Basic Math 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 back0020

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 here0213

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 that0787

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 sure1146

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 lessons1201

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