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CBSE Class 7 Mathematics★ 8-12 marks in CBSE Class 7 Mathematics exams through fraction/decimal operations and word problems

Fractions and Decimals

CBSE Class 7 Mathematics chapter on Fractions and Decimals. Covers multiplication and division of fractions, multiplication and division of decimals, and word problems with NCERT-aligned depth and practice.

⏱ 14 min readEasy difficulty✓ Free · NCERT-aligned

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

1Multiply a fraction by a whole number and by another fraction
2Divide fractions using the reciprocal rule
3Multiply and divide decimals, including by 10, 100, 1000
4Divide a decimal by a decimal by converting the divisor to a whole number
5Solve real-life word problems involving fractions and decimals

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Why this chapter matters

Fractions and decimals appear everywhere in daily life -- cooking measurements, money transactions, distances on maps, and exam percentages. Mastery of fraction and decimal operations is essential for higher topics like ratio, proportion, algebra, and data interpretation. This chapter extends Class 6 fraction work to multiplication and division.

Before you start — revise these

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

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Class 6 Mathematics: Fractions and Decimals

Types of fractions, equivalent fractions, addition and subtraction of fractions and decimals

Fractions and Decimals - Class 7 Mathematics (CBSE)

Based on the 2025-26 NCERT syllabus for Class 7 Mathematics. This chapter focuses on multiplication and division operations on fractions and decimals, building on the foundational concepts from Class 6.

1. Why this chapter matters

2. Multiplication of fractions

Multiplication of a fraction by a whole number

Multiply the numerator by the whole number; keep the denominator same.

(a/b) x c = (a x c) / b

Example: (3/7) x 5 = 15/7 = 2 1/7

Multiplication of a fraction by a fraction

Multiply numerators together and denominators together.

(a/b) x (c/d) = (a x c) / (b x d)

Example: (2/3) x (5/7) = 10/21

Product of proper fractions

Product of two proper fractions is less than each of the fractions.

(1/2) x (3/4) = 3/8. Check: 3/8 < 1/2 and 3/8 < 3/4.

3. Division of fractions

Reciprocal

The reciprocal of a fraction a/b is b/a (where a and b are non-zero).

Division rule

Dividing by a fraction is the same as multiplying by its reciprocal.

(a/b) / (c/d) = (a/b) x (d/c) = (a x d) / (b x c)

Example: (5/6) / (2/3) = (5/6) x (3/2) = 15/12 = 5/4 = 1 1/4

Division of a whole number by a fraction

Example: 4 / (2/3) = 4 x (3/2) = 12/2 = 6

4. Multiplication of decimals

Multiplying a decimal by 10, 100, 1000

Shift the decimal point to the right by the number of zeros.

3.45 x 10 = 34.5
3.45 x 100 = 345
3.45 x 1000 = 3450

Multiplying two decimals

Multiply as whole numbers, then place decimal point. Total decimal places in product = sum of decimal places in factors.

Example: 2.5 x 1.4

25 x 14 = 350
2.5 has 1 decimal place, 1.4 has 1 decimal place. Total = 2 places.
Answer: 3.50 or 3.5

5. Division of decimals

Dividing a decimal by a whole number

Divide as usual, keep decimal point aligned.

Example: 6.4 / 2 = 3.2

Dividing by 10, 100, 1000

Shift decimal point to the left.

Example: 45.6 / 100 = 0.456

Dividing a decimal by a decimal

Convert the divisor to a whole number by multiplying both dividend and divisor by 10, 100, or 1000.

Example: 4.8 / 1.2 = (4.8 x 10) / (1.2 x 10) = 48 / 12 = 4

6. Worked examples

Example 1: Multiply (3/5) x (10/9)

(3 x 10) / (5 x 9) = 30/45 = 2/3 (after simplification)

Example 2: Divide (7/12) / (14/15)

(7/12) x (15/14) = (7 x 15) / (12 x 14) = 105/168 = 5/8

Example 3: Multiply 0.75 x 0.6

75 x 6 = 450. Total decimal places = 2 + 1 = 3. Answer = 0.450 = 0.45

Example 4: A car travels 45.6 km in 3.8 litres of petrol. Find distance per litre.

Distance per litre = 45.6 / 3.8 = (45.6 x 10) / (3.8 x 10) = 456 / 38 = 12 km per litre

7. Common mistakes and how to fix them

Mistake	Fix
Adding denominators during fraction multiplication	Multiply denominators too, don't add them
Forgetting to take reciprocal during division	(a/b) / (c/d) = (a/b) x (d/c), not (a/b) x (c/d)
Wrong decimal placement in product	Count total decimal places in both factors
Dividing by a decimal without converting	Convert divisor to whole number first
Forgetting to simplify final answer	Always reduce fractions to lowest terms

8. CBSE exam focus

Topic	Marks	Question style
Fraction multiplication/division	2-3 marks	Direct and simplify
Decimal multiplication/division	2-3 marks	Direct calculation
Word problems on fractions	3 marks	Real-life applications
Word problems on decimals	3 marks	Money, distance, capacity
Mixed operations	4 marks	Combined fraction and decimal

9. Self-test

Multiply: (4/9) x (15/16).
Divide: (9/11) / (18/22).
Find: 0.056 x 1000.
Evaluate: 7.2 / 0.09.
A rope is 12.5 m long. It is cut into 5 equal pieces. How long is each piece?
Ravi ate 2/5 of a pizza and Sita ate 1/3 of the same pizza. Who ate more and by how much?

10. Answer key

(4 x 15) / (9 x 16) = 60/144 = 5/12.
(9/11) x (22/18) = 198/198 = 1.
0.056 x 1000 = 56 (decimal shifts 3 places right).
7.2 / 0.09 = (7.2 x 100) / (0.09 x 100) = 720 / 9 = 80.
Each piece = 12.5 / 5 = 2.5 m.
Ravi's share = 2/5 = 6/15. Sita's share = 1/3 = 5/15. Ravi ate more by 1/15.

11. Quick revision

Multiply fractions: numerator x numerator, denominator x denominator.
Divide fractions: multiply by reciprocal.
Multiply decimals: multiply as whole numbers, place decimal at sum of places.
Divide decimals: convert divisor to whole number, adjust dividend accordingly.
Simplify answers to lowest terms.

Key formulas & results

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

Multiplication of fractions

(a/b) x (c/d) = (a x c) / (b x d)

Multiply numerators together and denominators together; never add denominators.

Division of fractions

(a/b) / (c/d) = (a/b) x (d/c)

Dividing by a fraction means multiplying by its reciprocal.

Decimal place rule (multiplication)

Total decimal places in product = sum of decimal places in the factors.

2.5 x 1.4 = 3.50 (1 + 1 = 2 decimal places)

Dividing by a decimal

Multiply both dividend and divisor by 10/100/1000 to make the divisor a whole number.

4.8 / 1.2 = 48 / 12 = 4

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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 denominators during fraction multiplication

✓ Multiply the denominators too -- do not add them. (2/3) x (5/7) = 10/21.

WATCH OUT

✗ Forgetting to take the reciprocal during division

✓ (a/b) / (c/d) = (a/b) x (d/c), not (a/b) x (c/d). Flip the second fraction.

WATCH OUT

✗ Wrong decimal placement in the product

✓ Count the total number of decimal places in both factors and place the point accordingly.

WATCH OUT

✗ Forgetting to simplify the final answer

✓ Always reduce fractions to lowest terms after multiplying or dividing.

NCERT exercises (with solutions)

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

Ex 2.1

Exercise 2.1

Multiplication of fractions by whole numbers and by fractions

Questions

Ex 2.2

Exercise 2.2

Division of fractions and reciprocals

Questions

Ex 2.3

Exercise 2.3

Multiplication and division of decimals with word problems

Questions

Practice problems

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

Q1EASY· Calculate

Multiply: (4/9) x (15/16).

▶ Show solution

(4 x 15) / (9 x 16) = 60/144 = 5/12 after simplification.

Q2MEDIUM· Calculate

Divide: (9/11) / (18/22).

▶ Show solution

(9/11) x (22/18) = 198/198 = 1.

Q3EASY· Decimals

Find: 0.056 x 1000.

▶ Show solution

Shift the decimal point 3 places to the right: 0.056 x 1000 = 56.

Q4MEDIUM· Decimals

Evaluate: 7.2 / 0.09.

▶ Show solution

Convert the divisor to a whole number: (7.2 x 100) / (0.09 x 100) = 720 / 9 = 80.

Q5MEDIUM· Word Problem

Ravi ate 2/5 of a pizza and Sita ate 1/3 of the same pizza. Who ate more and by how much?

▶ Show solution

Ravi = 2/5 = 6/15; Sita = 1/3 = 5/15. Ravi ate more by 6/15 - 5/15 = 1/15.

5-minute revision

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

•Multiply fractions: numerator x numerator, denominator x denominator.
•Divide fractions: multiply by the reciprocal of the second fraction.
•Product of two proper fractions is smaller than each of them.
•Multiply decimals: multiply as whole numbers, then place the decimal at the sum of places.
•Divide decimals: convert the divisor to a whole number first.
•Always simplify answers to lowest terms.

CBSE marks blueprint

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

Typical chapter weightage: 8-12 marks depending on school paper design

Question type	Marks each	Typical count	What it tests
Fraction operations	2-3	1-2	Multiplication and division of fractions, simplification
Decimal operations	2-3	1-2	Multiplying and dividing decimals
Word problem	3-4	1	Money, distance, capacity applications

Prep strategy

Practise converting between mixed numbers and improper fractions
Master the reciprocal rule for division
Always count decimal places when multiplying decimals
Reduce every fraction answer to lowest terms

Where this shows up in the real world

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

Cooking and recipes

Scaling a recipe up or down uses fraction multiplication -- doubling 3/4 cup gives 1 1/2 cups.

Money calculations

Splitting bills, calculating change, and computing rates per unit all use decimal multiplication and division.

Fuel efficiency

Distance per litre (km / litre) is a decimal division problem used by every driver.

Exam strategy

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

Convert mixed numbers to improper fractions before multiplying or dividing
For decimal division, write the conversion step that makes the divisor a whole number
Show the reciprocal step explicitly when dividing fractions
Always end with a simplified answer and correct units in word problems

Going beyond the textbook

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

Investigate continued fractions and how repeated reciprocals approximate irrational numbers.
Explore why every terminating decimal can be written as a fraction with a denominator that is a power of 10.

Where else this chapter is tested

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

CBSE Class 7 School ExamHigh

International Mathematics Olympiad (IMO) Level 1Medium

NTSE foundation (arithmetic)Low now, useful as foundation

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Questions students ask

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

Multiplying by a proper fraction (less than 1) means taking only a part of a quantity, so the result is smaller. (1/2) x (3/4) = 3/8, which is less than both 1/2 and 3/4.

Multiply the whole number by the reciprocal of the fraction. For example, 4 / (2/3) = 4 x (3/2) = 6.

Practice more, ask doubts, find a tutor

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