Topic 1.2 — Lesson

Writing and Reading Fractions

In our previous lesson, we learned what a fraction is: dividing a whole into equal parts.Review Lesson 1.1 ↗ Now, let us discover how we express fractions mathematically and how we read them correctly.

🧱 1. Unit Fractions: The Building Blocks

When we divide a whole into equal parts, each single piece is called a Unit Fraction.

A unit fraction always represents exactly 1 equal piece of the whole. Look at how a whole bar breaks down into unit fractions:

When a whole is divided into 2 equal parts:

When a whole is divided into 3 equal parts:

When a whole is divided into 4 equal parts:

Expressing Unit Fractions Mathematically

Now we express each single equal piece mathematically. Notice how as the whole is divided into more equal parts, each unit piece becomes smaller:

Each part is12

Each part is13

Each part is14

Each part is15

Each part is16

Each part is17

Each part is18

🪜 2. Building Fractions from Units (Step-by-Step)

Let us take a whole bar divided into 4 equal parts (each piece is the unit fraction14) and shade pieces one by one, all the way up to 3 wholes:

The Golden Foundation:Every single fraction is built out of unit fractions! Just like a wall is built of single bricks, any fraction is simply a count of unit fractions.

1 unit piece of14→ One fourth

2 unit pieces of14→ Two fourths

3 unit pieces of14→ Three fourths

4 unit pieces of14→ Four fourths

5 unit pieces of14→ Five fourths

6 unit pieces of14→ Six fourths

7 unit pieces of14→ Seven fourths

8 unit pieces of14→ Eight fourths

9 unit pieces of14→ Nine fourths

104

10 unit pieces of14→ Ten fourths

114

11 unit pieces of14→ Eleven fourths

124

12 unit pieces of14→ Twelve fourths

📐 3. Anatomy of a Fraction: Numerator & Denominator

Now that we have seen how fractions are built by counting unit parts, let us look at the two numbers that make up every fraction:

Visual Example: 3 out of 4 parts shaded

3 → Count of shaded parts (Top)

— Dividing line (Fraction Bar)

4 → Total parts in 1 whole (Bottom)

Top Number

NUMERATOR

Tells you how many equal parts you are counting, shading, or taking.

In 3/4 → 3 parts

Dividing Line

FRACTION BAR

The horizontal line that separates the numerator from the denominator.

Dividing line: —

Bottom Number

DENOMINATOR

Tells you the total number of equal pieces that make up 1 whole.

In 3/4 → 4 pieces total

🗣️ 4. How to Read Fractions Properly

Before reading larger fractions, we must first know the proper names of the unit fractions (a single equal piece).

Part 1: The Reading of Unit Fractions (From 1/2 to 1/12)

Notice that unit fractions use ordinal names (like third, fifth, sixth), with special historic names for half and quarter:

12→ one half (or a half)

13→ one third (or a third)

14→ one fourth (or a quarter)

15→ one fifth (or a fifth)

16→ one sixth (or a sixth)

17→ one seventh (or a seventh)

18→ one eighth (or an eighth)

19→ one ninth (or a ninth)

110→ one tenth (or a tenth)

111→ one eleventh (or an eleventh)

112→ one twelfth (or a twelfth)

Part 2: Reading Fractions by Counting Unit Pieces

Just like we count objects by saying "3 apples" or "3 meters", we read fractions by counting their unit pieces:

14→ one fourth (or a quarter)

24→ two fourths (or two quarters)

34→ three fourths (or three quarters)

44→ four fourths

54→ five fourths

64→ six fourths

74→ seven fourths

84→ eight fourths

Examples Across Different Units:

Notice how the rule never changes: state the count of pieces, then the unit piece name:

23→ two thirds

35→ three fifths

58→ five eighths

710→ seven tenths

66→ six sixths

75→ seven fifths

118→ eleven eighths

97→ nine sevenths

63→ six thirds

73→ seven thirds

136→ thirteen sixths

175→ seventeen fifths

Important Language & Conceptual Tip

How should we read this fraction?

"3 over 5" or "3 divided by 5"Casual / Misleading

"Three fifths"✓ Mathematically Correct

Sometimes in casual speech, we might say "3 over 5" or "3 divided by 5". While others might understand what we write on paper, that is not the true conceptual reading.

The meaningful and proper reading is "three fifths" — because we are simply counting 3 copies of the unit fraction15!

🎯 Test What You Learned

Unit Fraction Challenge & Counting Practice!

Find the unit fraction for 10 fractions, build fractions by counting their unit pieces, and practice reading them aloud. Can you score 10/10?

Start Practice