🍕 Understanding Fractions

What ARE Fractions, Really?

Let's build a strong foundation for working with fractions!

What we'll learn:

✓ What fractions represent

✓ Parts of a fraction

✓ Fractions in real life

✓ Adding fractions with common denominators

✓ Introduction to unlike denominators

What is a Fraction?

The Big Idea

A fraction is a way to represent a part of a whole.

Think About Pizza! 🍕

If you have a whole pizza cut into 8 slices and you eat 3 slices, you've eaten 3 out of 8 pieces.

We write this as: 3/8

📝 Write in Your Journal:

Fraction: A number that represents a part of a whole.

Fractions show us equal parts of something.

Parts of a Fraction

Every Fraction Has Two Numbers

3 8

The TOP number (3) is the NUMERATOR

• This tells us how many parts we have

• It's the number of parts we're talking about

The BOTTOM number (8) is the DENOMINATOR

• This tells us how many equal parts make up the whole

• It's the total number of pieces

📝 Write in Your Journal:

Numerator: The top number - how many parts we have

Denominator: The bottom number - how many equal parts in the whole

Parts of a Fraction

How to Remember Which is Which

🔼 NUMERATOR (Top)

Numerator = North

North is UP, so the numerator goes on top!

🔽 DENOMINATOR (Bottom)

Denominator = Down

Down is below, so the denominator goes on the bottom!

Another Way to Remember:

Denominator = Down

Both start with D!

Seeing Fractions

Let's Look at 2/5

2/5 means 2 out of 5 equal parts

1

2

3

4

5

2 parts are shaded (numerator)

5 total equal parts (denominator)

The denominator (5) tells us the whole is divided into 5 equal pieces.

The numerator (2) tells us we're looking at 2 of those pieces.

Seeing Fractions

Let's Look at 3/4

3/4 means 3 out of 4 equal parts

1

2

3

4

3 parts are shaded (numerator)

4 total equal parts (denominator)

Real Life Example:

If you have 4 cookies and you eat 3 of them, you ate 3/4 of the cookies!

🎯 Activity Time!

Fraction Strips Activity

📐 What We'll Use: Paper strips or construction paper

Your Task:

Take a strip of paper (this is your "whole" or 1)
Fold it in half - now you have 2 equal parts
Unfold it and color 1 part. What fraction did you color? 1/2
Take another strip and fold it into fourths (fold in half, then in half again)
Color 3 parts. What fraction did you color? 3/4
Make more strips showing 2/3, 5/8, and 3/5

Key Point: All the parts must be equal in size!

Important Rule!

Parts Must Be EQUAL

✅ This IS a fraction:

1

2

3

These 3 parts are EQUAL, so this shows 2/3

❌ This is NOT a proper fraction:

1

2

3

These parts are NOT equal!

📝 Write in Your Journal:

For something to be a fraction, all the parts must be EQUAL in size.

Fractions Everywhere!

Where Do We Use Fractions?

🍕 Food

• Eating 2/8 of a pizza

• Drinking 1/2 of your milk

• Sharing 1/4 of a candy bar

⏰ Time

• A quarter of an hour = 1/4 hour = 15 minutes

• Half past two = 1/2 hour past 2:00

💵 Money

• A quarter = 1/4 of a dollar

• A dime = 1/10 of a dollar

📏 Measurement

• 1/2 inch, 3/4 cup, 2/3 mile

Practice Time!

Identifying Fractions

Look at this shape:

1

2

3

4

5

6

What fraction is shaded?

Answer: 4/6

Why?

• There are 6 equal parts total (denominator)

• 4 parts are shaded (numerator)

• So the fraction is 4/6

Practice Time!

Identifying Fractions

Sarah has 8 markers. 5 of them are red.

What fraction of her markers are red?

Answer: 5/8

Why?

• The total number of markers is 8 (denominator)

• The number of red markers is 5 (numerator)

• So 5/8 of the markers are red

🎯 Activity Time!

Building Fractions with Omnifix Cubes

🧱 What We'll Use: Omnifix Cubes or Base-Ten Blocks

Your Task:

Build a train of 10 cubes (this is your whole)
Use 2 different colors to show 3/10
How many cubes are each color?
Now build a train of 8 cubes
Show 5/8 with two colors
Challenge: Build trains to show 2/5, 7/10, and 1/4 (you may need different total cubes!)

Think: What does the denominator tell you about how many cubes to use?

Same Fractions, Different Sizes?

The Whole Matters!

Important Concept:

1/2 of a pizza is NOT the same amount as 1/2 of a cookie!

Why? Because the whole is different.

1/2 of a large circle:

1/2 of a small circle:

Both are 1/2, but the amounts are different because the wholes are different!

Special Fractions

When Fractions Equal One Whole

When the numerator equals the denominator:

3/3 = 1

5/5 = 1

8/8 = 1

Why does 4/4 = 1?

1

2

3

4

All 4 parts are included - that's the whole thing!

📝 Write in Your Journal:

When the numerator and denominator are the same, the fraction equals 1 whole.

Special Fractions

Fractions Greater Than One Whole

When the numerator is larger than the denominator:

5/4 is more than 1 whole

This is called an improper fraction.

What does 5/4 look like?

1

2

3

4

+

1

One whole (4/4) plus one more fourth (1/4) = 5/4

Adding Fractions

The Big Rule for Adding

📝 Write in Your Journal:

To add fractions with the SAME denominator:

1. Keep the denominator the same

2. Add the numerators

3. Write the sum over the same denominator

Why does this work?

If you have 2 slices of pizza out of 8 slices, and someone gives you 3 more slices, you now have 5 slices out of 8.

2/8 + 3/8 = 5/8

The denominator stays 8 because the pizza is still cut into 8 slices!

Adding Fractions

Let's See It Visually

1/5 + 2/5 = ?

Start with 1/5:

1

2

3

4

5

Add 2/5 more:

1

2

3

4

5

= 3/5

We added the numerators: 1 + 2 = 3

We kept the denominator: 5

Practice: Adding Fractions

Same Denominators

Problem 1: 2/7 + 3/7 = ?

Solution:

Step 1: Check the denominators - they're both 7 ✓

Step 2: Add the numerators: 2 + 3 = 5

Step 3: Keep the denominator: 7

Answer: 5/7

Problem 2: 1/6 + 4/6 = ?

Solution:

Step 1: Check the denominators - they're both 6 ✓

Step 2: Add the numerators: 1 + 4 = 5

Step 3: Keep the denominator: 6

Answer: 5/6

Practice: Adding Fractions

Same Denominators

Problem 3: 3/10 + 2/10 = ?

Solution:

Step 1: Check the denominators - they're both 10 ✓

Step 2: Add the numerators: 3 + 2 = 5

Step 3: Keep the denominator: 10

Answer: 5/10

Problem 4: 2/8 + 5/8 = ?

Solution:

Step 1: Check the denominators - they're both 8 ✓

Step 2: Add the numerators: 2 + 5 = 7

Step 3: Keep the denominator: 8

Answer: 7/8

Practice: Adding Fractions

Same Denominators

Problem 5: 1/12 + 7/12 = ?

Solution:

Step 1: Check the denominators - they're both 12 ✓

Step 2: Add the numerators: 1 + 7 = 8

Step 3: Keep the denominator: 12

Answer: 8/12

Problem 6: 4/9 + 2/9 = ?

Solution:

Step 1: Check the denominators - they're both 9 ✓

Step 2: Add the numerators: 4 + 2 = 6

Step 3: Keep the denominator: 9

Answer: 6/9

Subtracting Fractions

Just Like Adding, But Backwards!

📝 Write in Your Journal:

To subtract fractions with the SAME denominator:

1. Keep the denominator the same

2. Subtract the numerators

3. Write the difference over the same denominator

Example:

5/8 - 2/8 = ?

• The denominators are the same (8), so we can subtract

• Subtract the numerators: 5 - 2 = 3

• Keep the denominator: 8

5/8 - 2/8 = 3/8

Subtracting Fractions

Let's See It Visually

4/6 - 2/6 = ?

Start with 4/6:

1

2

3

4

5

6

Take away 2/6:

1

2

3

4

5

6

= 2/6

Practice: Subtracting Fractions

Same Denominators

Problem 1: 5/7 - 2/7 = ?

Solution:

Subtract the numerators: 5 - 2 = 3

Keep the denominator: 7

Answer: 3/7

Problem 2: 7/10 - 3/10 = ?

Solution:

Subtract the numerators: 7 - 3 = 4

Keep the denominator: 10

Answer: 4/10

Practice: Subtracting Fractions

Same Denominators

Problem 3: 8/12 - 5/12 = ?

Solution:

Subtract the numerators: 8 - 5 = 3

Keep the denominator: 12

Answer: 3/12

Problem 4: 6/8 - 1/8 = ?

Solution:

Subtract the numerators: 6 - 1 = 5

Keep the denominator: 8

Answer: 5/8

What About Different Denominators?

A New Challenge!

The Problem:

Can we add 1/2 + 1/3?

The denominators are different (2 and 3).

1/2 looks like this:

1

2

1/3 looks like this:

1

2

3

We can't just add the numerators! The pieces are different sizes.

It's like trying to add apples and oranges.

Adding Unlike Denominators

The Key: Make Them the Same!

📝 Write in Your Journal:

To add fractions with DIFFERENT denominators:

1. Find a common denominator (a number both denominators divide into)

2. Convert both fractions to have that common denominator

3. Then add the numerators

4. Keep the common denominator

We'll learn more about this soon!

For now, just know that we need to make the denominators match before we can add or subtract.

This is a sneak peek of what's coming in our next lessons!

Adding Unlike Denominators

A Simple Example

Let's try: 1/2 + 1/4

Step 1: Notice that 4 can be divided by 2, so let's use 4 as our common denominator.

Step 2: Convert 1/2 to fourths:

1/2 = 2/4 (we multiply top and bottom by 2)

Step 3: Now we can add:

2/4 + 1/4 = 3/4

1

2

3

4

The answer is 3/4!

🎯 Activity Time!

Fractions Around the Classroom

🔍 Fraction Hunt!

Your Task:

Look around the classroom
Find things that can be described with fractions
Write down at least 5 examples in your journal

Examples to look for:

What fraction of the windows are open?
What fraction of the class is wearing sneakers?
What fraction of the bulletin board is covered?
What fraction of your pencils have erasers?

Challenge: Can you find a situation where you could add two fractions?

📋 Knowledge Check

Question 1 of 6

What is the bottom number of a fraction called?

A) Numerator

B) Denominator

C) Fraction

D) Whole number

Correct Answer: B) Denominator

The denominator is the bottom number that tells us how many equal parts make up the whole.

📋 Knowledge Check

Question 2 of 6

Look at this shape:

1

2

3

4

5

What fraction is shaded?

A) 2/5

B) 3/5

C) 5/3

D) 3/8

Correct Answer: B) 3/5

There are 5 total equal parts (denominator = 5) and 3 are shaded (numerator = 3).

📋 Knowledge Check

Question 3 of 6

Solve: 3/8 + 2/8 = ?

A) 5/16

B) 5/8

C) 6/8

D) 3/8

Correct Answer: B) 5/8

When adding fractions with the same denominator, add the numerators (3 + 2 = 5) and keep the denominator (8).

📋 Knowledge Check

Question 4 of 6

What does 4/4 equal?

A) 0

B) 1

C) 4

D) 1/2

Correct Answer: B) 1

When the numerator and denominator are equal, the fraction equals 1 whole because all parts are included.

📋 Knowledge Check

Question 5 of 6

Solve: 7/10 - 3/10 = ?

A) 10/10

B) 4/20

C) 4/10

D) 4/7

Correct Answer: C) 4/10

When subtracting fractions with the same denominator, subtract the numerators (7 - 3 = 4) and keep the denominator (10).

📋 Knowledge Check

Question 6 of 6

Before adding 1/3 + 1/4, what must you do first?

A) Add the numerators

B) Add the denominators

C) Find a common denominator

D) Multiply the fractions

Correct Answer: C) Find a common denominator

When fractions have different denominators, you must first convert them to have the same denominator before adding.

🎉 Amazing Work!

You're on Your Way to Mastering Fractions!

What you learned today:

✓ What fractions represent (parts of a whole)

✓ Numerator (top) and Denominator (bottom)

✓ All parts must be EQUAL

✓ Adding fractions with common denominators

✓ Subtracting fractions with common denominators

✓ Introduction to unlike denominators

Coming Soon:

Finding common denominators

Simplifying fractions

Multiplying & dividing fractions

Keep up the great work! 🌟