For more information, please see full course syllabus of Basic Math

For more information, please see full course syllabus of Basic Math

### Mixed Numbers and Improper Fractions

#### Related Links

- 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

- 4 ×7 + 3 = 28 + 3 = 31

**31**)/(

**4**)]

- 6 ×12 + 5 = 72 + 5 = 77

**77**)/(

**6**)]

**3**[(

**1**)/(

**5**)]

**7**[(

**5**)/(

**6**)]

**5**[(

**5**)/(

**6**)]

**8**[(

**3**)/(

**5**)]

- 4 ×8 + 3 = 32 + 3 = 35

**35**)/(

**4**)]

- 9 ×12 + 8 = 108 + 8 = 116

**116**)/(

**9**)]

- 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.

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

### Basic Math Online Course

### 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 1*0069

*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 number*0178

*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 fraction*0283

*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 number*0693

*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

2 answers

Last reply by: Jorge Abalo

Mon Dec 9, 2013 5:10 PM

Post by Wasay Ahmad on January 30, 2013

i have a question Mary what if in the part where you make the improper fraction a mixed number what if it doesn't have a leftover? ( 28/4 = 7 but there is no leftover)

0 answers

Post by Wasay Ahmad on January 15, 2013

thanks you so much i used to be very bad at fractions but now i know them really well this helped me with my homework thank you so much Mary also i hope he/she isnt skipping a grade

0 answers

Post by patrick elsworth on October 24, 2012

what a remarkable website is he/she really skipping a grade

0 answers

Post by Ramez Hajelsawi on October 1, 2012

I am skipping a grade with this education!!!!!!!! :)

0 answers

Post by Valdo Ribeiro on December 9, 2011

Outstanding!

0 answers

Post by Michelle Giacalone on June 7, 2011

Good: These videos are fantastic for helping me review my maths.

Bad: Now I'm craving pieces of candy and slices of cake!