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

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

## Discussion

## Study Guides

## Practice Questions

## Download Lecture Slides

## Table of Contents

## Transcription

## Related Books

### Comparing and Ordering Fractions

#### Related Links

- > means “greater than”
- < means “less than”

### Comparing and Ordering Fractions

- [(1 ×2)/(4 ×2)] = [2/8]
- [2/8] < [3/8]

**1**)/(

**4**)] < [(

**3**)/(

**8**)]

- [(1 ×6)/(2 ×6)] = [6/12]
- [6/12] > [2/12]

**1**)/(

**2**)] > [(

**2**)/(

**12**)]

- [(4 ÷4)/(8 ÷4)] = [1/2]
- [(6 ÷6)/(12 ÷6)] = [1/2]
- [1/2] = [1/2]

**4**)/(

**8**)]

**=**[(

**6**)/(

**12**)]

- [(5 ÷5)/(20 ÷5)] = [1/4]
- [(8 ÷4)/(16 ÷4)] = [2/4]
- [1/4] < [2/4]

**5**)/(

**20**)] < [(

**8**)/(

**16**)]

- [(9 ÷3)/(27 ÷3)] = [3/9]
- [(27 ÷9)/(81 ÷9)] = [3/9]
- [3/9] = [3/9]

**9**)/(

**27**)]

**=**[(

**27**)/(

**81**)]

- [(11 ÷11)/(121 ÷11)] = [1/11]
- [8/11] > [1/11]

**8**)/(

**11**)] > [(

**11**)/(

**121**)]

- [(12 ÷3)/(18 ÷3)] = [4/6]
- [(35 ÷7)/(42 ÷7)] = [5/6]
- [4/6] < [5/6]

**12**)/(

**18**)] < [(

**35**)/(

**42**)]

- [(2 ×7)/(3 ×7)] = [14/21]
- [14/21] < [15/21]

**2**)/(

**3**)] < [(

**15**)/(

**21**)]

- [(3 ×4)/(4 ×4)] = [12/16], [(1 ×8)/(2 ×8)] = [8/16], [(5 ×2)/(8 ×2)] = [10/16]
- [6/16] < [8/16] < [10/16] < [12/16]

**6**)/(

**16**)] < [(

**1**)/(

**2**)] < [(

**5**)/(

**8**)] < [(

**3**)/(

**4**)]

- [(3 ×8)/(4 ×8)] = [24/32], [(4 ×4)/(8 ×4)] = [16/32], [(6 ×2)/(16 ×2)] = [12/32]
- [2/32] < [12/32] < [16/32] < [24/32]

**2**)/(

**32**)] < [(

**6**)/(

**16**)] < [(

**4**)/(

**8**)] < [(

**3**)/(

**4**)]

*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

### Comparing and Ordering 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
- Terms Review 0:14
- Greater Than
- Less Than
- Compare the Fractions 1:00
- Example: Comparing 2/4 and 3/4
- Example: Comparing 5/8 and 2/5
- Extra Example 1: Compare the Fractions 3:28
- Extra Example 2: Compare the Fractions 6:06
- Extra Example 3: Compare the Fractions 8:01
- Extra Example 4: Least to Greatest 9:37

### Basic Math Online Course

### Transcription: Comparing and Ordering Fractions

*Welcome back; this lesson is going to be on comparing fractions.*0000

*Since we are going to be comparing fractions, we are going to be able to order them least to greatest.*0007

*This symbol right here means greater than.*0017

*If I were to use it, if I said 5 with that symbol and another number 2,*0023

*then I can read this is as 5 is greater than 2.*0034

*This means less than; I can say 2 is less than 4.*0040

*You have to make sure that this opening is going to face the bigger number; the same with this.*0051

*We are going to use those symbols to compare fractions.*0062

*We have a fraction 2/4 and another fraction 3/4.*0069

*Let's say that this is me; this is you.*0075

*Let's say we both have the same number of candy pieces.*0086

*You have 4 pieces; I have 4 pieces.*0091

*If I ate 2 out of the 4 pieces and you ate 3 out of the 4 pieces, who ate more?*0094

*You did; my fraction, what I ate, is less than what you ate which is 3 out of 4.*0103

*We know that 2 out of 4 is less than 3 out of 4.*0115

*In the same way, 5 out of 8 with 2/5.*0124

*These denominators are different; we have different number of parts.*0131

*If I look at this, 5/8, I know that half of 8 is 4.*0141

*If I look at this, this would be greater than half because 4 out of 8 is half.*0152

*5 out of 8 is bigger than half.*0163

*2/5, if you have 5 candy pieces and you ate 2 out of those 5, then you ate less than half.*0168

*5/8 is greater than half; 2/5 is less than half.*0180

*Which one do you think is a bigger fraction?*0188

*This is bigger than half; this is less than half.*0191

*I know that this one right here, 5/8, is going to be greater than 2/5.*0197

*Let's compare this one; 1/2 and 3/4.*0211

*Again these parts, the number of parts, this is 1 out of 2 parts; this is 3 out of 4.*0219

*The total number of parts are different between the two fractions.*0226

*What I can do is I can either look at this as 1/2 and this as 3/4, 3 parts out of the 4.*0230

*That is bigger than 1/2; I can compare it that way.*0241

*Or I can make these denominators the same.*0245

*Try to make them the same equal number of parts.*0249

*That way we can just compare the number on top.*0253

*1/2, I can change this 2 to a 4 because a 4 is a multiple of 2.*0260

*If I change the 2 to a 4, to get it from 2 to 4, I multiplied by 2.*0271

*I can do the same thing for the top numbers.*0283

*If I take the top number and I multiply it by 2, then I get 2.*0285

*If you want to demonstrate this fraction becoming this fraction...*0292

*Say I have a circle, I can either cut it in half that way.*0299

*This would become 1 out of 2 parts.*0306

*Or I can cut this into 4 pieces and say that I am going to eat 1, 2 out of 4 parts.*0312

*Either way I represent this, they are the same fraction.*0325

*I changed 1/2 to 2/4; I am going to compare it to 3/4.*0335

*Again 4 pieces, I ate 2; out of 4 pieces, let's say you ate 3.*0342

*Who ate more? 2/4 is less than 3/4.*0350

*I am going to write this symbol to show that this fraction is less than this fraction.*0359

*Another example, 3/9 with 4/12.*0369

*3/9, I can take this fraction; I can change it to look different*0380

*because this fraction and this fraction, they have different number of parts.*0393

*I am going to change them so that I can look at this in a more simpler way.*0399

*3/9; if I divide a common factor of 3 to both numbers, this is the same thing as 1/3.*0405

*Out of 3 parts, this is 1.*0421

*For 4/12, I also know that there is a common factor between the top number and the bottom number.*0426

*I am going to take the common factor which is 4, divide it to the top and to the bottom.*0436

*4 divided by 4 is 1; 12 divided by 4 is 3.*0447

*3/9 became 1/3; 4/12 also became 1/3.*0456

*These two fractions are actually the same; this is 1/3, 1 out of 3 parts.*0465

*This is also 1 out of 3 parts.*0472

*I am going to write equals; these two fractions are the same.*0475

*This next example, 8/11 and 21/100; these numbers are of big.*0483

*What I can do is I can look at these fractions and see how they compare with each other.*0495

*8/11, if I have 11 total number of parts and I use up 8,*0504

*or let's say you have 11 pieces of candy and you are going to eat 8 of them.*0513

*Did you eat more than half or less than half?*0522

*I know about 5 and 1/2 is half of 11.*0525

*8 is more than half; 8 is more than half of 11.*0529

*Let's look at this one, 21/100; 21 is smaller than half of 100.*0536

*Half of 100 is 50; 21 is less than that.*0547

*This one right here is bigger than half.*0552

*This one right here is smaller than half.*0555

*If I compare them, I know, even though these numbers are smaller than these numbers,*0558

*this fraction is actually more than this fraction.*0563

*This 8/11 is going to be greater than 21/100.*0568

*This example, we are going to compare these four fractions.*0580

*We are going to order them from least to greatest.*0586

*Since we are able to compare fractions, let's see which fraction is the smallest and which fraction is the greatest.*0593

*Let's look at these--3/4, 1/6, 1/2, and 4/4.*0604

*3/4, if I think of this fraction, 3/4 is 3 out of 4 parts.*0615

*Say you have a cake that is cut up into 4 pieces.*0624

*You ate 3 out of the 4 slices; that is more than half.*0630

*1/6, if you take that same cake and you cut it up into 6 pieces.*0635

*now the pieces are smaller and you ate 1 of those.*0642

*Then you are eating less than half of your cake.*0645

*You are eating a small piece; same thing for this fraction.*0651

*You are going to take the same cake.*0655

*You are going to cut it up into 2 pieces.*0657

*You are going to eat 1 of those.*0661

*Imagine, is that going to be a big slice or a small slice?*0663

*It is going to be half of your cake.*0667

*This last one right here, 4 out of the 4.*0671

*If you cut your cake into 4 pieces and you eat all 4, you are eating the whole cake.*0674

*Which fraction is the smallest?*0684

*3/4, 3 slices out of 4, 1 slice out of 6, 1 out of 2, or 4/4?*0689

*Which one represents the smallest piece of cake?*0699

*1/6 would actually be the smallest because if you cut it up into 6 pieces,*0707

*that means you are cutting them up into smaller pieces.*0713

*You are only going to be eating one of those.*0715

*The smallest fraction is going to be 1/ 6.*0719

*The next one... I am done with this one.*0726

*The other three, the next smallest would be 1/2*0731

*because I know this one is going to be more than half the cake.*0739

*4 out of 4, that is the whole cake.*0745

*Half the cake would be the next smallest.*0748

*Then 3/4 is going to be the next smallest*0752

*because if you eat 3 out of 4 slices, you still have some cake left over.*0758

*Whereas if you eat 4 out of 4 slices, then you ate the whole cake.*0763

*The next fraction is going to be 3/4.*0768

*Then the greatest fraction is going to be 4/4.*0774

*This was the lesson on comparing fractions; thank you for watching Educator.com.*0784

0 answers

Post by Jose Guerrero on July 5, 2017

She pointed at the wrong fractions when she said bigger than half and less than half.

0 answers

Post by Genevieve Carisse on June 3, 2017

Awesome explanation!!

0 answers

Post by Karina Herrera on December 28, 2016

Thank you for the terrific instruction, Mary! :)

0 answers

Post by Sameh Mahmoud on May 11, 2014

Great, Thanks

0 answers

Post by Ana Chu on February 6, 2014

you can also do for 5/8 and 2/5 this method: 5/8= 25/40 because 8x5=40 and 5x5=25. and then, 2x8=16 and 5x8=40. they will have the same denominator of 40. 25/40 is greater than 16/40! :)

1 answer

Last reply by: Professor Pyo

Thu Jan 2, 2014 4:11 PM

Post by amera arshed on November 23, 2013

Or did you do who has more?

0 answers

Post by amera arshed on November 23, 2013

But you ate more "pieces of candy" shouldn't the opening face you?

0 answers

Post by PABLO AGREDANO on November 24, 2012

can't u also use cross multiplication to compare fractions. multiplying the denominator of one fraction to the numerator of the other fraction and then comparing the two

0 answers

Post by Leili Reza on November 14, 2012

thanks

1 answer

Last reply by: Mary Pyo

Sat Aug 20, 2011 12:28 AM

Post by judy lee on August 17, 2011

but the signs depend on what number it have on sides to decide if it is greater than or less than.Am I right?

0 answers

Post by IVAN STRICKLAND on January 30, 2011

VERY GOOD. Thanks.