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CBSE Class 5 Mathematics★ 5-7 marks in Class 5 Mathematics assessments; fractions

Parts and Wholes

Parts and Wholes is a current Class 5 CBSE Mathematics chapter from NCERT Math Magic. These notes cover fractions — equivalent fractions, comparison, addition and subtraction, fraction of a collection, and word problems with clear examples and practice.

⏱ 12 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 and types of fractions
2Find and simplify equivalent fractions
3Compare fractions using denominators or a common denominator
4Add and subtract like and unlike fractions
5Find a fraction of a collection and solve word problems

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Why this chapter matters

'Parts and Wholes' builds a strong understanding of fractions -- what they mean, how to compare them, find equivalents, and add or subtract them. These skills are the foundation for decimals, percentages, ratios, and algebra in later classes, and appear in everyday sharing and measuring.

Before you start — revise these

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

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Class 4 Mathematics: Introduction to fractions

Halves, quarters, and simple fractions

Parts and Wholes — Class 5 Mathematics (CBSE)

Based on the NCERT Math Magic Grade 5 textbook. Understand how fractions represent parts of a whole, then solve the practice set without looking at the answers.

1. Why this chapter matters

Fractions are everywhere — half a glass of water, a quarter of a chocolate bar, three-fourths of a pizza. This chapter builds a solid understanding of fractions: what they mean, how to compare them, how to find equivalent fractions, and how to add and subtract them. Students also learn to find a fraction of a collection (for example, one-third of 12 apples) and solve real-world word problems. This lays the groundwork for decimals, percentages, ratios, and algebra in higher classes.

2. What is a fraction?

A fraction represents a part of a whole. It has two parts:

Numerator: The number of parts we have (top number).
Denominator: The total number of equal parts the whole is divided into (bottom number).

Example: In the fraction 3/4 (three-fourths), the whole is divided into 4 equal parts and we take 3 of them.

Types of fractions

Type	Description	Example
Proper fraction	Numerator < Denominator	2/5, 3/8, 7/12
Improper fraction	Numerator > Denominator	7/3, 11/4, 5/2
Mixed fraction	Whole number + proper fraction	1 1/2, 2 3/4, 3 1/3
Like fractions	Fractions with same denominator	2/7, 4/7, 5/7
Unlike fractions	Fractions with different denominators	2/3, 5/8, 7/12
Unit fraction	Numerator is 1	1/2, 1/3, 1/4, 1/5
Equivalent fractions	Different fractions with same value	1/2 = 2/4 = 3/6 = 4/8

3. Equivalent fractions

Equivalent fractions look different but represent the same amount.

To get an equivalent fraction, multiply or divide the numerator and denominator by the same number (except zero).

Example: Find three equivalent fractions for 2/3.

2/3 = (2 x 2)/(3 x 2) = 4/6 2/3 = (2 x 3)/(3 x 3) = 6/9 2/3 = (2 x 4)/(3 x 4) = 8/12

Example: Find an equivalent fraction for 8/12 by simplifying.

8/12 = (8 / 4)/(12 / 4) = 2/3

The simplest form of 8/12 is 2/3.

4. Comparing fractions

Rule 1: Same denominator

If denominators are the same, the fraction with the larger numerator is larger.

Example: 5/8 > 3/8 (because 5 > 3)

Rule 2: Same numerator

If numerators are the same, the fraction with the smaller denominator is larger.

Example: 3/4 > 3/8 (because 4 < 8, so the parts are bigger)

Rule 3: Different numerators and denominators

Make the denominators the same (find LCM), then compare numerators.

Example: Compare 2/3 and 3/5.

LCM of 3 and 5 = 15 2/3 = 10/15 3/5 = 9/15 Since 10/15 > 9/15, we have 2/3 > 3/5.

5. Addition and subtraction of like fractions

When denominators are the same, add or subtract only the numerators.

3/8 + 2/8 = (3 + 2)/8 = 5/8
7/12 — 4/12 = (7 — 4)/12 = 3/12 = 1/4 (simplify)

When denominators are different, first convert to equivalent fractions with a common denominator.

1/2 + 1/3 = 3/6 + 2/6 = 5/6
3/4 — 1/3 = 9/12 — 4/12 = 5/12

Word problem: Ravi ate 1/4 of a pizza and Sita ate 2/5 of the same pizza. How much did they eat together?

1/4 + 2/5 = 5/20 + 8/20 = 13/20

6. Fraction of a collection

To find a fraction of a collection, divide the total by the denominator and multiply by the numerator.

Example: Find 2/3 of 24 apples.

Step 1: 24 / 3 = 8 (one-third of 24) Step 2: 8 x 2 = 16 (two-thirds of 24)

So 2/3 of 24 apples = 16 apples.

Example: Find 3/4 of 20 marbles.

Step 1: 20 / 4 = 5 Step 2: 5 x 3 = 15

So 3/4 of 20 marbles = 15 marbles.

7. Mixed fractions

A mixed fraction combines a whole number and a proper fraction.

Converting mixed to improper: Multiply the whole number by the denominator, then add the numerator.

2 1/3 = (2 x 3 + 1)/3 = 7/3

Converting improper to mixed: Divide the numerator by the denominator. The quotient is the whole number, the remainder is the numerator.

7/3 = 2 remainder 1 = 2 1/3

8. Word problems

Problem 1: A chocolate bar has 12 pieces. Rohan ate 1/3 of it. How many pieces did he eat?

12 / 3 = 4 pieces

Problem 2: Meera read 3/5 of a 25-page story. How many pages did she read?

25 / 5 = 5, then 5 x 3 = 15 pages

Problem 3: A farmer has 60 cows. 1/4 are black and the rest are white. How many are white?

Black cows = 60 / 4 = 15. White cows = 60 — 15 = 45.

9. Activity corner

Activity 1: Take a paper rectangle. Fold it into 4 equal parts. Colour 1 part red, 2 parts blue, and 1 part green. Write the fraction for each colour.

Activity 2: Take 20 objects (buttons, beads, stones). Find 1/2 of 20, 1/4 of 20, 3/4 of 20, 2/5 of 20. Record your answers.

Activity 3: Draw a rectangle on a grid of 12 squares. Colour 1/2 of it one colour and 1/3 another colour. How many squares of each colour?

10. Common mistakes

Mistake: Adding both numerators and denominators (2/5 + 1/5 = 3/10 instead of 3/5) Fix: When adding like fractions, add only the numerators. The denominator stays the same.
Mistake: Thinking a larger denominator always means a larger fraction Fix: When numerators are the same, a smaller denominator means a larger fraction (because each part is bigger).
Mistake: Forgetting to simplify the final answer Fix: Always check whether the answer can be reduced to its simplest form.

11. Key facts

Fraction = part of a whole (numerator / denominator).
Equivalent fractions are made by multiplying or dividing both parts by the same number.
To compare unlike fractions, find a common denominator first.
To find a fraction of a collection: divide by denominator, multiply by numerator.
Always simplify fractions to their lowest terms.
A mixed fraction has a whole number and a proper fraction.

12. Self-test

Write three equivalent fractions for 1/3.
Which is larger: 3/7 or 5/7? Explain why.
Find 3/5 of 30 mangoes.
Add: 2/9 + 4/9. Simplify your answer.
A ribbon is 24 cm long. Priya uses 3/8 of it. How much ribbon does she use?

13. Answer key

Write three equivalent fractions for 1/3. Answer: 2/6, 3/9, 4/12 (or any fraction where numerator and denominator are multiplied by the same number).
Which is larger: 3/7 or 5/7? Explain why. Answer: 5/7 is larger. When denominators are the same (both 7), the larger numerator means the larger fraction (5 > 3).
Find 3/5 of 30 mangoes. Answer: 30 / 5 = 6. 6 x 3 = 18 mangoes.
Add: 2/9 + 4/9. Simplify your answer. Answer: (2 + 4)/9 = 6/9 = 2/3.
A ribbon is 24 cm long. Priya uses 3/8 of it. How much ribbon does she use? Answer: 24 / 8 = 3. 3 x 3 = 9 cm.

14. Quick revision

A fraction has a numerator (parts taken) and denominator (total parts).
Equivalent fractions = same value, different numbers.
Compare: same denominator = compare numerators. Same numerator = compare denominators.
Add/subtract: same denominator first, then work on numerators.
Fraction of a collection = (Total / Denominator) x Numerator.
Practise with real objects (chapatis, chocolates, fruits) to build understanding.

Key formulas & results

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

Equivalent fractions

Multiply or divide numerator and denominator by the same number

1/2 = 2/4 = 3/6.

Fraction of a collection

(Total / Denominator) x Numerator

For example, 2/3 of 24 = (24/3) x 2 = 16.

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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

✗ Adding both numerators and denominators

✓ When adding like fractions, add only the numerators; the denominator stays the same (2/5 + 1/5 = 3/5).

WATCH OUT

✗ Thinking a larger denominator always means a larger fraction

✓ When numerators are equal, a smaller denominator means a larger fraction because each part is bigger.

WATCH OUT

✗ Forgetting to simplify the answer

✓ Always reduce the final fraction to its simplest form.

NCERT exercises (with solutions)

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

Fractions basics

Equivalent fractions and comparison

Questions

Operations and word problems

Adding, subtracting, and fraction of a collection

Questions

Practice problems

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

Q1EASY· Equivalent

Write three equivalent fractions for 1/3.

▶ Show solution

2/6, 3/9, and 4/12 (multiplying numerator and denominator by the same number).

Q2EASY· Compare

Which is larger, 3/7 or 5/7? Why?

▶ Show solution

5/7 is larger, because with equal denominators the fraction with the larger numerator is bigger.

Q3EASY· Collection

Find 3/5 of 30 mangoes.

▶ Show solution

30 / 5 = 6, then 6 x 3 = 18 mangoes.

Q4MEDIUM· Add

Add 2/9 + 4/9 and simplify.

▶ Show solution

(2 + 4)/9 = 6/9 = 2/3.

5-minute revision

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

•A fraction has a numerator (parts taken) and a denominator (total parts).
•Equivalent fractions have the same value but different numbers.
•Same denominator: compare numerators; same numerator: smaller denominator is larger.
•Add or subtract like fractions by working with the numerators.
•For unlike fractions, find a common denominator first.
•Fraction of a collection = (Total / Denominator) x Numerator.
•Always simplify to the lowest terms.

CBSE 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
Equivalent / compare	2-3	1-2	Equivalent fractions and comparison
Operations / word problems	3-4	1-2	Add, subtract, fraction of a collection

Prep strategy

Practise finding and simplifying equivalent fractions
Use the comparison rules carefully
Add and subtract by matching denominators
Learn the fraction-of-a-collection method

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

Fractions describe sharing pizzas, chocolates, and rotis fairly.

Cooking and measuring

Recipes use fractions like half a cup or a quarter teaspoon.

Foundation for maths

Fractions lead to decimals, percentages, and ratios.

Exam strategy

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

State the comparison rule you are using
Match denominators before adding or subtracting
Use the divide-then-multiply method for collections
Simplify every final answer

Going beyond the textbook

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

Order a set of unlike fractions from smallest to largest.
Solve multi-step word problems combining fractions.

Where else this chapter is tested

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

CBSE Class 5 School ExamHigh

Maths Olympiad / IMOMedium

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Questions students ask

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

When you multiply both the numerator and the denominator of a fraction by the same number, you are just cutting the same whole into more, smaller pieces and taking proportionally more of them. So 1/2 means one of two equal parts, and 2/4 means two of four equal parts, which cover exactly the same amount of the whole. That is why 1/2, 2/4, 3/6, and 4/8 are all equal -- they describe the same quantity in different numbers.

First change them into equivalent fractions that share a common denominator, usually the lowest common multiple of the two denominators. For example, to add 1/2 and 1/3, the common denominator is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6. Now that the denominators match, add only the numerators: 3/6 + 2/6 = 5/6. Finally, simplify the answer if possible.

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