Basic Math 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 multiples0531

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 fractions0983

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