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 Mixed Numbers

#### Related Links

- When adding/subtracting mixed numbers, add/subtract the whole numbers together and the fractions together
- If the new mixed number contains an improper fraction, convert the improper fraction into a mixed fraction

### Adding and Subtracting Mixed Numbers

2[2/6] + 3[1/2]

- 2[2/6] + 3[3/6]

3[1/7] + 3[1/4]

- 3[4/28] + 3[7/28]

6[1/2] − 2[2/6]

- 6[3/6] − 2[2/6]

12[7/8] − 5[1/2]

- 12[7/8] − 5[4/8]

6[3/5] − 2[1/10]

- 6[6/10] − 2[1/10]

6[3/5] + 7[1/10]

- 6[6/10] + 7[1/10]

9[2/9] + 6[1/2]

- 9[4/18] + 6[9/18]

4[3/7] + 12[1/3]

- 4[9/21] + 12[7/21]

15[3/4] − 3[1/6]

- 15[18/24] − 3[4/24]

6[8/9] − 2[4/6]

- 6[16/18] − 2[12/18]

*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 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
- Example 0:05
- Adding Mixed Numbers
- Extra Example 1: Adding Mixed Numbers 1:57
- Extra Example 2: Subtracting Mixed Numbers 8:13
- Extra Example 3: Adding Mixed Numbers 12:01
- Extra Example 4: Subtracting Mixed Numbers 14:54

### Basic Math Online Course

### Transcription: Adding and Subtracting Mixed Numbers

*This lesson, we are going to be adding and subtracting mixed numbers.*0000

*Remember a mixed number is a fraction with a whole number in the front.*0006

*If I have a whole number with a proper fraction, then I have a mixed number.*0012

*When I am adding mixed numbers together, the main thing here is the fraction.*0018

*We are look at fractions here.*0024

*Whole numbers, 3 and 1, we can just add them together.*0026

*For the wholes, we have 4 wholes.*0032

*Then we have the fractions that we have to worry about.*0036

*In this case, I am going to just add the whole numbers and I am going to add the fractions.*0040

*3 plus 1, the whole numbers, that is going to become my new whole number.*0047

*Then 3/5 plus 1/5.*0054

*Again from the last few lesson in adding fractions, we have to make sure that they have a common denominator.*0059

*In this case, this fraction and this fraction both have a denominator of 5.*0068

*We can go ahead and add those fractions.*0073

*It is going to be 3 plus 1; I am adding the numerators; 3 plus 1 is 4.*0075

*My denominator stays the same as always as a 5.*0081

*This mixed number plus this mixed number equals this mixed number.*0088

*When you have your answer, when you find the answer,*0095

*you have to make sure that this fraction here is a proper fraction.*0098

*Meaning the top number must be smaller than the bottom number.*0104

*If that is the case, then that is your answer, 4 and 4/5.*0110

*Let's do a few problems; we are adding 2 and 1/2 plus 2 and 2/3.*0118

*Again I am going to add the whole numbers together, this whole number and this whole number.*0129

*That is going to become 4.*0136

*Then I am going to add my fractions together, 1/2 plus 2/3.*0139

*But there is a problem; our denominators are different.*0145

*Whenever you have fractions with different denominators,*0150

*then you can't add them or subtract them until you make the denominators the same.*0155

*In order to make the denominators the same,*0162

*you have to look for the least common denominator or the least common multiple.*0165

*Between 2 and 3, the least common denominator will be 6.*0170

*The multiples of 2 would be 2, 4, 6, 8, so on.*0178

*For 3, 3, 6, 9, and so on; the least common multiple is 6.*0188

*I have to change these fractions.*0203

*I have to convert the fractions so that the denominators will become a 6.*0206

*1/2, I am going to multiply this 2 by 3 to get a 6.*0214

*2 times 3 is 6.*0226

*Whatever I do to this part, I have to do to the top.*0228

*1 times 3 is 3.*0233

*Again you have to multiply the top and the bottom by the same number.*0235

*If you don't, then it is going to be wrong because these fractions have to stay the same.*0240

*All you are doing is changing the numbers, but it is still the same fraction.*0246

*Then we have to do this next one, 2/3.*0253

*2/3, I have to change this so the denominator will become a 6.*0258

*3 times 2 became 6.*0264

*I have to multiply the top number by the same number.*0269

*It is going to be 4.*0272

*This mixed number could be the same thing as 2 and 3/6.*0276

*This one can change to 2 and 4/6.*0286

*They might look different; but they are the same thing.*0294

*This problem is the same problem as this one as long as you did everything correctly.*0297

*All you did was just change the fractions so that their denominators would be the same.*0301

*Again I am going to add the whole numbers.*0309

*It is 2 plus 2 which is 4.*0312

*Then since their denominators are the same for the fractions, I can add them.*0317

*It is going to be 3 plus 4 which is 7 over...*0322

*The denominator always stays the same; it is going to be 6.*0328

*Let's look at this answer right here; I have a problem.*0333

*Because I have 4 and 7/6, remember my mixed number, this is supposed to be a mixed number.*0339

*The mixed number has to be a whole number with a proper fraction.*0346

*But since my numerator is bigger than my denominator, this is actually an improper fraction.*0351

*I have to change this so that this will no longer be an improper fraction.*0359

*Let's just look at just this part right here, 7/6.*0366

*7/6, since it is an improper fraction, we can change this so that it becomes a mixed number.*0371

*Remember I ask myself how many times can 6 fit into the top number 7?*0381

*I know that 6 can only fit into 7 one time.*0389

*If 6 fits into 7 one time, how many do I have left over?*0395

*I only have 1 because I have 7; 7 minus 6 would be 1.*0400

*Again my denominator stays the same.*0408

*This right here, 7/6, became 1 and 1/6.*0412

*But then again I have a 4 right here; I have another whole number, 4.*0418

*I have a whole number 4; I have a whole number of 1.*0422

*Since this 4 and 7/6 is the same thing as 4 plus 7/6,*0429

*I can just take this whole number and add them together.*0442

*This will become 5 and 1/6.*0451

*Again if your answer, your mixed number, has an improper fraction, you have to take out the whole number,*0458

*change your improper fraction into a mixed number, and then add your whole number to it.*0469

*7/6 became 1 and 1/6.*0478

*I have a whole number 4 that I have to consider.*0481

*I am going to add that 4 to that mixed number.*0484

*It is going to be 5 and 1/6; that is my answer.*0487

*Another example here, I have 6 and 5/7 minus 2 and 1/5.*0495

*The main problem here is my fraction.*0505

*I have to look at my fractions, 5/7 and 1/5; my denominators are different.*0507

*I have to make sure to make a common denominator.*0516

*Normally you can do the factor tree to find the least common denominator.*0523

*But for 7 and for 5, they are both prime numbers.*0527

*If they are both prime numbers, then you can just list out all the multiples*0531

*or the first few until you find the common multiple--7, 14, 21, 28, 35.*0536

*For 5, the multiples are 5, 10, 15, 20, 25, let me continue right here, 30, 35.*0553

*I found one, 35.*0568

*You have to make sure when you find the least common denominator that it is the smallest one.*0570

*They are going to have more than one common denominator or common multiple.*0575

*You just have to make sure it is the least common multiple.*0580

*It is the smallest common multiple; in this case, it is 35.*0583

*I am going to change just this fraction.*0590

*I am going to ignore my whole number for now.*0592

*I am just going to change the fractions.*0596

*5/7, I want to make the denominator become 35.*0599

*7, what did I multiply by 7 to get 35?--multiplied 5.*0607

*Then I have to multiply this top number by 5; this becomes 25.*0614

*Then I am going to look at this fraction right here, 1/5.*0621

*5 times 7 became 35; multiply this top number by 7; get 7.*0630

*I am going to rewrite my mixed numbers, my problem, so that I will have common denominators for each of these.*0639

*This becomes 6 and 25/35 minus 2 and 7/35.*0648

*Now that I have common denominators, I can go ahead and subtract these two fractions.*0666

*Let's do 6 minus 2; the whole number is 6 minus 2 which is 4.*0673

*Then I can take my numerator here, subtract it by this numerator.*0680

*25 minus 7 is 18; my denominator stays the same as 35.*0685

*My answer here is 4 and 18/35.*0700

*Again you have to look at this fraction right here, this mixed number.*0707

*Make sure that this is a proper fraction.*0710

*Your top number, your numerator, is going to be smaller than the denominator.*0712

*This next example, 3 and 3/4 plus 4 and 1/10.*0722

*Again I have to look at my fractions because I can't add them until I have a common denominator.*0729

*In this case, you can either, just like the other examples, to find the LCD, you can list out their multiples.*0738

*Since these are not prime numbers, you can do factor trees.*0746

*I am just going to do the factor tree; this is 2 and 2.*0751

*For 10, it is going to be 5 and 2.*0759

*There is a common number of 2; cross one out.*0765

*My LCD, my least common denominator... I am going to write out all the remaining circled numbers.*0771

*2 times 2 is 4; times 5 is 20; my LCD is 20.*0783

*I am going to change these two fractions so that my denominators will become 20.*0792

*3/4; 4, I multiplied it by 5 to get a 20.*0797

*I am going to do the same thing to the top, 15.*0806

*The other fraction, 1/10; 10 times 2 became 20; 1 times 2 is 2.*0813

*Again this fraction 3/4 is the same thing as 15/20 and 1/10 is 2/20.*0825

*I am going to rewrite this problem, 3 and 15/20 plus 4 and 2/20.*0833

*I add my whole numbers together; it is going to be 7.*0851

*Then I have to add my fractions.*0856

*They have a common denominator so I can add them together.*0859

*I am going to take my numerators, 15 and 2; add them up.*0862

*I get 17 over... guess what my denominator is going to be?*0866

*20, your denominator has to stay the same.*0873

*I look at this answer.*0877

*Is my top number in my fraction smaller than my bottom number?*0879

*If it is, then it is a proper fraction.*0883

*This is going to be my answer, 7 and 17/20.*0887

*This next example, 12 and 9/11 minus 12 and 3/22.*0895

*Before I begin here, I have to make sure that the denominators for these fractions are the same.*0904

*I am looking at this fraction here and this fraction here.*0910

*Here I have an 11 as my denominator; this one, I have a 22.*0916

*I have to change these denominators so that they are the same in order for me to be able to subtract these fractions.*0922

*I need to find the least common denominator.*0930

*I am going to write out the multiples of 11--11, 22, 33, and so on.*0935

*For 22, it is going to be 22, 44, and so on.*0944

*My least common multiple is 22.*0952

*Since they are denominators, it becomes the least common denominator.*0961

*Make sure, if you are going to list out the multiples to find the LCD,*0965

*then you have to find the one that is smallest.*0969

*It has to be the smallest common multiple because these two numbers,*0973

*they are going to have more than one common multiple.*0976

*It has to be the smallest one.*0979

*Now that I have my LCD, I have to make sure that these fractions*0983

*will be converted so that I will have my denominator as 22.*0994

*This fraction right here, 9/11... I know that I have whole numbers here.*0999

*But I am just going to worry about my proper fractions first.*1004

*9/11, I want to make that denominator 22.*1009

*I take this number, 22, divide it by 11.*1017

*Or I can just figure out 11 times 2 gave me 22.*1020

*Whatever I do to that number, I have to do to the top number.*1026

*I have to multiply the top number by 2 as well.*1030

*9 times 2 is 18.*1034

*This next fraction, 3/22, the denominator is already 22.*1039

*We don't have to change it; we can just keep it the way it is.*1045

*I know that 9/11 is the same thing, is the same fraction as 18/22.*1050

*I can just rewrite this whole problem so that they will have common denominators.*1059

*12 and 18... let me erase that.*1069

*12 and 18... it has to change to this fraction right here.*1076

*12 and 18/22 minus 12 and 3/22; again double check your denominators.*1082

*Make sure that they are the same; then we can go ahead and subtract those.*1094

*For this, my whole numbers, 12 minus 12, is going to be 0.*1101

*Then I don't have to worry about my whole numbers for now.*1109

*I have to subtract my numerators; 18 minus 3 is 15.*1113

*My denominator again, it is the same as 22.*1124

*My denominator for my answer has to also stay the same; it is 15/22.*1129

*I don't have a whole number because 12 minus 12 gave me 0.*1136

*I don't have a whole number here.*1140

*Here I have to make sure when I have my fraction that this top number is smaller than the bottom number.*1144

*This is a proper fraction.*1150

*I can't simplify it because 15 and 22 do not have any common factors.*1154

*There is no number that can go into both the top number and the bottom number.*1160

*Once I ask myself all those questions and I can't simplify, then this would be my answer.*1165

*12 and 9/11 minus 12 and 3/22 became 15/22.*1173

*That is it for this lesson; thank you for watching Educator.com.*1181

0 answers

Post by Karina Herrera on December 29, 2016

Thank you for another great lesson taught, Mary! :) I like how you pace the lessons to help us follow through. It's such a bummer when a teacher is going too fast, making it harder to fully understand.

0 answers

Post by antonio cooper on March 17, 2015

On example 4 did you mean to say and write LCM instead of LCD?

1 answer

Last reply by: Professor Pyo

Sat Jan 18, 2014 2:24 PM

Post by Robin Alsoffi on January 4, 2014

Since both the numbers are prime, can we just assume that the LCM would be achieved by multiplying or are there cases where that is not least? Thanks and you have given me some good tips and reminders for improving my math skills.

0 answers

Post by Aimet Ruiz on January 29, 2013

why do you hesitate