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

Class 6 Maths Worksheet — Free PDF with Answers

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Chapter 7 Overview: Fractions and Decimals

Looking for a class 6 math worksheet or maths worksheet for class 6 with answers? This comprehensive resource covers everything you need. 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.

Beyond this worksheet, SparkEd offers interactive online practice for Fractions with step-by-step solutions and progress tracking — perfect for daily revision.

Exercise 7.1 — Understanding Fractions

This exercise builds the foundational understanding of what fractions represent.

Problem: Identifying fractions from figures

Question: A circle is divided into $8$ equal parts, and $3$ parts are shaded. Write the fraction for the shaded portion and the unshaded portion.

Solution:

Shaded fraction:

Unshaded fraction:

Verification: $\frac{3}{8} + \frac{5}{8} = \frac{8}{8} = 1$ (the whole) ✓

Answer: Shaded $= \frac{3}{8}$, Unshaded $= \frac{5}{8}$.

Problem: Converting between mixed and improper fractions

Question: Convert $3\frac{2}{5}$ to an improper fraction and convert $\frac{17}{4}$ to a mixed fraction.

Solution:

Mixed to improper:

Improper to mixed:

Answer: $3\frac{2}{5} = \frac{17}{5}$ and $\frac{17}{4} = 4\frac{1}{4}$.

Problem: Finding equivalent fractions

Question: Find three fractions equivalent to $\frac{3}{4}$.

Solution:

Multiply numerator and denominator by the same number:

Answer: $\frac{6}{8}$, $\frac{9}{12}$, and $\frac{15}{20}$ are all equivalent to $\frac{3}{4}$.

Exercise 7.2 — Comparing and Ordering Fractions

This exercise covers methods for comparing fractions of different types.

Problem: Comparing unlike fractions

Question: Compare $\frac{4}{7}$ and $\frac{3}{5}$.

Solution:

Method — Cross multiplication:

Since $20 < 21$:

Alternative — LCM method:
LCM of $7$ and $5 = 35$.

Answer: $\frac{4}{7} < \frac{3}{5}$.

Problem: Arranging fractions in ascending order

Question: Arrange $\frac{2}{3}$, $\frac{5}{6}$, $\frac{1}{2}$, $\frac{3}{4}$ in ascending order.

Solution:

LCM of $3, 6, 2, 4 = 12$.

Convert all fractions:

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

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

Exercise 7.3 — Addition and Subtraction of Fractions

This exercise covers adding and subtracting like and unlike fractions.

Problem: Adding unlike fractions

Question: Compute $\frac{3}{4} + \frac{2}{3}$.

Solution:

LCM of $4$ and $3 = 12$.

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

Problem: Subtracting mixed fractions

Question: Compute $3\frac{1}{2} - 1\frac{3}{4}$.

Solution:

Convert to improper fractions:

LCM of $2$ and $4 = 4$:

Answer: $3\frac{1}{2} - 1\frac{3}{4} = 1\frac{3}{4}$.

Exercise 7.4 — Introduction to Decimals

This exercise connects fractions to their decimal representations.

Problem: Converting fractions to decimals

Question: Convert $\frac{3}{4}$, $\frac{7}{10}$, and $\frac{13}{25}$ to decimals.

Solution:

$\frac{3}{4}$: Make the denominator $100$.

$\frac{7}{10} = 0.7$ (denominator is already $10$)

$\frac{13}{25}$: Make the denominator $100$.

Answer: $\frac{3}{4} = 0.75$, $\frac{7}{10} = 0.7$, $\frac{13}{25} = 0.52$.

Problem: Adding decimals

Question: Compute $12.35 + 7.8 + 0.456$.

Solution:

Align the decimal points (add zeros if needed):

Answer: $12.35 + 7.8 + 0.456 = 20.606$.

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

Question: In the number $35.274$, what is the place value of each digit?

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 | $0.004 = \frac{4}{1000}$ |

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

Key Concepts and Formulas

Tips for Solving Fractions and Decimals Problems

1. Never add denominators. $\frac{1}{2} + \frac{1}{3} \ne \frac{2}{5}$. Find a common denominator first.

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.

5. Verify fraction-to-decimal conversions by multiplying back. For example, $0.75 \times 4 = 3$, confirming $\frac{3}{4} = 0.75$.

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.

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