How many exercises are in NCERT Class 6 Maths Chapter 7 Fractions and Decimals?

Chapter 7 Fractions and Decimals in the 2024-25 NCERT textbook has 4 main exercises covering understanding fractions, comparing and ordering fractions, addition and subtraction of fractions, and introduction to decimals.

What are the important topics in Chapter 7 Fractions and Decimals?

The important topics are: types of fractions (proper, improper, mixed), equivalent fractions, comparing unlike fractions using LCM or cross multiplication, adding and subtracting like and unlike fractions, converting fractions to decimals, and decimal operations.

Where can I download NCERT Solutions for Chapter 7 Class 6 Maths PDF?

You can find complete solutions on this page. For printable PDF versions, visit the official NCERT website at ncert.nic.in or use SparkEd's practice section which has 60 solved questions on Fractions.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. Alternatively, convert the fraction so the denominator is 10 or 100. For example, 3/4 = 75/100 = 0.75. For 7/10, it is simply 0.7.

What is the most common mistake in adding fractions?

The most common mistake is adding both numerators and denominators separately. For example, writing 1/2 + 1/3 = 2/5, which is wrong. The correct method is to find a common denominator first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

How many exercises are in NCERT Class 6 Maths Chapter 7 Fractions and Decimals?

Chapter 7 Fractions and Decimals in the 2024-25 NCERT textbook has 4 main exercises covering understanding fractions, comparing and ordering fractions, addition and subtraction of fractions, and introduction to decimals.

What are the important topics in Chapter 7 Fractions and Decimals?

The important topics are: types of fractions (proper, improper, mixed), equivalent fractions, comparing unlike fractions using LCM or cross multiplication, adding and subtracting like and unlike fractions, converting fractions to decimals, and decimal operations.

Where can I download NCERT Solutions for Chapter 7 Class 6 Maths PDF?

You can find complete solutions on this page. For printable PDF versions, visit the official NCERT website at ncert.nic.in or use SparkEd's practice section which has 60 solved questions on Fractions.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. Alternatively, convert the fraction so the denominator is 10 or 100. For example, 3/4 = 75/100 = 0.75. For 7/10, it is simply 0.7.

What is the most common mistake in adding fractions?

The most common mistake is adding both numerators and denominators separately. For example, writing 1/2 + 1/3 = 2/5, which is wrong. The correct method is to find a common denominator first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

Solved Examples

NCERT Solutions for Class 6 Maths Chapter 7: Fractions and Decimals — Free PDF

Complete step-by-step solutions for all exercises in NCERT Class 6 Maths Chapter 7. Covers fractions, equivalent fractions, comparison, operations, and decimals with solved examples.

CBSEClass 6

The SparkEd Authors (IITian & Googler)15 March 202614 min read

Chapter 7 Overview: Fractions and Decimals

$Chapter 7 of the NCERT Class 6 Maths textbook (2024-25) covers one of the most important topics in elementary mathematics — fractions and their decimal representations. Building on the concept of whole numbers, this chapter teaches students to work with parts of a whole.$

$The key topics covered are:- Types of fractions — proper, improper, mixed, like, unlike, unit fractions- Equivalent fractions — different representations of the same value- Comparing and ordering fractions- Addition and subtraction of fractions- Introduction to decimals — tenths, hundredths, and their relation to fractions- Operations with decimals — addition and subtraction$

$For a comprehensive guide on fractions concepts, also see our detailed Fractions Class 6 Guide.$

Exercise 7.1 — Understanding Fractions

$This exercise builds the foundational understanding of what fractions represent.$

Problem: Identifying fractions from figures

$8$

$Solution:$

$Shaded fraction:$

\frac{\text{shaded parts}}{\text{total parts}} = \frac{3}{8}

$Unshaded fraction:$

\frac{\text{unshaded parts}}{\text{total parts}} = \frac{8 - 3}{8} = \frac{5}{8}

$\frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1$

$= \frac{3}{8}$

Problem: Converting between mixed and improper fractions

$3\frac{2}{5}$

$Solution:$

$Mixed to improper:$

3\frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}

$Improper to mixed:$

\frac{17}{4}: \quad 17 \div 4 = 4 \text{ remainder } 1

\frac{17}{4} = 4\frac{1}{4}

$3\frac{2}{5} = \frac{17}{5}$

Problem: Finding equivalent fractions

$\frac{3}{4}$

$Solution:$

$Multiply numerator and denominator by the same number:$

\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}

\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}

\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}

$\frac{6}{8}$

Exercise 7.2 — Comparing and Ordering Fractions

$This exercise covers methods for comparing fractions of different types.$

Problem: Comparing unlike fractions

$\frac{4}{7}$

$Solution:$

$Method — Cross multiplication:$

4 \times 5 = 20 \quad \text{and} \quad 7 \times 3 = 21

$20 < 21$

\frac{4}{7} < \frac{3}{5}

$7$

\frac{4}{7} = \frac{20}{35}, \quad \frac{3}{5} = \frac{21}{35}

\frac{20}{35} < \frac{21}{35}

$\frac{4}{7} < \frac{3}{5}$

Problem: Arranging fractions in ascending order

$\frac{2}{3}$

$Solution:$

$3, 6, 2, 4 = 12$

$Convert all fractions:$

\frac{2}{3} = \frac{8}{12}, \quad \frac{5}{6} = \frac{10}{12}, \quad \frac{1}{2} = \frac{6}{12}, \quad \frac{3}{4} = \frac{9}{12}

$\frac{6}{12} < \frac{8}{12} < \frac{9}{12} < \frac{10}{12}$

$\frac{1}{2} < \frac{2}{3} < \frac{3}{4} < \frac{5}{6}$

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Exercise 7.3 — Addition and Subtraction of Fractions

$This exercise covers adding and subtracting like and unlike fractions.$

Problem: Adding unlike fractions

$\frac{3}{4} + \frac{2}{3}$

$Solution:$

$4$

\frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12}

\frac{9}{12} + \frac{8}{12} = \frac{17}{12} = 1\frac{5}{12}

$\frac{3}{4} + \frac{2}{3} = 1\frac{5}{12}$

Problem: Subtracting mixed fractions

$3\frac{1}{2} - 1\frac{3}{4}$

$Solution:$

$Convert to improper fractions:$

3\frac{1}{2} = \frac{7}{2}, \quad 1\frac{3}{4} = \frac{7}{4}

$2$

\frac{7}{2} = \frac{14}{4}

\frac{14}{4} - \frac{7}{4} = \frac{7}{4} = 1\frac{3}{4}

$3\frac{1}{2} - 1\frac{3}{4} = 1\frac{3}{4}$

Exercise 7.4 — Introduction to Decimals

$This exercise connects fractions to their decimal representations.$

Problem: Converting fractions to decimals

$\frac{3}{4}$

$Solution:$

$\frac{3}{4}$

\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 0.75

$\frac{7}{10} = 0.7$

$\frac{13}{25}$

\frac{13}{25} = \frac{13 \times 4}{25 \times 4} = \frac{52}{100} = 0.52

$\frac{3}{4} = 0.75$

Problem: Adding decimals

$12.35 + 7.8 + 0.456$

$Solution:$

$Align the decimal points (add zeros if needed):$

12.350

+\ 7.800

+\ 0.456

\overline{20.606}

$12.35 + 7.8 + 0.456 = 20.606$

$Tip: Always align the decimal points vertically and fill in trailing zeros so all numbers have the same number of decimal places.$

Problem: Place value in decimals

$35.274$

$Solution:$

$Digit$	$Place$	$Value$
$3$	$Tens$	$30$
$5$	$Ones$	$5$
$2$	$Tenths$	$0.2 = \frac{2}{10}$
$7$	$Hundredths$	$0.07 = \frac{7}{100}$
$4$	$Thousandths$	$0.004 = \frac{4}{1000}$

35.274 = 30 + 5 + \frac{2}{10} + \frac{7}{100} + \frac{4}{1000}

$Answer: The expanded form shows that each position after the decimal point represents tenths, hundredths, thousandths, etc.$

Key Concepts and Formulas

$Here is a summary of the important concepts from Chapter 7.$

$<$

$Conversion formulas:$

a\frac{b}{c} = \frac{ac + b}{c} \quad \text{(mixed to improper)}

$\frac{a}{b} = \frac{a \times k}{b \times k}$

$Comparing fractions: Cross multiply or convert to like fractions using LCM.$

$Adding/subtracting unlike fractions: Convert to like fractions (common denominator = LCM), then add/subtract numerators.$

$Decimals and fractions:$

0.1 = \frac{1}{10}, \quad 0.01 = \frac{1}{100}, \quad 0.001 = \frac{1}{1000}

$Adding decimals: Align decimal points, fill trailing zeros, then add column by column.$

Tips for Solving Fractions and Decimals Problems

$\frac{1}{2} + \frac{1}{3} \ne \frac{2}{5}$

$2. Always simplify your answer. Reduce fractions to lowest terms by dividing by the HCF.$

$3. Convert mixed fractions to improper fractions before adding or subtracting. Convert back at the end.$

$4. For decimal addition/subtraction, align the decimal points vertically. Add trailing zeros to match decimal places.$

$0.75 \times 4 = 3$

Practice on SparkEd

$Fractions and Decimals is one of the most important chapters in Class 6 Maths. SparkEd has 60 practice questions on Fractions for Class 6 CBSE, with detailed step-by-step solutions for every question.$

$www.sparkedmaths.com | info@sparkedmaths.com$

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