Fractions | Fourth Grade

Complete Notes & Formulas

1. Halves and Quarters

Definition: A fraction represents part of a whole. Halves and quarters are the most common fractions used in everyday life.

🔢 Understanding Halves:

Half (½):

When a whole is divided into 2 EQUAL parts, each part is called one-half.

½ = 1/2 = One Half

• 1 = Numerator (parts taken)

• 2 = Denominator (total equal parts)

Understanding Quarters:

When a whole is divided into 4 EQUAL parts, each part is called one-quarter.

¼ = 1/4 = One Quarter

• 1 = Numerator (parts taken)

• 4 = Denominator (total equal parts)

📊 Common Fractions Table:

Fraction	Name	What it Means
½	One Half	1 part out of 2 equal parts
¼	One Quarter	1 part out of 4 equal parts
¾	Three Quarters	3 parts out of 4 equal parts
2/2 or 4/4	Whole	All parts = 1 whole

🔑 Important Relationships:

2 halves = 1 whole

2 quarters = 1 half

4 quarters = 1 whole

✏️ Real-Life Examples:

If you cut a pizza into 2 equal pieces, each piece is ½ (half) of the pizza
If you cut a sandwich into 4 equal pieces, each piece is ¼ (quarter) of the sandwich
If you eat 3 out of 4 equal slices, you ate ¾ (three quarters)
An hour has 60 minutes, so 15 minutes is ¼ of an hour

2. Equal Parts

Definition: For something to be divided into fractions, all parts must be EQUAL in size. Equal parts mean that each part has the same size or area.

🔑 Key Rule:

Fractions ONLY work with EQUAL parts!

✅ Equal Parts vs ❌ Unequal Parts:

✅ Equal Parts (Correct):

• All parts are the SAME size

• Each part has the SAME area

• Fair division - everyone gets the same amount

Example: A circle cut into 4 equal slices like a pizza

❌ Unequal Parts (Incorrect):

• Parts are DIFFERENT sizes

• Each part has DIFFERENT area

• Unfair division - not proper fractions

Example: A circle with one big piece and one tiny piece

📝 Names of Equal Parts:

Number of Equal Parts	Name	Each Part Is
2	Halves	1/2
3	Thirds	1/3
4	Quarters/Fourths	1/4
5	Fifths	1/5
8	Eighths	1/8
10	Tenths	1/10

💡 Important Note:

Equal parts can be different SHAPES but must have the same SIZE (area)!

3. Simple Fractions: What Fraction Does the Shape Show?

Definition: When looking at a shape, we need to identify what fraction is shaded (colored) by counting the shaded parts and total equal parts.

📐 How to Write a Fraction:

Fraction = Shaded Parts / Total Equal Parts

Parts of a Fraction:

Numerator (Top Number) = Parts shaded/colored

Denominator (Bottom Number) = Total equal parts

📝 Steps to Find the Fraction:

Step 1: Count the total number of EQUAL parts
Step 2: Count how many parts are SHADED (colored)
Step 3: Write the fraction: shaded parts on top, total parts on bottom
Step 4: Read the fraction correctly

✏️ Examples:

Example 1: Circle divided into 4 parts, 3 are shaded

Total equal parts = 4

Shaded parts = 3

Fraction = 3/4 (three-fourths or three-quarters)

Answer: 3/4

Example 2: Rectangle divided into 8 parts, 5 are shaded

Total equal parts = 8

Shaded parts = 5

Fraction = 5/8 (five-eighths)

Answer: 5/8

Example 3: Square divided into 2 parts, 1 is shaded

Total equal parts = 2

Shaded parts = 1

Fraction = 1/2 (one-half)

Answer: 1/2

4. Simple Fractions: Which Shape Matches the Fraction?

Definition: Given a fraction, we need to identify or draw a shape that correctly shows that fraction with the right number of parts shaded.

📝 Steps to Match Fraction to Shape:

Step 1: Look at the DENOMINATOR (bottom) - this tells you how many TOTAL equal parts
Step 2: Look at the NUMERATOR (top) - this tells you how many parts should be SHADED
Step 3: Find the shape divided into that many equal parts
Step 4: Check that the correct number of parts are shaded

✏️ Examples:

Example 1: Find the shape that shows 2/3

Looking for:

• Denominator = 3 → Shape divided into 3 equal parts

• Numerator = 2 → 2 parts shaded

✓ Correct: Circle with 3 equal parts, 2 shaded

✗ Wrong: Circle with 4 parts (denominator doesn't match)

Example 2: Find the shape that shows 3/4

Looking for:

• Denominator = 4 → Shape divided into 4 equal parts

• Numerator = 3 → 3 parts shaded

✓ Correct: Square with 4 equal parts, 3 shaded

✗ Wrong: Square with 4 parts but only 2 shaded

💡 Remember:

DENOMINATOR tells you how many PARTS to divide into
NUMERATOR tells you how many PARTS to shade
All parts must be EQUAL in size

5. Simple Fractions: Parts of a Group

Definition: Fractions can also represent part of a GROUP or SET of objects, not just parts of one whole shape. The fraction tells us what part of the total group has a certain characteristic.

📐 Formula for Fractions of a Group:

Fraction = Objects with Property / Total Objects in Group

• Numerator = Number of objects with the specific property

• Denominator = Total number of objects in the group

📝 Steps to Find Fraction of a Group:

Step 1: Count the TOTAL number of objects in the group
Step 2: Count how many objects have the property you're looking for
Step 3: Write: objects with property / total objects
Step 4: Simplify if possible

✏️ Examples:

Example 1: Colored Marbles

There are 8 marbles: 3 red, 5 blue

What fraction are red?

Total marbles = 8

Red marbles = 3

Fraction = 3/8

Answer: 3/8 are red

Example 2: Fruit Basket

A basket has 12 fruits: 4 apples, 8 oranges

What fraction are apples?

Total fruits = 12

Apples = 4

Fraction = 4/12 = 1/3 (simplified)

Answer: 1/3 are apples

Example 3: Students in Class

20 students in class: 12 girls, 8 boys

What fraction are boys?

Total students = 20

Boys = 8

Fraction = 8/20 = 2/5 (simplified)

Answer: 2/5 are boys

🔑 Finding a Fraction of a Number:

To find ½ of a number → Divide by 2

To find ¼ of a number → Divide by 4

To find ¾ of a number → Divide by 4, then multiply by 3

✏️ Calculation Example:

Find ¾ of 20 marbles

Solution:

Step 1: Find ¼ of 20 → 20 ÷ 4 = 5

Step 2: Multiply by 3 → 5 × 3 = 15

Answer: ¾ of 20 = 15 marbles

Fractions Quick Reference Chart

Concept	Key Formula/Rule
Writing Fractions	Numerator (top) / Denominator (bottom)
Half	1/2 = 1 part out of 2 equal parts
Quarter	1/4 = 1 part out of 4 equal parts
Equal Parts Rule	All parts must be the SAME size
Fraction of Shape	Shaded parts / Total equal parts
Fraction of Group	Objects with property / Total objects
Whole	2/2 = 4/4 = Any fraction where numerator = denominator