CBSE Class 7 Mathematics Chapter 2: Fractions and Decimals NCERT Solutions

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NCERT Solutions PDF Class 7 PDF

This comprehensive set of NCERT Solutions for CBSE Class 7 Mathematics, Chapter 2: Fractions and Decimals, provides detailed explanations and step-by-step solutions for all exercises. The chapter focuses on understanding and performing operations with fractions, including addition, subtraction, and arranging them in ascending or descending order. It also introduces the concept of mixed fractions and their manipulation. These solutions are designed to help students grasp the fundamental concepts of fractions and decimals, build confidence in solving related problems, and prepare effectively for their examinations. By working through these expertly crafted solutions, students can reinforce their learning and achieve academic success in mathematics.

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BoardCBSE
ClassClass 7
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 2

Chapter summary

Chapter 2 of the CBSE Class 7 Mathematics curriculum delves into the operations of fractions and decimals. This NCERT Solutions set covers exercises on adding and subtracting fractions, converting between mixed and improper fractions, and ordering fractions. It also includes problems related to magic squares, reinforcing the concept of consistent sums across rows, columns, and diagonals using fractional values. The solutions aim to provide clarity and accuracy for students practicing these essential arithmetic skills.

Learning outcomes

  • Understand the concept of fractions and their representation.
  • Perform addition and subtraction of fractions with different denominators.
  • Convert mixed fractions to improper fractions and vice versa.
  • Arrange fractions in descending order.
  • Apply fraction operations in real-world contexts like magic squares.

Topics covered

Paper topics

  • Fractions
  • Addition of Fractions
  • Subtraction of Fractions
  • Mixed Fractions
  • Improper Fractions
  • Comparing Fractions
  • Ordering Fractions
  • Magic Squares
  • Least Common Multiple (LCM)
  • Common Denominators

Important topics

  • Addition and Subtraction of Fractions
  • Converting Mixed to Improper Fractions
  • Ordering Fractions
  • Finding Common Denominators
  • Operations with Mixed Numbers

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Questions and Solutions

Question 1

Solve the following expressions:

(i) $2 - \frac{3}{5}$

(ii) $4 + \frac{7}{8}$

(iii) $\frac{3}{5} + \frac{2}{7}$

(iv) $\frac{9}{11} - \frac{4}{15}$

(v) $\frac{7}{10} + \frac{2}{5} + \frac{3}{2}$

(vi) $2\frac{2}{3} + 3\frac{1}{2}$

(vii) $8\frac{1}{2} - 3\frac{5}{8}$

Solution:

To solve these expressions, we perform the indicated operations (addition or subtraction) on fractions. When fractions have different denominators, we first find a common denominator.

(i) $2 - \frac{3}{5}$

We can write 2 as $\frac{2}{1}$. To subtract, we find a common denominator, which is 5.

2 - \frac{3}{5} = \frac{2 \times 5}{1 \times 5} - \frac{3}{5} = \frac{10}{5} - \frac{3}{5} = \frac{10 - 3}{5} = \frac{7}{5}

As a mixed fraction, $\frac{7}{5} = 1\frac{2}{5}$.

(ii) $4 + \frac{7}{8}$

We can write 4 as $\frac{4}{1}$. The common denominator is 8.

4 + \frac{7}{8} = \frac{4 \times 8}{1 \times 8} + \frac{7}{8} = \frac{32}{8} + \frac{7}{8} = \frac{32 + 7}{8} = \frac{39}{8}

As a mixed fraction, $\frac{39}{8} = 4\frac{7}{8}$.

(iii) $\frac{3}{5} + \frac{2}{7}$

The least common multiple (LCM) of 5 and 7 is 35. We convert both fractions to have a denominator of 35.

\frac{3}{5} + \frac{2}{7} = \frac{3 \times 7}{5 \times 7} + \frac{2 \times 5}{7 \times 5} = \frac{21}{35} + \frac{10}{35} = \frac{21 + 10}{35} = \frac{31}{35}

(iv) $\frac{9}{11} - \frac{4}{15}$

The LCM of 11 and 15 is 165. We convert both fractions to have a denominator of 165.

\frac{9}{11} - \frac{4}{15} = \frac{9 \times 15}{11 \times 15} - \frac{4 \times 11}{15 \times 11} = \frac{135}{165} - \frac{44}{165} = \frac{135 - 44}{165} = \frac{91}{165}

(v) $\frac{7}{10} + \frac{2}{5} + \frac{3}{2}$

The LCM of 10, 5, and 2 is 10. We convert the fractions to have a denominator of 10.

\frac{7}{10} + \frac{2}{5} + \frac{3}{2} = \frac{7}{10} + \frac{2 \times 2}{5 \times 2} + \frac{3 \times 5}{2 \times 5} = \frac{7}{10} + \frac{4}{10} + \frac{15}{10} = \frac{7 + 4 + 15}{10} = \frac{26}{10}

Simplifying the fraction, $\frac{26}{10} = \frac{13}{5}$. As a mixed fraction, $\frac{13}{5} = 2\frac{3}{5}$.

(vi) $2\frac{2}{3} + 3\frac{1}{2}$

First, convert the mixed fractions to improper fractions. $2\frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{8}{3}$. $3\frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{7}{2}$.

The LCM of 3 and 2 is 6. We convert the fractions to have a denominator of 6.

\frac{8}{3} + \frac{7}{2} = \frac{8 \times 2}{3 \times 2} + \frac{7 \times 3}{2 \times 3} = \frac{16}{6} + \frac{21}{6} = \frac{16 + 21}{6} = \frac{37}{6}

As a mixed fraction, $\frac{37}{6} = 6\frac{1}{6}$.

(vii) $8\frac{1}{2} - 3\frac{5}{8}$

Convert the mixed fractions to improper fractions. $8\frac{1}{2} = \frac{(8 \times 2) + 1}{2} = \frac{17}{2}$. $3\frac{5}{8} = \frac{(3 \times 8) + 5}{8} = \frac{29}{8}$.

The LCM of 2 and 8 is 8. We convert the fractions to have a denominator of 8.

\frac{17}{2} - \frac{29}{8} = \frac{17 \times 4}{2 \times 4} - \frac{29}{8} = \frac{68}{8} - \frac{29}{8} = \frac{68 - 29}{8} = \frac{39}{8}

As a mixed fraction, $\frac{39}{8} = 4\frac{7}{8}$.

Question 2

Arrange the following fractions in descending order:

(i) $\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$

(ii) $\frac{1}{5}, \frac{3}{7}, \frac{7}{10}$

Solution:

To arrange fractions in descending order, we need to compare them. The easiest way to compare fractions is to convert them into equivalent fractions with a common denominator.

(i) $\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$

First, find the Least Common Multiple (LCM) of the denominators 9, 3, and 21. The LCM is 63.

Now, convert each fraction to an equivalent fraction with a denominator of 63:

  • $\frac{2}{9} = \frac{2 \times 7}{9 \times 7} = \frac{14}{63}$
  • $\frac{2}{3} = \frac{2 \times 21}{3 \times 21} = \frac{42}{63}$
  • $\frac{8}{21} = \frac{8 \times 3}{21 \times 3} = \frac{24}{63}$

Now we compare the numerators: 42, 24, and 14. Arranging these in descending order (largest to smallest) gives 42, 24, 14.

Therefore, the fractions in descending order are: $\frac{42}{63} > \frac{24}{63} > \frac{14}{63}$, which means $\frac{2}{3} > \frac{8}{21} > \frac{2}{9}$.

(ii) $\frac{1}{5}, \frac{3}{7}, \frac{7}{10}$

Find the LCM of the denominators 5, 7, and 10. The LCM is 70.

Convert each fraction to an equivalent fraction with a denominator of 70:

  • $\frac{1}{5} = \frac{1 \times 14}{5 \times 14} = \frac{14}{70}$
  • $\frac{3}{7} = \frac{3 \times 10}{7 \times 10} = \frac{30}{70}$
  • $\frac{7}{10} = \frac{7 \times 7}{10 \times 7} = \frac{49}{70}$

Now we compare the numerators: 14, 30, and 49. Arranging these in descending order gives 49, 30, 14.

Therefore, the fractions in descending order are: $\frac{49}{70} > \frac{30}{70} > \frac{14}{70}$, which means $\frac{7}{10} > \frac{3}{7} > \frac{1}{5}$.

Question 3

In a "magic square", the sum of the numbers in each row, in each column and along the diagonals is the same. Verify if the given square is a magic square:

\begin{pmatrix}

\frac{4}{11} & \frac{9}{11} & \frac{2}{11} \\

\frac{3}{11} & \frac{5}{11} & \frac{7}{11} \\

\frac{8}{11} & \frac{1}{11} & \frac{6}{11}

\end{pmatrix}

(Along the first row $\frac{4}{11} + \frac{9}{11} + \frac{2}{11} = \frac{15}{11}$)

Solution:

To determine if the given square is a magic square, we need to calculate the sum of the numbers in each row, each column, and both diagonals. If all these sums are equal, then it is a magic square.

The given square is:

\begin{pmatrix}

\frac{4}{11} & \frac{9}{11} & \frac{2}{11} \\

\frac{3}{11} & \frac{5}{11} & \frac{7}{11} \\

\frac{8}{11} & \frac{1}{11} & \frac{6}{11}

\end{pmatrix}

1. Sum of Rows:

  • Row 1: $\frac{4}{11} + \frac{9}{11} + \frac{2}{11} = \frac{4+9+2}{11} = \frac{15}{11}$
  • Row 2: $\frac{3}{11} + \frac{5}{11} + \frac{7}{11} = \frac{3+5+7}{11} = \frac{15}{11}$
  • Row 3: $\frac{8}{11} + \frac{1}{11} + \frac{6}{11} = \frac{8+1+6}{11} = \frac{15}{11}$

All row sums are equal to $\frac{15}{11}$.

2. Sum of Columns:

  • Column 1: $\frac{4}{11} + \frac{3}{11} + \frac{8}{11} = \frac{4+3+8}{11} = \frac{15}{11}$
  • Column 2: $\frac{9}{11} + \frac{5}{11} + \frac{1}{11} = \frac{9+5+1}{11} = \frac{15}{11}$
  • Column 3: $\frac{2}{11} + \frac{7}{11} + \frac{6}{11} = \frac{2+7+6}{11} = \frac{15}{11}$

All column sums are equal to $\frac{15}{11}$.

3. Sum of Diagonals:

  • Diagonal 1 (Top-left to Bottom-right): $\frac{4}{11} + \frac{5}{11} + \frac{6}{11} = \frac{4+5+6}{11} = \frac{15}{11}$
  • Diagonal 2 (Top-right to Bottom-left): $\frac{2}{11} + \frac{5}{11} + \frac{8}{11} = \frac{2+5+8}{11} = \frac{15}{11}$

Both diagonal sums are equal to $\frac{15}{11}$.

Since the sum of numbers in each row, each column, and both diagonals is the same ($\frac{15}{11}$), the given square is indeed a magic square.

Common mistakes

  • Errors in finding the Least Common Multiple (LCM) for denominators.
  • Incorrectly adding or subtracting numerators without a common denominator.
  • Mistakes in converting mixed fractions to improper fractions.
  • Errors in comparing fractions when they have different denominators.

Revision tips

  • Review the rules for adding and subtracting fractions with unlike denominators.
  • Practice converting mixed numbers to improper fractions and back.
  • Work through the ordering of fractions problems to solidify comparison skills.
  • Understand the 'magic square' concept and how to verify it using fraction addition.

Practice MCQs

Q1. What is the result of $2 - \frac{3}{5}$?

Q2. Which of the following fractions is the largest when arranged in descending order: $\frac{2}{9}, \frac{2}{3}, \frac{8}{21}$?

Q3. What is the sum of $\frac{3}{5} + \frac{2}{7}$?

Q4. To arrange fractions in descending order, what is the first step?

Q5. What is the result of $8\frac{1}{2} - 3\frac{5}{8}$?

Frequently asked questions

What is the main topic of Chapter 2 for Class 7 Mathematics?

Chapter 2 of Class 7 Mathematics NCERT Solutions covers Fractions and Decimals, focusing on operations like addition, subtraction, and ordering of fractions.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each problem, helping students understand the methods for solving fraction and decimal problems and reinforcing their learning for exams.

What is a 'magic square' as discussed in this chapter?

A magic square is a grid where the sum of numbers in each row, each column, and both diagonals is the same. This chapter uses fractions to create and verify magic squares.

What is the key to adding or subtracting fractions with different denominators?

The key is to find a common denominator, usually the Least Common Multiple (LCM) of the denominators, and then rewrite each fraction with this common denominator before performing the addition or subtraction.

How can I arrange fractions in descending order?

To arrange fractions in descending order, first convert them to equivalent fractions with a common denominator. Then, compare the numerators and arrange them from largest to smallest.

Important links

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