Maths

Fractions

Class 3

🎯 Learning Objectives

Understand what a fraction is — parts of a whole.
Identify the numerator and denominator of a fraction.
Recognise proper fractions and unit fractions.
Find a fraction of a collection (e.g., 1/3 of 12).
Compare like fractions (fractions with the same denominator).
Understand the basic idea of equivalent fractions.

📖 What Is a Fraction?

Imagine your mother makes a round roti and cuts it into 2 equal parts. She gives one part to you and one part to your sister. Each of you gets one out of two equal parts. We write this as ½ (one-half).

A fraction tells us how many equal parts of a whole we are talking about. When we divide something into equal parts and take some of those parts, we get a fraction.

For example, if a cake is cut into 4 equal pieces and you eat 1 piece, you have eaten ¼ (one-quarter) of the cake. The remaining cake is ¾ (three-quarters).

$Pizza divided into equal parts showing fractions — halves, thirds and quarters$

Numerator and Denominator

Every fraction has two numbers separated by a line:

3	← Numerator (top number) — tells how many parts we have taken
4	← Denominator (bottom number) — tells how many equal parts the whole is divided into

So in the fraction ¾:

Numerator = 3 → We have taken 3 parts.
Denominator = 4 → The whole was divided into 4 equal parts.

Think: In the fraction 2/5, the denominator is 5 (the whole is cut into 5 equal parts) and the numerator is 2 (we are talking about 2 of those parts).

More Examples

½ → Numerator = 1, Denominator = 2 (1 part out of 2 equal parts)

3/8 → Numerator = 3, Denominator = 8 (3 parts out of 8 equal parts)

5/6 → Numerator = 5, Denominator = 6 (5 parts out of 6 equal parts)

Types of Fractions

1. Unit Fractions

A fraction with 1 as the numerator is called a unit fraction. It means we have taken exactly one part out of the whole.

Examples: ½, ⅓, ¼, ⅕, ⅙, ⅛

Sita cut a laddoo into 3 equal pieces and ate 1 piece. She ate ⅓ of the laddoo — a unit fraction!

2. Proper Fractions

A fraction where the numerator is less than the denominator is called a proper fraction. It is always less than 1 whole.

Examples: ½, ⅔, ¾, 3/5, 5/8, 7/10

In all these fractions, the top number is smaller than the bottom number.

Is it a proper fraction?

4/7 → Yes (4 < 7) ✓

5/5 → No (5 = 5, this equals 1 whole)

2/9 → Yes (2 < 9) ✓

Fractions of a Collection

We can also find a fraction of a group of objects. To find a fraction of a collection, we divide the total number of objects by the denominator, then multiply by the numerator.

Example 1: Find ⅓ of 12 laddoos

Step 1: Divide 12 by 3 (the denominator) → 12 ÷ 3 = 4

Step 2: Multiply by 1 (the numerator) → 4 × 1 = 4

Answer: ⅓ of 12 = 4 laddoos

Example 2: Find ¼ of 20 mangoes

Step 1: 20 ÷ 4 = 5

Step 2: 5 × 1 = 5

Answer: ¼ of 20 = 5 mangoes

Example 3: Find 2/5 of 15 pencils

Step 1: 15 ÷ 5 = 3

Step 2: 3 × 2 = 6

Answer: 2/5 of 15 = 6 pencils

Arjun has 18 marbles. He gives ⅓ to his friend. How many does he give? 18 ÷ 3 = 6. He gives 6 marbles.

$Shapes showing equivalent fractions — ½, 2/4 and 4/8 with same amount shaded$

Comparing Like Fractions

Like fractions are fractions that have the same denominator (same number of equal parts).

To compare like fractions, we simply compare their numerators. The fraction with the bigger numerator is the bigger fraction.

Example: Compare 3/7 and 5/7

Both fractions have denominator 7 (like fractions).

Compare numerators: 3 and 5. Since 5 > 3, we get 5/7 > 3/7.

Example: Arrange in order — 2/9, 7/9, 4/9, 1/9

All have denominator 9. Compare numerators: 1, 2, 4, 7.

Ascending order: 1/9 < 2/9 < 4/9 < 7/9

Ravi ate 3/8 of a pizza and Meena ate 5/8 of the same pizza. Who ate more? Since 5 > 3, Meena ate more (5/8 > 3/8).

Rule for like fractions:

If numerator of first fraction > numerator of second fraction → first fraction is greater.
If numerators are equal → the fractions are equal.

Equivalent Fractions

Equivalent fractions are fractions that look different but represent the same value.

If you cut a roti into 2 equal parts and take 1 part, you get ½. If you cut the same roti into 4 equal parts and take 2 parts, you get 2/4. Both are the same amount!

½ = 2/4 = 3/6 = 4/8 — all these are equivalent fractions.

How to find equivalent fractions

Multiply (or divide) both the numerator and denominator by the same number.

½ → multiply both by 2 → 2/4

½ → multiply both by 3 → 3/6

⅔ → multiply both by 2 → 4/6

⅔ → multiply both by 3 → 6/9

Sita says: "I ate 2/4 of the cake." Arjun says: "I ate ½ of the cake." Did they eat the same amount? Yes! Because 2/4 = ½ (divide both by 2).

$Shapes showing equivalent fractions — 1/2, 2/4 and 4/8 with same amount shaded$

📝 Key Words

Word	Meaning
Fraction	A part of a whole, written as one number over another (e.g., ¾)
Numerator	The top number — tells how many parts are taken
Denominator	The bottom number — tells how many equal parts the whole is divided into
Unit Fraction	A fraction with 1 as the numerator (e.g., ½, ⅓, ¼)
Proper Fraction	A fraction where the numerator is less than the denominator
Like Fractions	Fractions with the same denominator (e.g., 2/7 and 5/7)
Equivalent Fractions	Fractions that have the same value (e.g., ½ = 2/4)
Whole	The complete object or group before it is divided
Equal Parts	Parts that are exactly the same size
Collection	A group of objects (e.g., 12 laddoos, 20 mangoes)

⭐ Key Points to Remember

A fraction represents equal parts of a whole or a collection.
The numerator (top) tells how many parts are taken; the denominator (bottom) tells total equal parts.
A unit fraction always has 1 as the numerator (½, ⅓, ¼, ⅕…).
In a proper fraction, the numerator is always less than the denominator.
To find a fraction of a collection: divide by the denominator, then multiply by the numerator.
To compare like fractions (same denominator), compare the numerators — bigger numerator means bigger fraction.
Equivalent fractions have the same value. Multiply or divide both numerator and denominator by the same number.
The parts must be equal for a fraction to be valid.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. If a chocolate is cut into 4 equal parts, each part is:

4 equal parts means each part is one quarter (1/4).

2. In the fraction 3/5, the number 5 is called the:

The bottom number (5) is the denominator. The top number (3) is the numerator.

3. One half is written as:

One half is written 1/2.

4. Which fraction is bigger: 1/2 or 1/4?

1/2 is bigger than 1/4 (half a chapati is more than a quarter).

5. In the fraction 2/7, what is the numerator (top number)?

The top number of 2/7 is the numerator: 2.

6. If a cake is cut into 3 equal pieces, each piece is what fraction? (like 1/2)

3 equal pieces means each is one third = 1/3.

7. 2/4 is the same as which simpler fraction?

2/4 = 1/2 (both halves are the same amount).

8. If you eat 3 out of 8 equal slices of pizza, what fraction did you eat?

3 slices out of 8 = 3/8.

✏️ Practice Questions

A. Fill in the Blanks (10 questions)

1. In the fraction 3/5, the numerator is and the denominator is .

2. A fraction with 1 as the numerator is called a fraction.

3. ½ of 10 =

4. ⅓ of 12 =

5. ¼ of 20 =

6. In a proper fraction, the numerator is always than the denominator.

7. 2/7 and 5/7 are called fractions because they have the same denominator.

8. ½ = 2/ = 3/ (equivalent fractions)

9. The fraction that shows "3 parts out of 8 equal parts" is .

10. ⅕ of 25 =

B. Choose the Correct Answer (MCQ)

1. What is the numerator in the fraction 5/9?

(a) 9(b) 5(c) 4(d) 14

2. Which of these is a unit fraction?

(a) 2/3(b) ¼(c) 3/4(d) 5/6

3. What is ⅓ of 15?

(a) 3(b) 5(c) 10(d) 15

4. Which fraction is greater: 4/9 or 7/9?

(a) 4/9(b) 7/9(c) Both are equal(d) Cannot compare

5. Which fraction is equivalent to ½?

(a) 2/3(b) 3/6(c) 2/5(d) 1/3

C. Solve These (Word Problems)

1. Meena's mother made 16 laddoos for Diwali. She gave ¼ of them to the neighbours. How many laddoos did she give?

2. A birthday cake was cut into 8 equal pieces. Ravi ate 3 pieces. What fraction of the cake did Ravi eat?

3. There are 24 students in a class. ⅓ of them are girls. How many girls are there?

4. Arjun has 30 marbles. He gives ⅕ of them to his friend. How many marbles does he give away?

5. A roti is divided into 6 equal parts. Sita eats 2 parts and her brother eats 3 parts. What fraction did each eat? Who ate more?

D. True or False

1. In the fraction ¾, the denominator is 3.

2. ½ and 2/4 are equivalent fractions.

3. A unit fraction always has 1 as the denominator.

4. 5/8 is greater than 3/8.

5. ⅓ of 9 is 3.

E. Match the Following

Column A	Column B
1. ½ of 14	(a) 5
2. ¼ of 20	(b) 7
3. ⅓ of 18	(c) 4
4. ⅕ of 20	(d) 6
5. ½ of 8	(e) 5

🎨 Think and Do — Fun Activity

Paper Folding Fractions:

Take a rectangular sheet of paper (A4 or any sheet).

Step 1: Fold it into 2 equal parts. Open it and colour one part. You have coloured ½ of the paper.

Step 2: Take another sheet. Fold it into 4 equal parts (fold in half, then fold in half again). Open it and colour 1 part. You have coloured ¼ of the paper.

Step 3: Take another sheet. Fold it into 4 equal parts. Colour 3 parts. You have coloured ¾ of the paper.

Step 4: Now fold a sheet into 8 equal parts. Colour 4 parts. What fraction did you colour? Is it the same as ½? (Yes! 4/8 = ½ — equivalent fractions!)

Challenge: Can you fold a paper into 3 equal parts? Try it! Colour 1 part to show ⅓ and 2 parts to show ⅔.

Want to review the lesson again?

🎯 Learning Objectives

Understand what a fraction is — parts of a whole.
Identify the numerator and denominator of a fraction.
Recognise proper fractions and unit fractions.
Find a fraction of a collection (e.g., 1/3 of 12).
Compare like fractions (fractions with the same denominator).
Understand the basic idea of equivalent fractions.

📖 What Is a Fraction?

A fraction tells us how many equal parts of a whole we are talking about. When we divide something into equal parts and take some of those parts, we get a fraction.

If a cake is cut into 4 equal pieces and you eat 1 piece, you have eaten ¼ (one-quarter) of the cake. The remaining cake is ¾ (three-quarters).

Numerator and Denominator

3	← Numerator (top) — parts taken
4	← Denominator (bottom) — total equal parts

In ¾: Numerator = 3 (parts taken), Denominator = 4 (total equal parts).

½ → Num = 1, Den = 2 | 3/8 → Num = 3, Den = 8 | 5/6 → Num = 5, Den = 6

Types of Fractions

1. Unit Fractions: Numerator is always 1. Examples: ½, ⅓, ¼, ⅕, ⅙, ⅛

Sita cut a laddoo into 3 equal pieces and ate 1 piece. She ate ⅓ — a unit fraction!

2. Proper Fractions: Numerator < Denominator. Always less than 1 whole.

Examples: ½, ⅔, ¾, 3/5, 5/8, 7/10. In all these, the top number is smaller than the bottom number.

Is it proper? 4/7 → Yes (4<7) ✓ | 5/5 → No (equals 1 whole) | 2/9 → Yes (2<9) ✓

Fractions of a Collection

To find a fraction of a group: divide total by denominator, then multiply by numerator.

⅓ of 12 laddoos: 12 ÷ 3 = 4, then 4 × 1 = 4 laddoos
¼ of 20 mangoes: 20 ÷ 4 = 5, then 5 × 1 = 5 mangoes
2/5 of 15 pencils: 15 ÷ 5 = 3, then 3 × 2 = 6 pencils

Arjun has 18 marbles. He gives ⅓ to his friend. 18 ÷ 3 = 6. He gives 6 marbles.

$Equivalent fractions shapes$

Comparing Like Fractions

Like fractions = same denominator. Compare numerators: bigger numerator = bigger fraction.

Compare 3/7 and 5/7: Same denominator (7). Since 5 > 3 → 5/7 > 3/7
Arrange: 2/9, 7/9, 4/9, 1/9 → Ascending: 1/9 < 2/9 < 4/9 < 7/9

Ravi ate 3/8 of a pizza, Meena ate 5/8. Since 5 > 3, Meena ate more.

Equivalent Fractions

Fractions that look different but have the same value. Multiply or divide both numerator and denominator by the same number.

½ = 2/4 = 3/6 = 4/8 — all equivalent!

½ × 2/2 = 2/4 | ½ × 3/3 = 3/6 | ⅔ × 2/2 = 4/6 | ⅔ × 3/3 = 6/9

$Equivalent fractions shapes$

📝 Key Words

Word	Meaning
Fraction	A part of a whole, written as one number over another
Numerator	Top number — how many parts are taken
Denominator	Bottom number — total equal parts
Unit Fraction	Numerator is 1 (e.g., ½, ⅓, ¼)
Proper Fraction	Numerator < Denominator
Like Fractions	Same denominator (e.g., 2/7 and 5/7)
Equivalent Fractions	Same value (e.g., ½ = 2/4)
Whole	The complete object before dividing
Equal Parts	Parts that are exactly the same size
Collection	A group of objects

⭐ Key Points to Remember

A fraction represents equal parts of a whole or a collection.
Numerator (top) = parts taken; Denominator (bottom) = total equal parts.
Unit fraction: numerator is always 1.
Proper fraction: numerator < denominator.
Fraction of a collection: divide by denominator, multiply by numerator.
Like fractions (same denominator): bigger numerator = bigger fraction.
Equivalent fractions: multiply/divide both by the same number.
Parts must be equal for a valid fraction.

A. Fill in the Blanks

1. In the fraction 3/5, the numerator is and the denominator is .

2. A fraction with 1 as the numerator is called a fraction.

3. ½ of 10 =

4. ⅓ of 12 =

5. ¼ of 20 =

6. In a proper fraction, the numerator is always than the denominator.

7. 2/7 and 5/7 are called fractions because they have the same denominator.

8. ½ = 2/ = 3/ (equivalent fractions)

9. The fraction that shows "3 parts out of 8 equal parts" is .

10. ⅕ of 25 =

B. Choose the Correct Answer

1. What is the numerator in the fraction 5/9?

(a) 9(b) 5(c) 4(d) 14

2. Which of these is a unit fraction?

(a) 2/3(b) ¼(c) 3/4(d) 5/6

3. What is ⅓ of 15?

(a) 3(b) 5(c) 10(d) 15

4. Which fraction is greater: 4/9 or 7/9?

(a) 4/9(b) 7/9(c) Both equal(d) Cannot compare

5. Which fraction is equivalent to ½?

(a) 2/3(b) 3/6(c) 2/5(d) 1/3

C. Word Problems

1. Meena's mother made 16 laddoos for Diwali. She gave ¼ of them to the neighbours. How many laddoos did she give?

2. A birthday cake was cut into 8 equal pieces. Ravi ate 3 pieces. What fraction of the cake did Ravi eat?

3. There are 24 students in a class. ⅓ of them are girls. How many girls are there?

4. Arjun has 30 marbles. He gives ⅕ of them to his friend. How many marbles does he give away?

5. A roti is divided into 6 equal parts. Sita eats 2 parts and her brother eats 3 parts. What fraction did each eat? Who ate more?

D. True or False

1. In the fraction ¾, the denominator is 3.

2. ½ and 2/4 are equivalent fractions.

3. A unit fraction always has 1 as the denominator.

4. 5/8 is greater than 3/8.

5. ⅓ of 9 is 3.

E. Match the Following

Column A	Column B
1. ½ of 14	(a) 5
2. ¼ of 20	(b) 7
3. ⅓ of 18	(c) 4
4. ⅕ of 20	(d) 6
5. ½ of 8	(e) 5

🎨 Think and Do — Paper Folding Fractions

Step 1: Take a sheet. Fold into 2 equal parts. Colour 1 part → you coloured ½.

Step 2: New sheet. Fold into 4 equal parts. Colour 1 part → you coloured ¼.

Step 3: Same sheet (4 parts). Colour 3 parts → you coloured ¾.

Step 4: New sheet. Fold into 8 parts. Colour 4 parts → 4/8 = ½ (equivalent fractions!)

Challenge: Fold a paper into 3 equal parts. Colour 1 part (⅓) and 2 parts (⅔).

You are viewing the worksheet layout. Click Print to save as PDF or print on A4 paper.

Fractions

🎯 Learning Objectives

📖 What Is a Fraction?

Numerator and Denominator

Types of Fractions

1. Unit Fractions

2. Proper Fractions

Fractions of a Collection

Comparing Like Fractions

Equivalent Fractions

📝 Key Words

🎯 Quick Quiz — Test Yourself!

✏️ Practice Questions

Fractions

Fractions (continued)

Fractions (practice)