What does 1/4 look like on a number line?

In the last lessons, you learned to think about fractions using bar models and area models.

Another way to think about fractions is using number lines!

Showing fractions on a number line can help you compare fractions.

Drawing Fractions on a Number Line

Let's try an example.

Show the fractions 1/4 and 3/4 on a number line.

1️⃣ First, draw a number line that spans from 0 to 1.

It doesn't matter how long the number line is, as long as it goes from 0 to 1. 🤓 

Be sure to mark 0 on one end, and 1 on the other end. 👍 

2️⃣ Next, look at the denominator of the fraction you want to show.

The denominator is the total number of parts the whole is divided into. It's the bottom number in a fraction.

Make 1/4

Since you want to show the fraction 1/4, you need to divide the number line into 4 equal parts or segments.

Tip: To make 4 parts, you only have to draw 3 marks! 👍

Each part of this number line is 1 out of 4 equal parts. 😎 

Each part is 1/4.

Make 3/4

Let's show the fraction 3/4 this time.

Look at the numerator.

The numerator shows the parts that we have. It's the top number.

This means that the fraction 3/4 is 3 out of 4 equal parts.

So, count 3 parts from 0, and you'll get 3/4.

That's it!

You just drew the fractions 1/4 and 3/4 on a number line!

How To Read Fractions On A Number Line

Let's learn with an example.

What fraction is shown by the yellow part on the number line?

1️⃣ First, count the number of parts the number line was divided into.

The total number of parts is the denominator.

Tip: Only count the parts between 0 and 1.

The number line is divided into 4 equal parts. ✅

This means the denominator is 4. 😃

2️⃣ Next, count the number of parts that are colored - this is your numerator.

There are 2 colored parts.

This is the numerator. 😃

3️⃣ The last step is to combine the numerator and the denominator to make the fraction.

That means the number line shows the fraction 2/4!

Great job!

Now, you know how to show and read fractions on a number line. 🎉

Next, complete the practice to help you understand more and remember for longer.

Page 2

Let's learn a few ways different ways to draw fractions.

But first...

Fractions Review

Fractions are parts of the whole.

Some examples of fractions are 1/2, 1/4, 2/3, and 3/4.

The number above the fraction bar is called the numerator. 

It describes the number of parts you have.

The number below the fraction bar is called the denominator.

It describes the total number of parts the whole is divided into.

In the last lessons, you learned how to draw fractions as bar models, as area models, and as number lines.

Let's review those 3 models, and learn 1 more!

By the end of this lesson, you'll be able to draw fractions as bar models, area models, number lines, and set models! 👍 

Fraction Bar Models - Review

A fraction bar model is where you draw a long rectangle and divide it into equal parts to show a fraction.

The denominator is how many equal parts you divide the bar into.

The numerator tells you how many parts to color.

Here are bar models for some unit fractions. 😸

Tip: unit fractions have 1 in the numerator.

Fraction Area Models - Review

In fraction area models, you color parts of a shape to show a fraction.

You can use any shape you want to represent one whole. 🤗

📣 The denominator tells you how many equal parts to divide the shape into.

📣 The numerator tells you how many parts to color.

Here are area models for some unit fractions using circles and squares. 😸

Tip: bar models are just a type of area model.

Fractions On Number Lines

Because fractions are parts of a whole, they go somewhere between 0 and 1 on the number line.

📣 The denominator tells you how many equal parts or segments to divide the line into.

📣 The numerator tells you how many parts or segments must be colored.

Here are number line models for some unit fractions. 😸

It's almost the same as the fraction bar model. But instead of a bar, we use a line! 👍

Fraction Set Model

Instead of drawing fractions as a part of one whole shape, we can draw fractions as parts of a set. Each object in the set represents one part. 

🏈 When creating fraction set models, you can use actual objects like counters, or blocks, or you can draw the objects. 🍔

Let's look at an example.

Draw a fraction set model to show that 3/8 of the counters are red.

👉 The denominator of the fraction you want to model is 8.

That means the set must have 8 counters.

😎 Each counter in the set represents 1/8 of the whole set.

This set model shows that 3/8 of the counters are red. 👇

What fraction of the counters in the set model are green?

That's right! 😁

✅ Two out of 8 counters are green.

That means 2/8 of the counters are green. 😎

Great job! 🤗

Now you've mastered fractions and their models, or drawings. 🎉

Now, complete the practice to help you remember fraction models for longer.

Page 3

Fractions tell us about parts of a whole.

The numerator is the number of parts you have. 

The denominator is the number of equal parts the whole is divided into.

There are three main types of fractions: proper fractions, improper fractions, and mixed numbers.

Let's learn a little about each type. 😺

What are Proper Fractions?

When the numerator is less than the denominator, you have a proper fraction.

Examples of Proper Fractions
1/2, 1/4, 2/3, and 5/6

What are Improper Fractions?

When the numerator is greater than or equal to the denominator, you have an improper fraction.

Examples of Improper Fractions
3/2, 4/3, 5/4, and 8/6.

Let's say you have one whole pizza plus a half pizza. 😛

You can express this using an improper fraction.

You can cut the whole pizza into two slices.

You can write this as an improper fraction:

Just imagine adding the 3 halves altogether.

1/2 + 1/2 + 1/2 = 3/2

Another Improper Fraction Example

What improper fraction does this model show?

There are 3 wholes and each whole is divided into 4 equal parts.

That means the denominator will be 4.

IMPORTANT: The denominator is not 12, even though you see a total of 12 small squares!

👉 11 parts are colored.

That's our numerator!

The improper fraction for this model is 11/4.

Another way to write an improper fraction is as the third type of fraction, called a mixed number. 😎

What are Mixed Numbers?

A mixed number is a whole number and a proper fraction combined.

Let's look at the last example again. 🤓

How many whole squares do you have colored? 🤔

Yes! 2 whole squares are colored.

What fraction can represent the third square? 🤔

That's right!

3/4 of the third square is colored.

When you combine the wholes and the fraction part, you get a mixed number 2 3/4.

These are the parts of a mixed number:

Types of Fractions Review

Now you know about the 3 types of fractions.

How to Turn Improper Fractions into Mixed Numbers

Every improper fraction can be turned into a mixed number and back.

They're just two ways of writing the same value. 

We just saw that the same drawing represents both 11/4 and 2 3/4. 😎

👉 To turn an improper fraction into a mixed number, divide the numerator by the denominator.

11 ÷ 4 = mixed number

👉 The remainder is the numerator of the mixed number.

👉 The quotient, or answer, is the whole number part.

👉 Then, just copy the denominator of the improper fraction.

Let's look at an example. 😎

What is 10/3 written as a mixed number?

Divide the numerator by the denominator. 

You get:

That means 10/3 = 3 1/3.

How to Turn Mixed Numbers Into Improper Fractions

👉 To turn mixed numbers into improper fractions, multiply the whole by the denominator.

👉 Then add the result to the numerator.

Let's look at another example. 😎

What is 1 5/8 written as an improper fraction?

1 5/8 = 13/8. ✅

Great job! You'll be able to write the book on fractions soon. 😂

Now, complete the practice. You'll learn more and remember for longer.

Page 4

In the previous lessons, you learned how to draw fraction models.  

You learned to use bar models, area models, number lines, and set models to draw fractions. 🤓

In this lesson, let's learn how to use area models to find equivalent fractions.

So What are Equivalent Fractions?

Equivalent fractions are fractions that have the same value, even though they have different numerators and denominators.

These fractions are equivalent. 👇

But how can they be equivalent if they all look different? 😣

Let's draw the area models for each fraction. 😃 

1️⃣ The first step is to draw a shape that you desire.

2️⃣ Next, divide the shape into equal parts.

The denominator tells you how many equal parts to divide the shape into.

3️⃣ The last step is to color some parts.

The numerator tells you how many parts to color.

This is the area model for the fraction 2/4. 👇

This is the area model for the fraction 4/8.

And here is the area model for the fraction 3/6.

Did you notice that the area of the colored part for each of the fractions is the same?

1/2 of each model is colored. 😁

That means the fraction 1/2 is also equivalent to these fractions!

How to Find Equivalent Fractions

Let's try to find a fraction equivalent to 2/3.

First, draw an area model for 2/3.

Next, draw an identical model.

To make an equivalent fraction, divide each part into more equal parts.

Let's divide each part of the identical model into 2 equal parts. ✅ 

What fraction does the identical model show now? 🤔

That's right!

👉 The identical model is divided into 6 equal parts and 4 parts are colored.

So the identical model shows the fraction 4/6. 👍

Here we can see that 2/4 = 4/6, because the two fractions show the same part of a whole.

Another Example

Find a fraction equivalent to 3/4.

👉 First, draw the area model for 3/4.

👉 Next, draw an identical model.

👉 Now divide each part of the identical model into 2 equal parts.

What fraction does the identical model show now? 🤔

That's right! 👍

👉 The identical model is divided into 8 equal parts and 6 parts are colored.

That means the identical model shows the fraction 6/8. 😁

✅ Therefore, 3/4 = 6/8.

🤔 What about if we divide each part of the identical model into 4 equal parts?

What fraction does the identical model show now? 🤔

👍 That's right!

👉 The identical model is divided into 16 equal parts, and 12 parts are colored.

So it shows the fraction 12/16. 😉

✅ That means 3/4 = 12/16.

🤓 We can see that:

These are all equivalent fractions!

Equivalent fractions may not look the same but as long as they refer to the same value, then they are equivalent.

Tip: If you multiply the numerator and the denominator by the same number, you'll get an equivalent fraction! 

1/1 = 2/2 = 3/3

Great job! 🎉

Now, complete the practice. 🏄 You'll understand more and remember for longer.

Page 5

Equivalent fractions are fractions that have equal value, even though they may look different.

Here are some examples of equivalent fractions:

You already learned to find equivalent fractions using area models. 🤗

👉 In this lesson, we'll learn to recognize, or spot, equivalent fractions using number lines.

Fractions On A Number Line Review

Draw a number line that goes from 0 to 1.

The denominator tells you how many equal parts to divide the number line into. 😀

The numerator tells you how many parts to color.

Here are some of the fractions marked on a number line.

These three fractions are equivalent.

How can you tell? 🤔

First, look at the number line model for 2/4.

Next, look at the number line model for 4/8.

Then, look at the number line model for 3/6.

They're all the same length!

Equivalent fractions have the same length on a number line.

Finding Equivalent Fraction

Let's try an example.

Find a fraction equivalent to 2/3.

First, draw a number line model for 2/3.

Next, draw a second identical one below that.

Now, divide the second line into smaller parts.

What fraction of the number line is colored? 🤔

Yes, 4/₆! Because 4 out of 6 parts are colored.

Are the two fractions the same length?

Yes.

This means 2/3 is equivalent to 4/6! ✅ 

Another Example

Are 3/4 and 4/6 equivalent?

👉 First, draw the number line model for 3/4.

👉 Next, draw the number line model for 4/6.

 Compare the length of 3/4 and 4/6.

Are they the same length?

👉 No, they're not!

3/4 is longer than 4/6.

 This means that 3/4 and 4/6 are NOT equivalent. ❎😎

Great job! 🎉 You just learned how to recognize equivalent fractions using number lines.

Now, complete the practice. 😺 

Page 6

There are three types of fractions: proper fractions, improper fractions, and mixed numbers.

Proper fractions have a numerator smaller than the denominator, like 1/2.

Improper fractions have numerators greater than or equal to their denominators. Examples are 7/6, 12/10, or 4/4.

Mixed numbers are combinations of a whole number and a proper fraction, like 2 1/4 or 6 3/5.

Whole numbers are numbers that don't have fractions, like 1, 2, and 10.

Did you know that every whole number can be written as a fraction, too? 🤔

👉 Yes, we can just divide it by 1! 

Writing Whole Numbers as Fractions

You can write any whole number as an equivalent fraction just by dividing it by 1.

An equivalent fraction for 1 is:

1/1

So what's an equivalent fraction to 2?

Yes, 2/1 !

Awesome.

Now, how can you tell if a fraction is equivalent, or equal to, a whole number? 🤔

Fractions Equivalent to Whole Numbers

If you can divide the numerator by the denominator without any remainder, the fraction is equivalent, or equal to, a whole number.

Let's look at the improper fraction 2/2.

Is it equivalent to a whole number? 🤔

Yes! We can divide the numerator (2) by the denominator (2) without any remainder. 

So 2/2 is equivalent to a whole number. 👍

Let's look at the area model for 2/2 to make sure:

Yes, 2/2 is equal to the whole number 1!

Another Example

Is 6/3 equivalent to a whole number?

The denominator is 3.

That means each part is 1/3 of the whole.

You have six 1/3 parts because the numerator is 6.

So the area model for the six 1/3 parts is:

Notice how you can combine three 1/3 parts to make one whole.

How many wholes do you have now? 🤔

👍 That's right! You have 2 wholes.

That means 6/3 is equivalent to 2 wholes!

Let's check using division:

6 ÷ 3 = 2

We get the same answer! 😀

When the numerator is divisible by the denominator, the fraction is equivalent to a whole number.

If the numerator is equal to the denominator, it always equals one whole, or 1.

Here are some examples of fractions equivalent to one whole.

Great job learning about fractions equivalent to whole numbers! 🎉

Now, complete the practice. It'll help you understand more and remember for longer. 💪

Page 7

Equivalent fractions are fractions with the same value, even if their numerators and denominators are different. 

3/6 is equivalent to 1/2.

Some equivalent fractions are simpler than others.

A fraction is in its simplest form when the numerator and denominator cannot both be divided by any number other than 1.

Can we simplify 3/6?

Yes! 3 and 6 are both multiples of 3. 

So we can divide both the numerator and denominator by 3.

(3 ÷ 3) / (6 ÷ 3)

We end up with:

1/2

Can we simplify 1/2 any further? 

Nope, there's no number, other than 1, that can divide both the numerator and denominator.

So 1/2 is the simplest form of 3/6! 🎉

Tip: You can also say 1/2 is the lowest term of 3/6.

Steps to Simplifying Fractions to their Lowest Terms

A fraction is in its simplest form if the numerator and the denominator can't be divided by a common number, other than 1.

So, how do you simplify a fraction to its lowest term? 🤔

👉 To simplify a fraction, divide both numerator and denominator by the same number until you can't divide away anymore.

Let's look at an example. 😀

Simplify the fraction 18/48.

What number can you use to divide both 18 and 48? 🤔

We can divide both by 2. Both are even numbers.

Tip: This doesn't change the value of the fraction, because we're dividing by (2 / 2), which is dividing by 1, which doesn't change the number. 👍🤯 

We get 9/24. It's a simpler fraction that's equivalent to 18/48.

But it's not the simplest form yet.  

What number can we divide 9 and 24 by? 🤔 

Yes! Both 9 and 24 are divisible by 3.

Let's further divide 9 and 24 by 3:

Now we have 3 equivalent fractions! 😃

18/48 = 9/24 = 3/8

🤔 Our numerator is now 3, and our denominator is 8. Can you divide 3 and 8 further?

Not anymore.

So the lowest term of 18/48 is 3/8. ✅

That's the simplest form of this fraction.

Simplifying Fractions Example

Simplify the fraction 135/180.

🤔 What number can we use to divide both 135 and 180?

5 could be a good choice since the numerator ends in 5, and the denominator ends in 0. ✅ 

Let's divide the numerator and denominator by 5. 😃

Wow! 27/36 is way more simple than 135/180. 😁

🤔 Can we further divide 27 and 36 by the same number?

✅ Yes! 27 and 36 are both divisible by 9.

We got 3/4! We can't simplify this any further.

That's the simplest we can go. 🤗

So, the simplest form of 135/180 is 3/4. ✅

Simplifying Fraction Tips

To simplify a fraction to its lowest term, divide the numerator and the denominator by the same number. 

Keep on dividing, until you can't find any common, or shared factors to divide away. 

The last fraction you get is the lowest term.

🌟 Always remember that you need to divide both the numerator and the denominator by the same number.

Now, practice simplifying fractions on your own. 😺 It's a useful skill.

Page 8

Equivalent fractions have the same value, even if their numerators and denominators are different.

In the last lessons, you learned to draw area models and number lines to recognize equivalent fractions.

But drawing models and number lines can be quite slow. 😌

Imagine drawing a model for 17/20!

Don't worry. 😃 There are faster ways to find equivalent fractions - you can use multiplication and division!

Equivalent Fractions Review

Equivalent fractions have the same value.

They look different, but their values are the same.

How to Use Division to Find Equivalent Fractions

In the last lesson, you learned to simplify fractions by dividing both the numerator and the denominator by the same number:

Simplifying fractions is a way of using division to find equivalent fractions! 

😎 Think about this: If you can find equivalent fractions by dividing, can you also find equivalent fractions by multiplying?

Yes, you can! 👍

Equivalent Fractions by Multiplication

If you multiply both the numerator and denominator by the same number, you'll get an equivalent fraction!

Just like when dividing, be sure to multiply the numerator and the denominator by the same number. 👍

Equivalent Fractions Practice

Try to use multiplication and division to solve this problem:

Find two fractions equivalent to 6/9.

Let's use division first.

What's the biggest number that you can divide both 6 and 9 by? 🤔 

That's right! Both numbers are divisible by 3. 👍

2/3 is equivalent to 6/9.

👉 Now, let's use multiplication.

Let's try to multiply 6 and 9 by 2.

We get 12/18.

We now have 2 equivalent fractions for 6/9! 🤗

They are 2/3 and 12/18! ✅ 

So What Did We Learn?

To make equivalent fractions, multiply or divide both the numerator and the denominator by the same number.

Great job learning how to find equivalent fractions! 😀

Now, complete the practice. You'll understand more and remember for longer.

Page 9

So far, you've learned how to draw fractions using models. 

You can also use those models to compare fractions!

Comparing fractions means seeing which fraction is larger or smaller.

Let's look at an example.

Your sister ate 3/8 of a pizza and your brother ate 5/8 of that pizza. Who ate the larger part of the pizza?

The pizza was divided into 8 equal slices. 😋

This means each slice is 1/8 of the whole pizza.

If your sister ate 3/8 of the pizza, how many slices did she eat? 👸

👍 That's right!

She ate 3 slices. ✅ 

If your brother ate 5/8 of the pizza, how many slices did he eat? 👲

👍 That's right!

 He ate 5 slices. ✅

😃 So your brother ate a larger part of the pizza.

Now let's learn another way to compare fractions.

Comparing Fractions Using Bar Models

Which fraction is bigger: 3/4 or 2/3?

Let's draw a bar model for 3/4, and another one for 2/3. 😀

Make sure that the 2 bar models have the same size.

Which fraction has more colored area? 🤔

👍 That's right!

3/4 has a bigger colored area than 2/3. 🤓

This means that 3/4 is bigger than 2/3. ✅ 

Now, complete the practice to help you understand more.

Page 10

In a previous lesson, you learned how to draw fractions on number lines. 

Now you can use your number line skills to compare fractions!

Comparing fractions means seeing which is larger or smaller.

A fraction is larger if it's farther from 0 on the number line.

A fraction is smaller if it's closer to 0 on the number line.

Let's learn from an example.

These are the number line models for halves and thirds.

The number lines show that 1/2 is farther from 0 than 1/3.

This means that 1/2 is greater than 1/3!

You can also see that 2/3 is farther from 0 than 1/2 or 1/3.

This means 2/3 is greater than 1/2 or 1/3.

Another Example

Compare these two fractions. 😀

Which fraction is bigger: 2/3 or 3/4?

First, draw a number line model for 2/3.

Next, draw the number line model for 3/4 . Place it under the number line model for 2/3.

Tip: Make sure the number lines are of the same length.

Which fraction is farther from 0? 🤔

That's right, 3/4 is farther from 0 than 2/3. 👍

This means that 3/4 is greater than 2/3.

Great job! 😃

Now, complete the practice. 💪 You'll learn more and remember for longer.

Page 11

Fractions describe parts of a whole.

Fractions with the same denominators are divided into the same number of equal parts.

To compare fractions with the same denominators, just compare their numerators!

Let's Compare Fractions

Example 1

Which is greater, 5/8 or 3/8?

How do you compare 2 fractions without drawing models? 🤔 

For fractions with the same denominators, the fraction with the larger numerator is greater!

Since 5 > 3, you know that 5/8 is greater than 3/8.

That was really fast! 🚀

Example 2

Which fraction is the largest: 4/6, 3/6, or 5/6?

These fractions have the same denominators.

So, all we need to do is to compare the numerators.

👉 4 is greater than 3.

That means 4/6 is bigger than 3/6.

👉 5 is greater than 4.

That means 5/6 is bigger than 4/6.

This means 5/6 is the biggest.

Let's check if we're right. 😁

We can see from the bar models that, yes, 5/6 is the biggest.

Final Example

June went to the hardware store to purchase a blue rope and a green rope. The length of the blue rope is 6/8 of a yard. The length of the green rope is 7/8 of a yard. Which rope was longer?

We need to find which rope is longer. 😀

How? 🤔

We need to compare the lengths of the 2 ropes. 😎

6/8 and 7/8 have the same denominators.

So, we just compare the numerators. 😁

Since 7 is greater than 6, that means 7/8 is bigger than 6/8.

So, the green rope is longer than the blue rope! 😁

Now, complete the practice. 😺 You'll learn more and remember for longer.

Page 12

So far, you've learned to compare fractions with the same denominators.

In this lesson, you'll learn how to compare fractions with the same numerators!

Let's Review

Fractions show parts of a whole.

The bigger the denominator, the smaller each part becomes.

Let's compare 1/6 and 1/8 using models.

From the models, you can see that 1/8 is smaller than 1/6.

To compare fractions with the same numerator, just compare their denominators. The fraction with the bigger denominator is smaller.

Let's Compare Fractions

Example 1

Which is greater, 5/8 or 5/6?

So, how do you compare these 2 fractions without drawing models? 🤔 

Since they have the same numerators, just compare their denominators! 😁

When the numerators are the same, the fraction with the larger denominator is the smaller fraction!

The denominators are 8 and 6.

8 is greater than 6.

So, we know that 5/8 is smaller than 5/6. ✅ 

Example 2

Which fraction is the smallest: 3/8, 3/6, or 3/4?

These fractions have the same numerators. They're all 3.

👉 So we just need to compare the denominators.

The denominators are 8, 6, and 4.

8 is the largest denominator. 

So the smallest fraction is 3/8.✅

Let's check our answer by using bar models. 👍

We can see from the bar models that, yes, 3/8 is the smallest.

So What Did You Learn?

Fractions with the same numerator but larger denominator are actually smaller!

Now, complete the practice. 😸 You'll learn more and remember for longer.

Page 13

In the last lessons, you learned how to compare fractions with like denominators and like numerators.

Now let's learn to compare fractions with both different denominators and different numerators.

First, we'll show you a slow way using equivalent fractions. Then we'll show you a secret superfast trick at the end. 🏎

Equivalent Fractions Review

Equivalent fractions have the same value, but different numerators and denominators, like 1/2 and 2/4.

You can find an equivalent fraction either by dividing or multiplying both the numerator and denominator by the same number.

Can you find any equivalent fractions for 6/9?

👉 Let's try to divide both the numerator and the denominator by 3.

We get 2/3, an equivalent fraction ✅. 

We can also multiply the numerator and the denominator of 6/9 by 2.

We get another equivalent fraction, 12/18.

Comparing Fractions Example

Which fraction is bigger: 1/2 or 2/3?

1/2 and 2/3 do not have the same numerators, nor do they have the same denominators. 🙈

So let's find some equivalent fractions for 1/2. 😁

We use multiplication to do this.

Tip: It's kind of like skip counting with fractions.

Next, list some equivalent fractions for 2/3. 😀

Can you see a pair of equivalent fractions that are easy to compare? 🤔 

Yes!

It's easy to compare 3/6 and 4/6 because they have the same denominators.

Since 3/6 and 4/6 have the same denominators, just compare the numerators.

3/6 is smaller than 4/6.

3/6 < 4/6
1/2 < 2/3 ✅

Secret Trick

Let's try comparing 1/2 and 2/3 using a secret trick!

Here's what it looks like. 👇 We'll explain it in words.

1️⃣ First, multiply the numerator and denominator of 1/2 by the denominator of the other fraction 2/3.

This shows us that 1/2 is equivalent to 3/6.

2️⃣ Then we multiply the numerator and denominator of the other fraction 2/3 with the denominator of 1/2.

So we see that 2/3 is equivalent to 4/6.

3️⃣ Finally, we compare 3/6 and 4/6 because they have the same denominator.

3/6 < 4/6
1/2 < 2/3 ✅

So What Did You Learn?

When comparing fractions with unlike, or different, denominators, you can multiply each fraction's denominator and numerator by the other fraction's denominator to get equivalent fractions with a common denominator. Then compare the equivalent fractions.

It's a math trick that works every time! 🧙‍♂️

Super Secret Mega Fast Comparing Fractions Trick

Did you think that was the fast trick? Nope!

Now, you're ready for the fastest trick of all! 🏎

Here's what it looks like:

To compare two fractions quickly, just multiply the denominator of one fraction with the numerator of the other. 

The numerator with the biggest crisscross is the largest fraction. 🏄

Let's try it. What's bigger, 1/4 or 5/6?

The first crisscross is 6.

The next crisscross is 20.

So 5/6 is greater!

Great job learning to compare fractions!

Now, complete the practice. 😺 You'll understand more and remember for longer.

Page 14

In the last lesson, you learned how to compare fractions.

Let's use this knowledge to order fractions, which means sorting them from smallest to largest. 👍

Comparing Fraction Review

There are shortcuts to comparing fractions with like numerators and like denominators.

When 2 fractions have the same numerator, just compare denominators.

The bigger the denominator, the smaller the fraction.

Remember: The bigger the denominator, the more parts the whole is split into, so each piece is smaller.

When 2 fractions have the same denominator, just compare numerators.

The bigger the numerator, the bigger the fraction.

If fractions don't have the same numerator or denominator, find equivalent fractions that have either the same numerator or denominator.

Ordering Fractions with the Same Numerators

When ordering fractions with the same numerators, look at the denominators and compare them 2 at a time.

👉 The fraction with the biggest denominator is the smallest.

Let's look at an example.

Order these fractions from least to greatest:

The fractions have the same numerators, so you just need to compare their denominators.

1/6 has the largest denominator.

This means 1/6 is the smallest fraction. 👍

The larger the denominator, the smaller the fraction.

We've re-arranged the fractions from least to greatest.

Ordering Fractions with the Same Denominators

When ordering fractions with the same denominators, look at the numerators and compare them 2 at a time.

👉 The fraction with the smallest numerator is the smallest.

Let's look at an example.

Order these fractions from least to greatest:

These fractions have the same denominators, so you just need to compare their numerators.

3/8 has the smallest numerator.

This means 3/8 is the smallest fraction. 👍

This is how we order these fractions from the least to the greatest:

Ordering Fractions with Different Numerators and Denominators

When ordering fractions with different numerators and denominators, write the fractions as equivalent fractions with like denominators.

Tip: Like means "the same". Unlike means "different".

Let's look at an example.

Order these fractions from least to greatest:

👉 First, find some equivalent fractions for each fraction using multiplication.

👉 Next, pick the equivalent fractions that have the same denominators for all three fractions.

Be careful when picking the equivalent fractions to compare!

Make sure that they all have the same denominators.

8/12, 6/12, and 9/12 have the same denominators.

Now that we've found equivalent fractions with matching denominators, it's easy to compare them!

Just look at the numerators:

👉 The fraction with the smallest numerator is the least.

Can you order these fractions from least to greatest? 🤔

That's right!

When written in order from least to greatest, you have 6/12 < 8/12 < 9/12.

Now we know that...

Great job learning how to order fractions!

Now, complete the practice to master sorting fractions on your own. 💪

Page 15

Imagine your friend Ruby bought a basket of apples.

She gave 1/2 of the apples to her brother. If there were 12 apples in the basket, how many apples did she give to her brother?

To solve this problem, we need to find the fraction of a number.

We need to figure out:

What is 1/2 of 12?

To figure this out, we can draw a model.

But that's quite slow.

Let's use multiplication instead! 😺 

Multiplying a Fraction and a Number

To find the fraction of a number, multiply the number by the numerator, then divide the answer you get by the denominator.

Let's try it with our example:

What is 1/2 of 12?

Pause and look at those steps.

We multiplied by the numerator and divided by the denominator.

We got 6!

Another Example

What is 2/3 of 24?

We just have to solve 24 × 2 ÷ 3!

Tip: If the math is easier for you, you can divide first, then multiply. Take a look at the difference:

We get the same answer, but the math is a little easier.

Let's check our answer using models. 😺

What is 2/3 of 24 circles?

We divide them into 3 parts, because our denominator is 3.

The numerator is 2, so we count what's in 2 parts.

So our model shows that 2/3 of 24 is 16 as well!

We found the same answer. ✅

So What Did You Learn?

To find the 'fraction of a number', multiply by the numerator, and divide by the denominator.

Now, complete the practice. You'll understand more and remember for longer.