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### Mixed Numbers and Improper Fractions

• Mixed Number: A fraction with a whole number (e.g. 1½)
• Proper Fraction: A fraction where the numerator (top number) is smaller than the denominator (bottom number), and the fraction is less than 1 (e.g. ¾)
• Improper Fraction: A fraction where the numerator is bigger than the bottom number, and the fraction is greater than 1 (e.g. 4/3)

### Mixed Numbers and Improper Fractions

Mixed Number to Improper Fraction: 7[3/4]
• 4 ×7 + 3 = 28 + 3 = 31
[(31)/(4)]
Mixed Number to Improper Fraction: 12[5/6]
• 6 ×12 + 5 = 72 + 5 = 77
[(77)/(6)]
Improper Fraction to Mixed Number: [8/3]
2[2/3]
Improper Fraction to Mixed Number: [16/5]
3[(1)/(5)]
Improper Fraction to Mixed Number: [47/6]
7[(5)/(6)]
Improper Fraction to Mixed Number: [35/6]
5[(5)/(6)]
Improper Fraction to Mixed Number: [43/5]
8[(3)/(5)]
Mixed Number to Improper Fraction: 8[3/4]
• 4 ×8 + 3 = 32 + 3 = 35
[(35)/(4)]
Mixed Number to Improper Fraction: 12[8/9]
• 9 ×12 + 8 = 108 + 8 = 116
[(116)/(9)]
Mixed Number to Improper Fraction: 6[4/5]
• 6×5 + 4 = 30 + 4 = 34
[(34)/(5)]

*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.

### Mixed Numbers and Improper Fractions

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
• Fractions 0:10
• Mixed Number
• Proper Fraction
• Improper Fraction
• Switching Between 2:47
• Mixed Number to Improper Fraction
• Improper Fraction to Mixed Number
• Examples: Switching Fractions 6:37
• Extra Example 1: Mixed Number to Improper Fraction 8:57
• Extra Example 2: Improper Fraction to Mixed Number 9:37
• Extra Example 3: Improper Fraction to Mixed Number 10:21
• Extra Example 4: Mixed Number to Improper Fraction 11:31

### Transcription: Mixed Numbers and Improper Fractions

Welcome back to Educator.com.0000

We are going over mixed numbers and improper fractions and how to switch between the two.0002

If we look at fractions, there is three different kinds.0012

There is the mixed number, proper fractions, and improper fractions.0015

Mixed number is a fraction with a whole number.0021

If I have 1 and 1/2, the number in the front, 1, is a whole number and then 1/2 is a fraction.0026

The whole number with a fraction is called a mixed number.0035

Another example would be 5 and 3/4; that is called a mixed number.0040

A proper fraction is a fraction where the top number is smaller than the bottom number.0047

3/4 with no whole number, just 3/4, that would be a proper fraction.0058

Keep in mind that proper fractions, because the top number,0067

the numerator, is smaller than the denominator, these fractions are smaller than 10069

because if you ate 3 out of 4 pieces, then you ate less than the whole thing.0077

A proper fraction would be a fraction that is smaller than 1.0083

Improper fraction would be the opposite.0090

It is when the top number, the numerator, is bigger than the denominator.0092

Like 4/3, this is an improper fraction; again there is no whole number.0100

If there was a whole number, it would be called a mixed number.0106

An improper fraction, the top number is bigger than the bottom number.0109

If you ate 4 pieces out of 3, then you actually ate more than 1.0115

You ate 1; and you ate a little more.0122

Improper fractions are actually bigger than 1.0126

Mixed number we know is bigger than 1 because you have a whole number and you have a fraction.0131

And improper fractions are bigger than 1.0137

Since proper fractions are smaller than 1, we can't do anything to that one.0142

That one, we can't change; that one has to stay the way it is.0147

But since mixed number and improper fractions are both bigger than 1,0151

we can actually change them from mixed number to improper fraction and improper fraction to mixed number.0157

For you to be able to switch between, let's start with this one--mixed number to improper fraction.0170

If I have a mixed number, 2 and 1/2, again that is a mixed number0178

because you have a whole number in the front and you have...this is like a proper fraction.0183

It is a whole number with a proper fraction.0188

Together it is called a mixed number.0190

If I want to switch a mixed number to make it look like an improper fraction,0194

the first thing I am going to do is take this number on the bottom which is the denominator.0202

Multiply it to the whole number; it would be 2 times 2 which is 4.0208

Then you are going to add the top number--plus 1.0218

Again take the bottom number, 2, multiply it to the whole number, and add it to the top number.0223

It is 2 times 2 which is 4; plus 1 is 5.0229

That number is going to be the top number of your improper fraction.0237

It is going to be the numerator; 5 over... the denominator stays the same.0242

The denominator of the improper fraction is going to be the same as the denominator of your mixed number.0252

That does not change; 5/2.0257

Again the top number, the numerator, is bigger than the denominator.0260

We have no whole number.0265

From a mixed number, we just change that to an improper fraction.0268

Again denominator times the whole number; then add the top number.0274

If you are going to go the other way, you are going to go from an improper fraction0283

and change it to a mixed number, say I have 10/3.0286

We know this is an improper fraction because the top number, the numerator, is bigger than the denominator.0294

In this case, I want to see how many times the bottom number can fit into the top number.0302

How many times can the bottom number go into the top number?0310

I know 3 times 3 is 9.0315

That means the 3 fits into 10 three times because 10 is bigger than 9.0319

I am going to write that number as my whole number because mixed number again has a whole number.0328

You are figuring out the biggest multiple of 3 that fits into 10.0335

Again 3 goes into 10 three times which makes it a 9.0343

How many do I have left over then?0349

If 3 times 3 is 9, but this number is 10, I have 1 left over.0351

My leftover is going to be the top number of the fraction.0358

Again my denominator has to stay the same; the denominator here is 3.0365

The denominator here is going to stay 3.0370

Again to change from an improper fraction to a mixed number,0374

you are going to see how many times the bottom number will fit into 10.0378

It fits in there three times with 1 left over.0385

Then denominators both stay the same.0389

Here are some examples.0398

This is an improper fraction because again the top number is bigger than the bottom number.0401

We know this is bigger than 1.0409

Since this is an improper fraction, I want to change it to a mixed number.0413

I don't have to, but if I want to, I can switch it over.0420

In order to switch it, I see how many times the bottom number will fit into the top number.0424

How many times does 3 fit into 5?0430

3 times 1 is 3; 3 times 2 is 6; but 6 is too big.0434

Only one time; that becomes my whole number.0442

If 3 fits into 5 one time, how many do I have left over?0448

3 times 1 is 3; I have 5 here; my leftover is 2.0453

What goes down here as my denominator?--the same denominator.0461

From improper fraction, I can change it to this mixed number.0468

These mean the same thing.0472

This fraction is the same fraction as this one right here.0474

You are just writing it in different form.0477

This example here, this fraction is... can you guess?0481

Good, it is a mixed number because we have a whole number with a proper fraction.0486

Here, since this is a mixed number, I can change it to an improper fraction.0494

I take my denominator; I multiply it to my whole number.0501

Then I add it to my numerator.0509

It is 2 times 4 which is 8; plus 1.0513

That is 9 over... my denominator stays the same as a 2.0520

4 and 1/2 is the same thing as 9/2.0529

Here is another example; this right here is a mixed number.0539

We can change it to an improper fraction.0543

You take the 4, the denominator; you are going to multiply it to the 5.0547

Then you are going to add the top.0554

It is 20; plus 3 is 23; it is 23.0556

Then the denominator stays the same; the denominator is 4.0564

5 and 3/4 is the same thing as 23/4.0571

Another example, 6/7; the top number is smaller than the bottom number.0578

If I look at this and ask myself how many times does 7 go into 6?0589

It doesn't go into it at all.0596

6 is smaller than 7; 7 doesn't fit into 6.0597

This fraction is a proper fraction; this is a proper fraction.0602

I can't switch it over to the other types of fractions.0607

I can't change this to a mixed number.0610

I can't change it to an improper fraction.0612

This fraction is smaller than 1; it is called the proper fraction.0614

This fraction here, the top number is bigger than the bottom number.0624

This is an improper fraction; therefore we can change it to a mixed number.0629

Again I ask myself how many times does 8 fit into 19?0636

8 times 1 is 8; 8 times 2 is 16; 8 times 3 is 24.0644

This number right here is 19; 8 fits into 19 only two times.0652

That becomes a whole number.0662

If 8 times 2 is 16, how many are left over?0665

We do 19; subtract the 16; I have 3 left over.0671

My denominator stays the same as an 8.0677

19/8 is the same thing as 2 and 3/8.0683

This fourth example, this fraction right here is called a mixed number0693

because we have a whole number and we have a proper fraction.0697

Since I have a mixed number, I can switch this over.0703

I can change this to make it look like an improper fraction.0705

The first thing I do here is I take the denominator of 5.0711

I am going to multiply it to the whole number.0715

Then I take that number and add it to the top number, the numerator.0721

I do 5 times 8 which is 40.0726

I am going to add the top number; it is going to be 44.0730

That goes in the numerator of my improper fraction.0737

Then the denominator has to stay the same.0741

The denominator for this fraction is 5; it is going to stay a 5 here.0745

This is an improper fraction because the top number is bigger than the bottom number.0752

8 and 4/5 would be the same thing as 44/5.0760

Thank you for watching Educator.com.0767