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### Comparing and Ordering Fractions

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

### Comparing and Ordering Fractions

Compare the fractions [1/4] and [3/8]
• [(1 ×2)/(4 ×2)] = [2/8]
• [2/8] < [3/8]
[(1)/(4)] < [(3)/(8)]
Compare the fractions [1/2] and [2/12]
• [(1 ×6)/(2 ×6)] = [6/12]
• [6/12] > [2/12]
[(1)/(2)] > [(2)/(12)]
Compare the fractions [4/8] and [6/12]
• [(4 ÷4)/(8 ÷4)] = [1/2]
• [(6 ÷6)/(12 ÷6)] = [1/2]
• [1/2] = [1/2]
[(4)/(8)] =[(6)/(12)]
Compare the fractions [5/20] and [8/16]
• [(5 ÷5)/(20 ÷5)] = [1/4]
• [(8 ÷4)/(16 ÷4)] = [2/4]
• [1/4] < [2/4]
[(5)/(20)] < [(8)/(16)]
Compare the fractions [9/27] and [27/81]
• [(9 ÷3)/(27 ÷3)] = [3/9]
• [(27 ÷9)/(81 ÷9)] = [3/9]
• [3/9] = [3/9]
[(9)/(27)] =[(27)/(81)]
Compare the fraction [8/11] and [11/121]
• [(11 ÷11)/(121 ÷11)] = [1/11]
• [8/11] > [1/11]
[(8)/(11)] > [(11)/(121)]
Compare the fraction [12/18] and [35/42]
• [(12 ÷3)/(18 ÷3)] = [4/6]
• [(35 ÷7)/(42 ÷7)] = [5/6]
• [4/6] < [5/6]
[(12)/(18)] < [(35)/(42)]
Compare the fraction [2/3] and [15/21]
• [(2 ×7)/(3 ×7)] = [14/21]
• [14/21] < [15/21]
[(2)/(3)] < [(15)/(21)]
List in order from least to greatest [3/4],[1/2],[5/8],[6/16]
• [(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)]
List in order from least to greatest [3/4],[4/8],[2/32],[6/16]
• [(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.

### 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

### 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 different0380

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 1/20731

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 smallest0752

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