NCERT Solutions for Class 7th Maths – Detailed Answers and Step-by-Step Explanations

NCERT solutions for class 7th maths are designed to help students master mathematical concepts effectively. These solutions provide step-by-step explanations, making complex topics like algebra, geometry, and fractions easy to understand. By practicing with these solutions, students can boost their problem-solving skills and excel in exams with confidence.

User-Friendly Heading: NCERT Solutions for Class 7th Maths Questions and Answers

Sample Questions and Answers:

1. What is the value of x if 5x = 35?
   To find the value of x, divide both sides by 5. So, x = 35 ÷ 5 = 7.

2. If a triangle has sides of 5 cm, 12 cm, and 13 cm, is it a right triangle?
   Yes, it is a right triangle. The sides satisfy the Pythagorean theorem: 5² + 12² = 13².

3. Simplify the expression: 3(4 + 5) – 2.
   First, solve inside the parentheses: 3(9) – 2 = 27 – 2 = 25.

1. What is the perimeter of a rectangle with length 8 cm and width 5 cm?
   The perimeter is given by 2 × (length + width). So, 2 × (8 + 5) = 2 × 13 = 26 cm.

2. A bag contains 12 red balls and 8 blue balls. What is the probability of drawing a red ball?
   The total number of balls is 12 + 8 = 20. So, the probability of drawing a red ball is 12/20 or 3/5.

3. How do you convert 3/4 into a percentage?
   Multiply 3/4 by 100: (3/4) × 100 = 75%. So, 3/4 is equivalent to 75%.

4. What is the area of a triangle with a base of 10 cm and height of 5 cm?
   The area of a triangle is given by 1/2 × base × height. So, 1/2 × 10 × 5 = 25 cm².

5. Solve the equation: 2x + 3 = 7.
   Subtract 3 from both sides: 2x = 4. Now divide by 2: x = 2.

6. What is the sum of angles in a quadrilateral?
   The sum of the interior angles of any quadrilateral is 360°.

7. If the length of one side of a square is 6 cm, what is its area?
   The area of a square is side². So, 6² = 36 cm².

8. What is the value of y if 3y – 4 = 11?
   Add 4 to both sides: 3y = 15. Now, divide by 3: y = 5.

1. How do you find the LCM of 8 and 12?
   List the multiples of each number: 8 (8, 16, 24, 32...), and 12 (12, 24, 36...). The LCM is 24.

2. What is the volume of a cube with side length 4 cm?
   The volume of a cube is side³. So, 4³ = 64 cm³.

3. A circle has a radius of 7 cm. What is its area?
   The area of a circle is πr². So, π × 7² = 3.14 × 49 ≈ 153.86 cm².

4. What is the mean of these numbers: 4, 8, 10, 12?
   The mean is the sum of the numbers divided by the number of terms: (4 + 8 + 10 + 12) ÷ 4 = 34 ÷ 4 = 8.5.

1. If a number is divided by 5 and the result is 9, what is the number?
   Multiply 9 by 5 to get the number. So, 9 × 5 = 45.

2. A train travels 60 km in 1 hour. How far will it travel in 4 hours?
   In 1 hour, the train travels 60 km. So in 4 hours, it will travel 60 × 4 = 240 km.

3. What is the ratio of 18 to 24 in simplest form?
   The GCD of 18 and 24 is 6. So, divide both by 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4. The ratio is 3:4.

4. A rectangular garden has a length of 15 m and a width of 10 m. What is its area?
   The area of a rectangle is length × width. So, 15 × 10 = 150 m².

5. How do you subtract fractions: 5/8 – 1/4?
   First, find a common denominator: 5/8 – 2/8 = 3/8.

6. What is the perimeter of a square with side length 9 cm?
   The perimeter of a square is 4 × side. So, 4 × 9 = 36 cm.

7. If a rectangle has a length of 20 cm and width of 5 cm, what is its perimeter?
   The perimeter is 2 × (length + width). So, 2 × (20 + 5) = 2 × 25 = 50 cm.

8. What is the area of a circle with a radius of 14 cm?
   Area = πr² = 3.14 × 14² = 3.14 × 196 ≈ 615.44 cm².

9. Solve for x: 4x – 7 = 13.
   Add 7 to both sides: 4x = 20. Now, divide by 4: x = 5.

10. A number is divisible by 6. What are the possible values of the number?
    The number must be divisible by both 2 and 3. So, possible values include 6, 12, 18, etc.

11. If the perimeter of a square is 24 cm, what is the length of one side?
    The perimeter of a square is 4 × side. So, 24 ÷ 4 = 6 cm.

12. A number is divisible by 9. What is the rule for divisibility by 9?
    The rule is that if the sum of the digits of a number is divisible by 9, then the number is divisible by 9.

13. What is the fraction equivalent of 0.75?
    To convert 0.75 into a fraction, write it as 75/100, then simplify it to 3/4.

14. If the area of a rectangle is 50 cm² and its width is 5 cm, what is its length?
    The area is length × width. So, 50 ÷ 5 = 10 cm.

15. What is the sum of the first 5 prime numbers?
    The first 5 prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28.

16. How do you simplify the expression: 7(2x – 4)?
    Distribute 7: 7 × 2x – 7 × 4 = 14x – 28.

17. If a box contains 20 red balls and 30 green balls, what is the probability of drawing a green ball?
    The total number of balls is 20 + 30 = 50. The probability of drawing a green ball is 30/50 or 3/5.

18. What is the average of 4, 8, 10, 12, and 16?
    The average is the sum of the numbers divided by the total number of numbers: (4 + 8 + 10 + 12 + 16) ÷ 5 = 50 ÷ 5 = 10.

19. How do you divide fractions: 3/4 ÷ 1/2?
    Multiply the first fraction by the reciprocal of the second fraction: 3/4 × 2/1 = 6/4 = 3/2.

20. What is the total cost of 6 pens if one pen costs 12 rupees?
    The total cost is 6 × 12 = 72 rupees.

21. A bottle contains 40 liters of water. If 12 liters are used, how much is left?
    The amount of water left is 40 – 12 = 28 liters.

22. What is the volume of a cylinder with radius 3 cm and height 5 cm?
    The volume of a cylinder is πr²h. So, π × 3² × 5 = 3.14 × 9 × 5 = 141.3 cm³.

23. How do you add fractions: 1/3 + 1/4?
    Find the least common denominator, which is 12. So, 1/3 = 4/12 and 1/4 = 3/12. Now, 4/12 + 3/12 = 7/12.

24. A number is divisible by 2 and 3. What are the possible values of the number?
    The number must be divisible by 6. Possible values include 6, 12, 18, etc.

25. If the area of a square is 36 cm², what is the length of its side?
    The area of a square is side². So, √36 = 6 cm.

26. What is the volume of a rectangular box with dimensions 4 cm by 5 cm by 6 cm?
    The volume is length × width × height. So, 4 × 5 × 6 = 120 cm³.

27. Solve the equation: x – 3 = 7.
    Add 3 to both sides: x = 10.

28. What is the perimeter of a triangle with sides 5 cm, 6 cm, and 7 cm?
    The perimeter is the sum of the sides: 5 + 6 + 7 = 18 cm.

29. What is the area of a parallelogram with a base of 8 cm and a height of 4 cm?
    The area of a parallelogram is base × height. So, 8 × 4 = 32 cm².

30. How do you simplify the expression: 6x + 3x?
    Combine like terms: 6x + 3x = 9x.

31. A rectangle has a length of 12 cm and width of 8 cm. What is its area?
    The area of the rectangle is length × width: 12 × 8 = 96 cm².

32. What is the square root of 64?
    The square root of 64 is 8.

33. How do you convert 25% into a fraction?
    25% is equal to 25/100, which simplifies to 1/4.

34. What is the sum of the interior angles of a hexagon?
    The sum of the interior angles of a hexagon is 720°.

35. What is the perimeter of a rhombus with side length 7 cm?
    The perimeter of a rhombus is 4 × side. So, 4 × 7 = 28 cm.

Top Indian Books for NCERT Solutions for Class 7th Maths

1. NCERT Mathematics Textbook for Class 7

   • Author: NCERT
   • Publication: NCERT
   • Content: This is the official NCERT textbook which covers all the essential concepts in a well-structured format. It includes chapter-wise problems, with theoretical explanations followed by practical examples. The questions range from basic exercises to challenging problems that develop critical thinking.

2. Mathematics for Class 7

   • Author: R.S. Aggarwal
   • Publication: S. Chand
   • Content: This book offers an extensive collection of questions for practice. It includes solutions for each exercise, step-by-step explanations, and helps students enhance their problem-solving skills. The questions focus on application and understanding of concepts like algebra, geometry, and data handling.

3. Class 7 Mathematics (Together with)

   • Author: R.P. Bhatnagar
   • Publication: S. Chand
   • Content: A well-organized guide that covers the NCERT syllabus. It includes solved examples, unsolved practice questions, and concept-building exercises to strengthen the foundation of the subject. It also includes practice tests and worksheets.

4. Mathematics for Class 7 by M.L. Agarwal

   • Author: M.L. Agarwal
   • Publication: Arya Publishing
   • Content: This book offers clear and concise explanations of all topics from the NCERT syllabus. It includes model test papers, chapter-wise exercises, and solutions, which can help in improving speed and accuracy in solving mathematical problems.

5. NCERT Solutions for Class 7 Mathematics

   • Author: Pradeep Publications
   • Publication: Pradeep Publications
   • Content: This solution book provides detailed step-by-step solutions for all the exercises in the NCERT Class 7 Mathematics textbook. The book helps students understand how to approach and solve problems efficiently.

6. Mathematics Class 7 by R.D. Sharma

   • Author: R.D. Sharma
   • Publication: Dhanpat Rai Publications
   • Content: R.D. Sharma's book provides explanations with examples and practice problems. It covers topics like fractions, decimals, linear equations, and geometry in a well-detailed and organized manner. The book is designed to give a deep understanding of the subject.

7. Maths Olympiad for Class 7

   • Author: A. Das Gupta
   • Publication: Arihant
   • Content: This book is designed for students who want to excel in mathematics beyond the standard curriculum. It includes Olympiad-level questions and exercises, helping students sharpen their problem-solving skills and logical thinking abilities.

8. Comprehensive Mathematics for Class 7

   • Author: V.K. Sharma
   • Publication: New Saraswati House
   • Content: The book offers a comprehensive collection of theory, examples, and exercises, designed according to the NCERT curriculum. It includes a variety of questions that range from basic to difficult, enabling students to practice rigorously.

9. Mathematics for Class 7 by S.K. Gupta

   • Author: S.K. Gupta
   • Publication: Laxmi Publications
   • Content: The book is filled with in-depth concepts and covers everything from arithmetic to algebra. It contains a vast array of exercises that focus on the improvement of mathematical skills and conceptual clarity.

10. Problems in Mathematics for Class 7

    • Author: A. K. Sharma
    • Publication: S. Chand
    • Content: This book provides a collection of challenging problems from various mathematical topics. It is ideal for students who want to test their skills and enhance their understanding of the concepts taught in class.

The NCERT Solutions for Class 7 Maths is an essential resource for students preparing for exams and looking to build a strong foundation in mathematics. NCERT textbooks are designed with the aim of making learning systematic and interactive. These solutions offer a well-structured approach to the various topics covered in Class 7 Maths, ensuring that every student understands the concepts thoroughly.

Class 7 Mathematics introduces students to a wide range of new topics. Key concepts include rational numbers, algebraic expressions, basic geometry, and probability. One of the primary benefits of using the NCERT Solutions is the clarity with which these concepts are explained. The solutions are crafted to break down each chapter into easy-to-understand steps, ensuring students can easily grasp complex mathematical problems.

Each chapter in the NCERT textbook includes a variety of exercises that cater to different learning levels. From basic questions aimed at improving understanding to more challenging problems that test application skills, these exercises cover all aspects of the curriculum. The solutions provide step-by-step explanations that can help students approach similar problems with confidence.

Another key feature of the NCERT Solutions is its focus on conceptual understanding. Students are not merely given answers to problems, but also taught the reasoning behind each solution. This approach helps students understand the 'why' behind each mathematical step, fostering a deeper comprehension of the subject matter.

The importance of practice cannot be stressed enough when it comes to mathematics. By working through the exercises provided in the NCERT textbook and checking the solutions, students can ensure that they are well-prepared for exams. These solutions also help students identify areas of weakness, allowing them to focus on improving those specific areas.

For students who wish to go beyond the NCERT textbook, there are several other resources available, including practice books, Olympiad question banks, and workbooks that complement the NCERT syllabus. These materials provide additional practice and challenge students to refine their skills.