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

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

### Adding and Subtracting Fractions with Different Denominators

#### Related Links

- Least common denominator (LCD): The same thing as least common multiple (LCM), but for the denominators of fractions
- To add and subtract fractions, they need to have the same denominator

### Adding and Subtracting Fractions with Different Denominators

[5/8] − [1/4]

- [5/8] − [2/8]

[6/16] − [1/4]

- [6/16] − [4/16]

[3/12] + [1/3]

- [3/12] + [4/12]

[4/15] + [3/5]

- [4/15] + [9/15]

[1/3] + [4/9]

- [3/9] + [4/9]

[12/20] − [4/10]

- [12/20] − [(4 ×2)/(10 ×2)]
- [12/20] − [8/20]

[14/15] − [2/30]

- [(14 ×2)/(15 ×2)] − [2/30]
- [28/30] − [2/30]

[3/4] − [1/2]

- [3/4] − [(1 ×2)/(2 ×2)]
- [3/4] − [2/4]

[41/95] + [2/5]

- [41/95] + [(2 ×19)/(5 ×19)]
- [41/95] + [38/95]

[1/6] + [21/42]

- [(1 ×7)/(6 ×7)] + [21/42]
- [7/42] + [21/42]

*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

### Adding and Subtracting Fractions with Different Denominators

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
- Least Common Multiple 0:12
- LCM of 6 and 4
- From LCM to LCD 2:25
- Example: Adding 1/6 with 3/4
- Extra Example 1: Add or Subtract 6:23
- Extra Example 2: Add or Subtract 9:49
- Extra Example 3: Add or Subtract 14:54
- Extra Example 4: Add or Subtract 18:14

### Basic Math Online Course

### Transcription: Adding and Subtracting Fractions with Different Denominators

*Welcome back to Educator.com.*0000

*This lesson, we are going to add and subtract fractions with different denominators.*0002

*Before we begin with that, let's review over the lesson on least common multiple, the LCM.*0013

*This I believe was a few lessons ago.*0022

*If you want, you can go back to that lesson.*0025

*We are just going to do a brief example here.*0028

*To find the LCM of 6 and 4, I am going to take the two numbers.*0031

*I am going to do the factor tree method on each of them.*0041

*For 6, a factor pair of 6 is going to be 2 and 3.*0046

*They are both prime; I am going to circle them both.*0053

*For 4, it is going to be 2 and 2; I am going to circle them.*0056

*Here, to find the LCM, I am going to look at what they have in common.*0072

*I know that I have a 2 here; I also have a 2 here.*0082

*I am going to write that 2 by itself.*0087

*This pair cancels out one of them; I am going to write a 2.*0093

*The other numbers, 3 and 2, the other remaining numbers are going to go tag along with it.*0098

*Again to find the LCM, I just find what they have in common.*0112

*Since there is a 2 here and a 2 here, one of those 2s get cancelled.*0119

*It is going to be 2 times 3 times 2.*0124

*2 times 3 is 6; 6 times 2 is 12; my LCM is 12.*0130

*The LCM of 6 and 4 is going to be 12.*0139

*LCM is the same thing as LCD.*0147

*LCM stands for least common multiple; LCD is least common denominator.*0154

*When I am using those two numbers as my denominators, then it is going to be called LCD.*0162

*But I am still going to find the LCM between those two denominators.*0170

*The reason for this, whenever I add fractions or subtract fractions,*0174

*I have to make sure that these denominators are the same.*0179

*In order to make them the same, I need to find the LCM or the LCD between the two numbers.*0184

*Here 6 and 4, just like what we did, the example, we know that the LCM is 12.*0193

*The LCM, 1/6, what I am going to do is I am going to make 1/6 the same fraction with the denominator becoming 12.*0204

*Same thing here, 3/4, the denominator is going to change to 12.*0221

*I want to figure out what these top numbers are going to be, my numerators.*0229

*How do I go from a 6 to a 12?--what do I multiply it by?*0235

*I multiplied this by 2; or I can do 12 divided by 6; I get 2.*0240

*Since I multiplied the 6 by 2 to get 12, I need to also multiply the top number by 2.*0250

*1 times 2 is 2; the fraction 1/6 became 2/12.*0258

*These are the same fractions; 1/6 is the same thing as 2/12.*0267

*Same thing here, 3/4; to go from 4 to 12, I have to multiply it by a 3.*0274

*Then I have to multiply the top number by 3; 3 times 3 is 9.*0285

*3/4, because I multiplied the top and the bottom by the same number, these fractions become the same.*0294

*They are the same fraction; 3/4 is the same thing as 9/12.*0304

*Now since I know that 2/12 is the same thing as 1/6 and 9/12 is the same thing as 3/4,*0310

*I can add these two fractions, this fraction and this fraction.*0318

*If I add these two, then my answer will be the same as if I add these two.*0330

*I have to do that because these denominators are different.*0337

*I have to make them the same by converting these fractions,*0341

*by changing these fractions so that the denominators will be the same.*0344

*Now that they are, I am going to take my numerators and add them together.*0351

*2 plus 9 is 11; here the denominator is 12; 12.*0357

*Then my denominator here has to stay the same as a 12.*0365

*2/12 plus 9/12 is 11/12; or I can say that 1/6 plus 3/4 is 11/12.*0369

*Let's do another example; here I am going to subtract.*0382

*But before I do that, I have to check my denominators.*0388

*This denominator is an 8; this one is a 4; they are different.*0391

*I have to find the LCD or the LCM between 8 and 4 so that I can make the denominators the same.*0397

*I am going to take 8 and 4; you could do the factor tree.*0407

*4 and 2; circle that one; that is a prime.*0419

*2 and 2; this is 2 and 2; look at this one.*0424

*There is a common one here; I am going to cancel out one of them.*0433

*I have another common between these two so I am going to cancel out one of them.*0438

*Then I just multiply all the remaining circled numbers.*0442

*It is 2 times 2 times 2 which is 8.*0447

*If I look at these, I can just look at them and figure out what the LCM is by looking at the multiples.*0455

*Multiples of 8 would be 8, 16, 24, and so on.*0464

*For 4, it would be 4, 8, 12, 16, and so on.*0469

*You are going to find the smallest common multiple between them which is 8.*0473

*Here I am going to change this fraction and this fraction so that their denominators will be the same.*0480

*For this fraction, 7/8, my LCM is already 8.*0489

*My LCM or my LCD, it is already 8.*0494

*For that one, I can just keep it the way it is.*0498

*For this one however, 1/4, I have to convert it; I have to change it.*0504

*I need a top number; 4; to get 8, I multiply it by 2.*0515

*Again I have to multiply the same number to the top which is 2.*0523

*Whenever you are converting fractions, as long as you multiply the top*0530

*and the bottom by the same number, then your fraction will stay the same.*0533

*Even if you change the numbers, it is still the same fraction; 1/4 became 2/8.*0538

*Now I am going to rewrite my problem, 7/8 minus 2/8.*0548

*Make sure the denominators are the same.*0556

*If they are not the same, then you did something wrong.*0558

*Go back and check your work.*0561

*Since they are the same, I can go ahead and subtract them.*0565

*7 minus 2 which is 5; then my denominator, 8.*0568

*8 here; it stays an 8 there; 7/8 minus 1/4 is going to equal 5/8.*0576

*Let's add this next problem, 9/10 plus 3/15.*0591

*Again I have to check my denominators; they are not the same.*0599

*I have to find the least common denominator with them.*0602

*I am going to take 10; do the factor tree which is 5 and 2.*0606

*Circle them if they are prime; only circle them if they are prime.*0612

*Then 15, this becomes 5 and 3.*0616

*If you are confused about how to find the LCD or LCM,*0625

*then you can go back and look at the lesson on that one before continuing.*0630

*My LCM or I am just going to call it the LCD since they are my denominators.*0636

*I look for any common numbers between them; they have a 5; 5 is common.*0642

*Whenever they have something in common, just cancel one of them out.*0650

*That is all they have in common.*0654

*Then for my LCD, I am just going to write out the remaining circled numbers.*0656

*Remember they can only be circled; 5 times 2 times 3.*0662

*5 times 2 is 10; 10 times 3 is 30; my LCD is going to be 30.*0667

*I have to change this fraction so that my denominator will become 30.*0676

*Same thing here, change this fraction so my denominator will be 30.*0681

*9/10, going to convert it; I can take 30 divided by 10; that is 3.*0688

*I know that I did 10 times 3 to get 30.*0702

*Again you have to do it to both the top and the bottom, the same number.*0707

*That is the only way you are going to have the same fraction because you don't want to change your fraction.*0711

*Even if you are changing the numbers, it is still the same fraction.*0715

*9 times 3 is 27.*0720

*I am going to do the same thing for the other fraction.*0727

*15 times 2 was 30; 3 times 2... again multiply it by the same number.*0733

*It is going to be 6.*0742

*Since 9/10 is the same thing as 27/30 and 3/15 is the same as 6/30, I need to add my new fractions.*0747

*Again double check your denominators; make sure they are the same.*0764

*It is going to be 27 plus 6.*0769

*27 plus 6 is 33 over... your denominator will stay the same.*0772

*It is 33/30; let's look at this fraction.*0785

*This is your answer; this is a solution to this problem.*0788

*But I have an improper fraction because the top number, the numerator, is bigger than the denominator.*0793

*You can either leave it like this; this is still the correct answer; or I can simplify it.*0800

*I know that a 3 goes into 33 and a 3 goes into 30.*0811

*I can take that number, the common number, the common factor between 33 and 30,*0819

*divide it to both the top and the bottom.*0828

*Remember as long as you are doing the same thing to the top and to the bottom of the fraction,*0831

*you are not changing it; you are just simplifying it.*0835

*33 divided by 3 is 11; 30 divided by 3 is 10.*0839

*This is your new improper fraction, 11/10.*0850

*Since it is an improper fraction, we can change it to a mixed number.*0854

*Or we can just leave it like that; that is fine too.*0858

*But if I do want to change it to a mixed number,*0861

*then this 10 fits into the top number 11 only one time.*0864

*10 fits into 11 only one time.*0873

*How many left over do I have?--only one.*0877

*My denominator always has to stay the same.*0881

*11/10 is the same thing as 1 and 1/10.*0884

*Another example, we are going to take 11/20 and subtract it to 11/30.*0896

*My denominators are different; I have to find the common denominator.*0903

*I can take 20; 5 is a prime number; I am going to circle it.*0910

*4, 2, and 2; I circle those; and then 30.*0918

*For this one, I can either do 3 and 10 or I can do 15 and 2, any factor pair.*0927

*Let's do 3 and 10; here 3 is a prime number; I am going to circle it.*0933

*10 is 5 and 2; they are both prime.*0939

*I am going to look for any numbers they have in common.*0945

*Here; I have a 2 here; and I have a 2 here.*0949

*I am going to cancel one of them out.*0954

*Here I have a 5; and I have a 5 here.*0957

*I am going to cancel just one of them out.*0960

*Any others?--nope, that is it.*0963

*My LCD or my LCM is going to be 2 times 2 times 5 times 3.*0967

*This is going to be 4 times 5 which is 20, times 3 which is 60; my LCD is 60.*0981

*Then my next step is going to be to change each fraction so that their denominator will become 60.*0993

*20, to figure out what you have to multiply to 20 to get 60,*1004

*I can just take 60 and divide it by 20.*1009

*This is going to be 3; 20 times 3 was 60.*1014

*Again you have to multiply the top number by the same number.*1019

*11 times 3 is 33.*1022

*For the second fraction, 11/30, 30 times 2 is 60.*1028

*Multiply the top number by that number; 22.*1040

*11/20 is the same thing as 33/60; I am going to subtract.*1047

*Then 11/30 is the same thing as 22/60.*1055

*Again double check your denominators; make sure that they are the same.*1061

*Since they are, now I can subtract; 33 minus 22 which is 11 over...*1068

*Keep your denominator the same; do not add or subtract your denominators.*1078

*11/20 minus 11/30 became 11/60.*1085

*Let's do another example; this example, 23/95 plus 4/5.*1093

*In order for me to add these two fractions, I have to make sure they have a common denominator.*1104

*In this case, they don't; 95 is this denominator; 5 is the other one.*1108

*I have to look for the common denominator.*1115

*For 95, I can either look for the LCM, the least common denominator or least common multiple, between 95 and 5.*1122

*Or I can list all the multiples out and see the smallest common multiple.*1134

*I know that 95 is divisible by 5 because any number that ends in a 5 or 0 is divisible by 5.*1143

*In this case, a 5, if this number is divisible by this number,*1156

*then this becomes the new common denominator, the least common denominator.*1162

*Or if you want to just do the factor tree to find the least common denominator, then you can do that too.*1167

*95 is going to be 5 times 19; these are both prime numbers.*1175

*I am going to circle them; 5 is just 5 and 1.*1189

*To find the LCD, I am going to look for any factors they have in common.*1197

*Here, there is a 5 here and a 5 here.*1207

*I am going to cancel only one of them out.*1210

*Whenever they have something in common, just cancel only one of them out.*1212

*Then I am going to write all the circled numbers again; 5 times 19.*1217

*This is just a 1 so I don't have to write that.*1225

*5 times 19 I know is 95.*1227

*My LCD, my least common denominator, is going to be 95.*1232

*For this fraction here, since the denominator is already 95, I don't have to change it.*1239

*This one can stay as it is.*1246

*This one however, I have to change that 5 to make it a 95 so they will have a common denominator*1250

*because that is the only way I can add these fractions, if their denominators are the same.*1256

*For this fraction right here, I need to change it so that the denominator will become 95.*1260

*I am going to take this 95, divide it by 5 to see what I have to multiply this by.*1271

*That is 19; here I am going to take this and multiply it by 19.*1281

*This will become 76; 4/5 became 76/95.*1296

*Make sure you multiply it by the same number.*1311

*You have to multiply the top and the bottom number by the same number.*1314

*That way you are not changing the fraction.*1318

*You are just changing the numbers; but they are still equal fractions.*1321

*Now I am going to do 23/95 plus 76/95.*1326

*Again I have to make sure the denominators are the same.*1340

*If they are not the same at this point, then there is something wrong.*1344

*Go back and check your work.*1347

*But since they are the same, I can go ahead and add the fractions.*1350

*23 plus 76, I am going to add the numerators together.*1354

*If I add them, it is going to be 99.*1358

*Here denominator stays the same; it is 95 here; 95 here.*1365

*My denominator is going to become 95; 23/95 plus 4/5 is 99/95.*1372

*That is it for this lesson; thank you for watching Educator.com.*1385

0 answers

Post by Karina Herrera on December 29, 2016

I really appreciate using the factor tree method for finding the LCM/LCD. I feel it's a much quicker alternative than the lengthy listing of multiples. Thank you so much for sharing it, Mary! :)

0 answers

Post by Bruno Fulep on April 5, 2014

Hi, there is a answer at the exercises that is wrong. 26/30 isn't 4/5.

0 answers

Post by Ana Chu on February 27, 2014

How did I got 14/18 and 4/16 and got the same answer???

2 answers

Last reply by: sahro AbdiOmar

Tue Nov 10, 2015 7:42 PM

Post by Wasay Ahmad on January 23, 2013

i have a question how do you know when to do LCM or LCD do you do both at the same time or one at a specific time? please help

0 answers

Post by tenzing amji on January 9, 2013

got a a+ on test!!! thanks but don't get example 2

0 answers

Post by Frank Bautista on December 17, 2012

good instructions....but...there are so many avenues where you can make mistakes because you are using too many long methods. you should also add examples in short methods.

1 answer

Last reply by: sahro AbdiOmar

Tue Nov 10, 2015 7:42 PM

Post by Leili Reza on November 16, 2012

love you, best teacher

1 answer

Last reply by: sahro AbdiOmar

Tue Nov 10, 2015 7:42 PM

Post by Ahmed Mahdi on September 17, 2012

this really great lectures. I could not emagine how much time it would have taken( time and money) if I went school for this.

I would like to know if i can get the accual book for practicing.

thanks.

2 answers

Last reply by: Julie Krills

Thu Aug 2, 2012 4:27 PM

Post by Joseph Craft on July 24, 2012

I some how missed the lesson on finding the LCM or LCD and the factor tree, plus prime numbers. Where can I find that lesson? Mary says they were in earlier lesson but I don't see them.

0 answers

Post by Walter Osborne on May 9, 2012

This lesson on fractions does help. It just seems that there are no standard rules with fractions and I guess that is what confuses me. It's starting to make sense though. Thank you.

0 answers

Post by Abdihakim Ibrahim on February 29, 2012

this helped me, thanks!

0 answers

Post by Hereaux Regis on April 9, 2011

She is a great instructor. The video is good.