Basic Math Dividing Fractions and Mixed Numbers

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The next lesson is on dividing fractions including fractions that are mixed numbers.0002

In the same way that we multiply fractions,0013

when we divide fractions, we have to make sure that we have no mixed numbers.0015

If you do have mixed numbers, make sure to change them to an improper fraction.0020

When you have a fraction A/B and you are dividing it by another fraction C/D,0028

what you are going to do is take the second fraction and you are going to flip it.0035

You are just going to make this number, the top number, the bottom number.0044

Then the bottom number becomes your top number.0049

When you do that, you are going to change the division to a multiplication sign.0052

Now your problem becomes A/B times D/C.0058

You are going to multiply the fractions the same way.0065

Again take the second fraction and flip it.0069

When you flip it, it is going to go from dividing to multiplying.0074

Let's do a few examples; 2/3 divided by 3/4; I have no mixed numbers.0083

I can go ahead and work with these fractions right here, 2/3.0094

I am going to switch this sign to a multiplication sign because I am going to take this fraction right here.0101

My 4, my denominator, becomes my numerator; my numerator becomes my denominator.0110

Don't forget; if you flip the first fraction, you are going to get it wrong.0119

Make it is not the first fraction; it is the second fraction that you flip.0124

From here, I am going to multiply my numerators.0129

2 times 4 is 8; 3 times 3 is 9.0135

2/3 divided by 3/4 is 8/9.0143

The next example, 1 and 2/5 divided by 2 and 3/5.0151

Both of my fractions are mixed numbers.0156

I have to make sure to change them to improper fractions before I go ahead and divide them.0159

When you change it from a mixed number to an improper fraction, you take the bottom number 5.0167

Multiply it to your whole number and add the top number.0172

You are going to go 5 times 1 is 5; plus 2 is 7.0177

It is 7/5 divided by... 5 times 2 is 10, plus 3 is 13; 13/5.0182

Look at how I kept the division sign.0199

I can only switch it to multiplication when I flip my top and bottom numbers.0201

For now, I didn't flip it yet.0209

All I did was just convert this mixed number to an improper fraction.0210

I had to keep this sign.0214

My next step, I am going to make it a multiplication problem by flipping these.0219

My 5 now goes on the top.0226

My 13 is going to go on the bottom.0228

Remember from last lesson, if I have this problem right here, I can see if a number from the top0233

and a number from the bottom can reduce, can simplify if they have common factors.0242

7 and 13 have no common factors because they are both prime.0249

7 is a prime number; 13 is a prime number.0253

The only common factor between them would be 1.0256

This 5 and the 5 up here, they have a common factor of 5.0260

They are the same numbers so their common factor would be itself.0267

I can simplify these numbers by dividing their common factor of 5.0272

I am going to take this 5; divide it by 5 which is 1.0277

Then this number divided by 5; that also becomes 1.0282

Now I can multiply the top numbers together and then multiply my bottom numbers together.0289

7 times 1 is 7; 1 times 13 is 13; that is my answer.0295

Some more examples, 6/5 divided by 3/4.0307

Since none of these are mixed numbers, I can go ahead and just work with those.0315

Since I am dividing, I can now multiply after switching these.0324

It becomes 4/3; again you can just multiply them.0329

Just do 6 times 4, 24, over 5 times 3 which is 15; then simplify that fraction.0338

Or you can simplify the problem--this is the problem--by seeing if any numbers have common factors.0346

Again 6 and 4, this number 6 and this number 4 have a common factor of 2 because they are both even numbers.0356

But I can't cancel those out because they are both on the top.0362

Whenever you cancel numbers out, make sure that one of them is on the top and one of them is on the bottom.0368

I can only do maybe 5 and 4.0374

But they don't have any common factors besides 1.0377

6 and 3 have a common factor of 3.0381

3 divided by 3 is 1; 6 divided by 3 is 2.0388

Make sure you divide both numbers by that same factor.0394

Now I am going to multiply; 2 times 4 is 8.0401

5 times 1 is 5; that is an improper fraction.0407

But I can leave it like; that is my answer.0412

The next example, 4 and 1/4 divided by 5/3.0417

I have a mixed number; I need to convert that.0423

4 times 4 is 16; plus 1 is 17; 17/4 divided by 5/3.0427

I didn't change it yet because I didn't flip this fraction.0443

17/4 times 3/5; make sure it is the second fraction that you flip.0448

From here, let's see, 17 with 5; no, they don't have any common factors.0461

4 with 3?--nope, no common factors besides 1.0469

I have to just solve it out; 17 times 3; and then 4 times 5.0474

17 times 3; let's do that problem.0481

7 times 3 is 21; the 2 up here; 1 down here.0485

Multiply these two and then add that number.0492

3, 5; 51 over... 4 times 5 is 20; this is my answer.0494

You can change it to a mixed number if you would like.0509

All you are going to do is see how many times 20 is going to fit into 51.0512

That is going to be your whole number.0518

How many you have left over is your numerator; keep the same denominator of 20.0521

Let's just do that; 20 is going to fit into 51 two times.0527

If you do it two times, it is 51 divided by 20.0534

It is going to fit in there two times; that becomes 40.0541

I have 11 left over; I can write it like this.0545

Or I can write it like... 2 is my whole number; I have 11 left over... over 20.0551

Either fraction, improper or mixed number, is going to be your answer.0564

You can leave it this way; or you can write it this way.0568

Few more examples, 7/8; you can divide and then change this fraction.0575

9 times 3 is 27; add the 2; that is 29/9.0586

I am going to do 7/8 times 9/29.0595

8 and 9 have no common factors; 7/9 have no common factors.0606

I can go 9 with 29; I can compare those two.0611

But nothing has any common factors for me to simplify or to reduce.0617

I am going to multiply; 9 times 7 is 63; 29 times 8.0623

29 times 8; 9 times 8 is 72; 8 times 2 is 16.0632

Plus 7 is 23; that is 232.0641

I know they have no common factors because none of these were able to reduce.0653

This will be my final answer.0658

The next example, 5/4 divided by 9/11; that is my problem.0663

Before I start cancelling numbers out, I have to make sure I change this to a multiplication problem first.0674

5/4 times 11/9; don't forget to flip this one.0683

Let's see; 11 with 9--no; 11 with 4--no; 5 with 9--no.0692

None of these have any common factors for me to cross cancel numbers out.0700

5 times 11 is 55; 4 times 9 is 36; that is my answer.0710

The next couple of examples, I have 3 and 3/7 divided by 6 and 1/4.0726

These are both mixed numbers; I have to convert them to improper fractions.0734

I take my denominator of 7, multiply it to my whole number, and then add the numerator.0743

7 times 3 is 21; plus 3 is 24;0749

Then 4 times 6 is 24; plus 1 is 25.0758

Make sure you keep the same denominator.0767

Now I can go ahead and divide these fractions.0772

For me to divide fractions, I have to take my second fraction and flip it.0774

My top number is going to become my bottom number.0780

My bottom number will become the top number; let's write it right here.0782

Once I flip it, I am going to change my sign to multiplication.0790

It is going to be 24/7 times 4/25.0797

Make sure you flip the second one and not the first one.0804

If you flip the first one, you are going to get the wrong answer.0806

It is 24/7 times 4/25.0809

You are going to see if you can cancel any of these numbers out.0816

Make sure that one number is the numerator and another number is in the denominator position.0820

7 with 4, they have no common factors because 7 is a prime number.0826

24 and 25 also have no common factors.0834

You are going to have to multiply the top numbers and then multiply the bottom numbers together to get your answer.0839

24 times 4; 24 times 4; 4 times 4 is 16.0845

I put the 1 right here; 6 down there.0853

4 times 2 is 8; add the 1; 9; this becomes 96 over... 25 times 7.0856

5 times 7 is 35; I put the 3 up here; 5 right there.0869

7 times 2 is 14; plus 3 is 17; this is 175.0875

Since none of these were able to reduce or cross cancel, I know that this is my answer.0887

The next example, 2 and 4/5 divided by 10/3.0898

10/3 is an improper fraction; I can leave that as it is.0903

This one I have to convert; 5 times 2 is 10.0908

Plus the 4 is 14; 14/5 divided by 10/3.0915

I am going to flip the second fraction so that the top number and my bottom number switch positions.0930

That changes this division to multiplication; 14/5 times 3/10.0938

From here, now that it is a multiplication problem, I can see if any numbers will cross cancel.0953

5 and 3 have no common factors because they are both prime numbers.0960

14 and 10 have a common factor.0965

Before we do that, let me just point out... 5 and 10, I have a common factor of 5.0969

5 goes into both of these numbers.0977

But remember you can't cancel those out because they are both denominators.0979

They are both on the bottom.0985

When you cancel numbers out, you have to make sure that0987

one of them is on the top and another one is on the bottom.0990

Since 14 is on the top and 10 is on the bottom, I can cross cancel those numbers out.0996

A common factor between 14 and 10 is 2 because they are both even numbers.1003

I am going to take both numbers and divide it by that common factor.1011

Since the common factor is 2, I am going to divide this number by 2.1017

That is 5; then take the 14, divide it by 2; that becomes 7.1021

You have to make sure that you are going to divide by the same factor.1028

There are no more; 7 and 5, they have no common factors.1036

I can go ahead and multiply them.1041

7 times 3 is 21; 5 times 5 is 25; that is your answer.1042

Make sure when you divide fractions, number one, convert all mixed numbers to improper fractions.1058

Then you are going to switch the second fraction.1065

The top number becomes the bottom number; the bottom number becomes the top number.1069

Then you are going to multiply those fractions together.1073

That is it for this lesson; thank you for watching Educator.com.1077