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ICSE Class 3 Mathematics★ 5-7 marks in Class 3 Mathematics; halves, quarters, and three-quarters

Fractions — Halves, Quarters, and Three-Quarters

Learn about FRACTIONS — half (1/2), quarter (1/4), and three-quarters (3/4) as parts of a whole and a collection. Numerator and denominator. Comparison of fractions. ICSE Class 3 Mathematics.

⏱ 9 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Identify the numerator and denominator of a fraction
2Recognise half, quarter, and three-quarters of shapes
3Find a fraction of a collection of objects
4Compare simple fractions
5Know that 2/4 equals 1/2 (equivalent fractions)

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Why this chapter matters

Fractions teach children to think about parts of a whole and parts of a collection, seen in sharing food, telling time, and money. Understanding halves, quarters, and three-quarters builds the base for decimals, ratios, and later fraction arithmetic.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Class 3 Mathematics: Multiplication and division

Dividing into equal groups

Fractions — Halves, Quarters, and Three-Quarters

1. What Is a Fraction?

A FRACTION is a PART of a WHOLE.

'If you cut a pizza into 4 equal slices and take 1 slice, you have taken ONE-FOURTH (1/4) of the pizza.'

Parts of a Fraction:

Part	Name	Meaning
1	Numerator	How many parts you HAVE
—	Fraction bar	Means 'out of'
4	Denominator	How many EQUAL parts the whole is divided into

2. Half (1/2)

HALF means ONE out of TWO equal parts.

'If you share a chocolate bar equally with your friend, each of you gets HALF (1/2) of the bar.'

Shape	Halves
Circle	Cut through the centre → 2 half-circles
Square	Cut through the middle → 2 equal rectangles
Rectangle	Cut lengthwise or widthwise → 2 equal parts

Examples of Half:

Half an apple
Half a glass of water
Half an hour (30 minutes)
Half a dozen (6 items)

Finding Half of a Collection:

Half of 10 = 10 ÷ 2 = 5 Half of 8 = 8 ÷ 2 = 4 Half of 20 = 20 ÷ 2 = 10

3. Quarter (1/4)

QUARTER means ONE out of FOUR equal parts.

'If you cut a pizza into 4 equal slices, each slice is ONE-QUARTER (1/4) of the pizza.'

Shape	Quarters
Circle	Cut into 4 equal parts (like a + sign)
Square	Cut into 4 equal small squares
Rectangle	Cut into 4 equal smaller rectangles

Examples of Quarter:

Quarter of a cake
Quarter of an hour (15 minutes)
Quarter of a year (3 months)
Quarter (25 paise coin)

Finding a Quarter of a Collection:

Quarter of 12 = 12 ÷ 4 = 3 Quarter of 20 = 20 ÷ 4 = 5 Quarter of 8 = 8 ÷ 4 = 2

4. Three-Quarters (3/4)

THREE-QUARTERS means THREE out of FOUR equal parts.

'If 4 friends share a pizza and you eat 3 slices, you have eaten THREE-QUARTERS (3/4) of the pizza.'

Comparing:

1/4 is SMALLER than 1/2.
3/4 is LARGER than 1/2.
1/2 = 2/4 (two quarters = one half).

Fraction	Words	Size
1/4	One-quarter	Smallest
2/4 or 1/2	One-half	Medium
3/4	Three-quarters	Biggest

5. Fraction of a Collection

Formula:

Fraction of a number = Total ÷ Denominator × Numerator

Examples:

What is 1/2 of 16? 16 ÷ 2 = 8

What is 1/4 of 20? 20 ÷ 4 = 5

What is 3/4 of 16? 16 ÷ 4 = 4 (this is 1/4), then 4 × 3 = 12 (this is 3/4)

Fraction	Of	Calculation	Answer
1/2	14	14 ÷ 2	7
1/4	24	24 ÷ 4	6
3/4	12	12 ÷ 4 = 3, × 3	9
1/2	30	30 ÷ 2	15

6. Comparing Fractions

Same Denominator:

Bigger numerator = Bigger fraction.

3/4 > 1/4 (3 is bigger than 1)
2/4 = 1/2 (same value)

Same Numerator:

Smaller denominator = Bigger fraction.

1/2 > 1/4 (half is bigger than a quarter)
1/3 > 1/4

'Think: If you cut a cake into 2 pieces, each piece is BIG. If you cut it into 4 pieces, each piece is SMALLER. So 1/2 is bigger than 1/4.'

7. Common Mistakes

Not making equal parts: 'When you cut something into fractions, ALL parts must be EQUAL. Unequal parts are NOT fractions!'
Confusing numerator and denominator: 'The DENOMINATOR is DOWN — it tells how many parts in total. The NUMERATOR is UP — it tells how many you have.'
Thinking 1/4 is bigger than 1/2: '1/4 is SMALLER than 1/2. A quarter of a pizza is less than half!'
Forgetting to divide first, then multiply: 'For 3/4 of 12, FIRST find 1/4 (12 ÷ 4 = 3), THEN multiply by 3 (3 × 3 = 9).'

8. Key Facts to Remember

'A fraction is a PART of a WHOLE.'
'1/2 (half) = 1 out of 2 equal parts.'
'1/4 (quarter) = 1 out of 4 equal parts.'
'3/4 (three-quarters) = 3 out of 4 equal parts.'
'2/4 = 1/2. They are EQUIVALENT (same value).'
'The denominator can NEVER be zero.'

9. Self-Test

Q1: What fraction of a pizza is one slice if the pizza is cut into 4 equal slices?

Q2: What is 1/2 of 18?

Q3: What is 1/4 of 28?

Q4: What is 3/4 of 20?

Q5: Which is bigger — 1/4 or 1/2? Why?

Q6: Color 1/4 of a group of 12 stars. How many stars do you color?

Q7: If you eat 2 slices of a pizza cut into 4 equal slices, what fraction have you eaten?

Q8: True or False: 2/4 is the same as 1/2.

Answers:

A1: 1/4 (one-quarter). A2: 9 A3: 7 A4: 20 ÷ 4 = 5, 5 × 3 = 15 A5: 1/2 is bigger. The more parts you cut something into, the smaller each part becomes. A6: 12 ÷ 4 = 3 stars colored. A7: 2/4 which is the same as 1/2. A8: True. Both represent the same amount — half of something.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Fraction of a collection

Fraction of a number = (Total / Denominator) x Numerator

For 3/4 of 12: 12 / 4 = 3, then 3 x 3 = 9.

Comparing fractions

Same denominator: bigger numerator wins; same numerator: smaller denominator wins

1/2 is bigger than 1/4 because larger pieces come from fewer cuts.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Cutting into unequal parts

✓ All parts of a fraction must be exactly equal.

WATCH OUT

✗ Mixing up numerator and denominator

✓ The denominator is down (total parts); the numerator is up (parts you have).

WATCH OUT

✗ Thinking 1/4 is bigger than 1/2

✓ More cuts make smaller pieces, so 1/4 is smaller than 1/2.

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Fractions of shapes

Identifying halves, quarters, and three-quarters

Questions

Fractions of collections

Finding fractions of groups and comparing fractions

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Identify

A pizza is cut into 4 equal slices. What fraction is one slice?

▶ Show solution

1/4 (one-quarter).

Q2EASY· Of a Collection

What is 1/2 of 18?

▶ Show solution

9.

Q3MEDIUM· Of a Collection

What is 3/4 of 20?

▶ Show solution

20 / 4 = 5, then 5 x 3 = 15.

Q4EASY· Compare

Which is bigger, 1/4 or 1/2?

▶ Show solution

1/2, because fewer cuts make bigger pieces.

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•A fraction is a part of a whole.
•Numerator is up (parts you have); denominator is down (total parts).
•1/2 means 1 of 2 equal parts; 1/4 means 1 of 4.
•3/4 means 3 of 4 equal parts.
•2/4 equals 1/2 (equivalent fractions).
•For a fraction of a group, divide first, then multiply.
•The denominator can never be zero.

ICSE marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 5-7 marks, depending on the school paper

Question type	Marks each	Typical count	What it tests
Identify / Shapes	2-3	1-2	Recognising fractions of shapes
Collections / Compare	3-4	2	Fractions of groups and comparison

Prep strategy

Fold paper to see halves and quarters
Divide a group first, then multiply for the numerator
Remember 2/4 equals 1/2
Use pictures to compare fractions

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Sharing food

Cutting pizza, cake, or chocolate into equal parts uses fractions.

Telling time

Quarter past and half past the hour are fractions of an hour.

Money

A quarter of a rupee or half a dozen are everyday fractions.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Check that parts are equal before naming a fraction
Label numerator and denominator correctly
Divide then multiply for a fraction of a group
Use a picture when comparing fractions

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Show three different ways to shade half of a square.
Find which is more: 3/4 of 8 or 1/2 of 12.

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

ICSE Class 3 School ExamHigh

Maths Olympiad / IMO (junior)Medium

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

The bottom number of a fraction tells you how many equal pieces the whole is cut into. If you cut a cake into only 2 pieces, each piece is large, but if you cut the same cake into 4 pieces, each piece is smaller. So 1/2 is a bigger share than 1/4, because the more pieces you cut something into, the smaller each piece becomes. A bigger denominator actually means smaller pieces.

Do it in two steps. First divide the total by the denominator to find one part: for 3/4 of 12, do 12 / 4 = 3, so one-quarter is 3. Then multiply by the numerator to find how many of those parts you want: 3 x 3 = 9, so three-quarters of 12 is 9. Always divide first and multiply second.

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