simplify that way.*0472

*4 divided by 2 is 2; 6 divided by 2 is 3.*0477

*When you cross cancel numbers, you have to make sure you are going to divide by that same number.*0484

*4 and 6, I have to divide by 2 to both numbers.*0490

*4 divided by 2; it becomes 2; 6 divided by 2; that becomes 3.*0494

*3 times 3 is 9; 5 times 2 is 10.*0504

*9/10, there are no common factors besides 1; that is my answer.*0512

*The next problem is 4 and 1/4 times 5/3.*0521

*This is a mixed number; I need to change that.*0527

*4 times 4, 16; add the 1; that is 17; 17/4 times 5/3.*0530

*Again here I need to check to see if any numbers can cancel out.*0548

*I can't because 17 and 3 have no common factors.*0555

*5 and 4 have no common factors besides 1 of course.*0559

*I can just multiply 17 times 5.*0563

*If you want to do that on the side, let's just do a little multiplication right here.*0567

*7 times 5 is 35; 5 times 1 is 5; plus 3 is 8.*0573

*Again when you have a double digit times a single digit, you are just going to do 7 times 5.*0584

*You are going to put that number, the 3... because it is 35.*0590

*The 3 goes up there; the 5 goes down here.*0594

*Then 5 times this number, 5; you are going to add this number right here.*0597

*5 times 1 plus 3; it becomes 8.*0603

*17 times 5 is 85 over... 4 times 3 is 12; this is my answer.*0606

*Some more examples; I want you guys to try to do these problems on your own.*0620

*You can just pause the video; look at these problems, write them out, and try them.*0628

*After you are done, you can play it again and just check your answers that way.*0636

*This problem, 7/8 times 3 and 2/9.*0641

*7/8 is a proper fraction; and we have a mixed number, 3 and 2/9.*0646

*Times... I need to change this.*0655

*It is 9 times 3 which is 27; plus 2 is 29; 29/9.*0657

*Remember the denominator has to stay the same.*0666

*When you are changing it from a mixed number to an improper fraction, you are going to keep the denominator.*0669

*7 and 9, do they have any common factors?--no.*0680

*8 and 29?--no, they have no common factors.*0684

*You are going to do 7 times 29; let's do that right here.*0689

*29 times 7; 9 times 7 is 63; the 6 goes up here.*0692

*The 3 goes down here below lined up with the 9 and the 7.*0702

*7 times 2 is 14; plus 6 is 20.*0707

*There is no number to carry over.*0712

*You are just going to write both numbers down here, 20; it becomes 203.*0714

*203; 8 times 9 is 72; that is your answer.*0720

*This is an improper fraction; you can leave it like that.*0732

*Or you can change it to a mixed number if you would like.*0734

*If you would like to do that, you would just take the 72.*0738

*See how many times it will fit into 203; you can do that by dividing.*0743

*You could just do 203 divided by 72 and see how many times it will go into there.*0748

*Then you find how many leftovers you have.*0755

*The leftover becomes your numerator; 72 becomes your denominator.*0759

*But otherwise just leave it like this, improper fraction.*0764

*The next example, 5/4 times 9/11.*0768

*Since we are multiplying these fractions, they are both...*0781

*5/4 is improper; 9/11 is a proper fraction; we can go ahead and multiply that*0787

*Let's see; can we cancel anything?*0794

*5 and 11, they have no common factors besides 1.*0795

*4 and 9 have no common factors besides 1.*0799

*5 times 9 is 45; 4 times 11 is 44; that is an improper fraction.*0806

*But we can still leave it like that; that is our answer, 45/44.*0820

*The last couple of examples, we have 3 and 3/7 times 6 and 1/4.*0828

*These are both mixed numbers.*0836

*Remember when we multiply fractions, we have to make sure that the fractions are not mixed numbers.*0838

*We have to change these mixed numbers to make it an improper fraction.*0846

*3 and 3/7, to change this to a mixed number, again I take the denominator of 7.*0852

*I am going to multiply it to my whole number.*0861

*It is going to be 7 times 3 which is 21.*0864

*Then you are going to add the numerator, plus 3.*0867

*It is 7 times 3 is 21; plus 3 is 24.*0871

*You are going to keep the same denominator of 7.*0879

*3 and 3/7 becomes 24/7; they are the same fraction.*0883

*But you are changing it from a mixed number to improper fraction.*0888

*We have to do this one because that is also a mixed number.*0894

*6 and 1/4, I am going to multiply my denominator to my whole number.*0898

*4 times is 6 is 24; add the 1; this is 25/4.*0904

*Now that I converted this to an improper fraction and this one as well, I can now multiply those fractions.*0913

*It becomes 24/7 times 25/4.*0921

*From here, you can just multiply your numerators.*0934

*24 times 25; get your answer; then 7 times the 4; get your denominator.*0940

*Before you do that, you can just see if you can cross cancel any numbers.*0950

*7 with 25, one has to be denominator; the other number has to be the numerator.*0956

*7 and 25, do they have any common factors?*0964

*I know that all the factors of 7 are just 1 and 7.*0969

*It is a prime number; in that case, no.*0972

*They do not have any common factors besides 1.*0975

*4 and 24, 4 and 24, they are both even numbers.*0979

*I know that since the factors of 4 are 2 and 4 and 4 goes into 26, I can reduce these numbers by 4.*0988

*I am going to take these two numbers and divide both by 4.*1000

*4 divided by 4 is 1; 24 divided by 4 is 6.*1006

*Again when you simplify it, you have to make sure that one is on the top and another one is on the bottom.*1014

*Then you are going to see what common factor they have and divide both numbers by that same factor.*1022

*That is the most I can simplify; I need to multiply 6 times 25.*1034

*You are just going to do that on the side; 25 times 6.*1043

*5 times 6 is 30; you put the 3 up here; 0 down there.*1047

*6 times 2 is 12; plus the 3 is 15.*1052

*Since you have no numbers to bring it up, you write the whole number down there.*1057

*150 over... 7 times 1 is 7; this is an improper fraction.*1062

*But you can just leave it like that; that would be the answer.*1073

*The next example, we have 2 and 4/5 times 10/3.*1078

*2 and 4/5 is a mixed number; we have to change that.*1084

*I am going to take my denominator, 5; multiply it to my whole number.*1091

*It is 5 times 2 which is 10; then add the top number.*1095

*That is 14; it will be 14/5 times 10/3.*1101

*Again you can just do numerator times the numerator and get the numerator of your solution.*1113

*5 times 3, that becomes your denominator.*1121

*Or first you can just see if any of these numbers will cancel; let's see.*1125

*14 and 10 have a common factor because they are both even numbers.*1133

*But I can't cancel those out; I can't reduce those because they are both on the top.*1139

*Remember if you want to reduce the numbers, you have to make sure*1146

*that one is on the top and one is on the bottom.*1148

*14 and 3 have no common factors.*1153

*5 and 10 have a common factor of 5.*1156

*I can take both numbers and divide it by that factor of 5.*1161

*5 divided by 5 is 1; 10 divided by 5 is 2.*1166

*You have to make sure that you are going to divide both numbers by that same factor.*1171

*Then you are going to do 14 times 2.*1178

*Now that everything is simplified here, we are going to go ahead and multiply.*1180

*It is 14 times 2 is 28; 1 times 3 is 3.*1184

*This becomes your answer; this is an improper fraction.*1197

*If you want to change it to a mixed number, you can go back a few lessons*1201

*to the lesson where I talk about how to change improper fractions to mixed numbers.*1206

*Just to change this real quick, if you want to change this to a mixed number,*1214

*I have to see how many times the 3 is going to fit into 28.*1218

*How many times 3 fits into 28; I can do that by dividing.*1223

*I do 28... this bar right here means divide.*1228

*I can do 28 divided by 3; 28; I do 3.*1231

*How many times does 3 go into 28?*1240

*Let's see, 9; 9 times 3 is 27; I have 1 left over.*1245

*You can leave it like this; this can be your answer.*1255

*Or if you need to change it to a mixed number, you are going to see how many whole numbers.*1257

*Since 3 fits into 28 nine times, 9 becomes your whole number.*1264

*Then how many you have left over, I had 1 left over.*1270

*That becomes your numerator; you are going to keep the same denominator.*1274

*28/3 or 9 and 1/3, they are both your answers.*1281

*That is it for this lesson; thank you for watching Educator.com.*1290

0 answers

Post by Rose A on February 24 at 10:21:13 PM

Hello Mary,

In example 3, you said we can divide 203/72... We end up with a decimal... Can you explain what to do than? you said how many left overs becomes your numerator, well when you divide you get 2.81...

Thanks!

0 answers

Post by Karina Herrera on December 29, 2016

Another great lesson! Thanks to you, I am now understanding cross-canceling. It is really going to come in handy.

0 answers

Post by faisal madar on November 12, 2013

cant show it better look at us

0 answers

Post by Pasi MatalamÃ¤ki on July 30, 2013

It would of been nice if you had explained cross cancelation of fractions

0 answers

Post by judy lee on August 19, 2011

Try dividing 600 wth 28, then you will get 150/7.

3 answers

Last reply by: faisal madar

Tue Nov 12, 2013 5:47 PM

Post by javier mancha on August 15, 2011

you say we can multiply , 24 our numerator x,s 25 and get our answer, which equels, 600, , . then you go on to say,, or we can , cross cancel any numbers, . which is a total diffrent answer from 600. on the second example