NCERT Solutions For Class 6 Maths Chapter 11 Algebra Exercise 11.1 - 2025-26
In Class 6 Maths Chapter 11 Exercise 11.1 students are introduced to the fundamental concepts of algebra. This exercise focuses on understanding variables and constants, which are the building blocks of algebra. Students learn how to form and solve simple algebraic expressions and equations. The exercise includes problems that help students grasp the idea of using letters to represent numbers, making it easier to generalize mathematical problems and find solutions. Students can access The Class 6 Maths NCERT Solutions from our page which is prepared in such a way that you can understand it easily.
Table of Content
These solutions are aligned with the updated Class 6 Maths Syllabus, ensuring students are well-prepared for exams. The Class 6 Maths Chapter 11 Exercise 11.1 Questions and Answers PDF provides accurate answers to textbook questions and assists in effective exam preparation and better performance.
Glance on NCERT Solutions Maths Chapter 11 Exercise 11.1 Class 6 | Vedantu
The Class 6 Maths Chapter 11 Exercise 11.1 covers the topic - Matchstick Patterns, The Idea of a Variable, More Matchstick Patterns, More Examples of Variables.
Class 6 Maths 11.1 Exercise introduces the concept of using matchsticks to create patterns and solve problems. It's basically about visualizing numbers or shapes using matchsticks. By manipulating these matchstick patterns, you can identify relationships and solve problems.
This section introduces variables as a placeholder for unknown numbers. Imagine a box (the variable) that can hold any number. You can use letters like 'n' or 'x' to represent this unknown value and use them in calculations. This allows you to write general rules and solve problems without getting stuck on specific numbers.
This builds on the initial concept by introducing more complex patterns made with matchsticks. By looking at these patterns, you can visualize operations like addition, subtraction, and multiplication in a fun way.
This section provides more examples of how variables can be used in different situations. It emphasizes how using variables makes things flexible and powerful because you can represent various unknown values with a single letter.
This exercise lays the foundation for understanding algebra by introducing basic concepts like variables and using matchstick patterns to represent mathematical relationships.
Class 6 Maths 11.1 Exercise has 11 fully solved Questions and Answers.
Exercise 11.1
1. Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.
(a) A pattern of letter T as T
Ans: In the given below diagram we can see that there are 2 matchsticks.
Hence, the pattern is \[2n\]
(b) A pattern of letter Z as Z
Ans: In the given below diagram we can see that there are 3 matchsticks.
Hence, the pattern is \[3n\]
(c) A pattern of letter U as U
Ans: In the given below diagram we can see that there are 3 matchsticks.
Hence, the pattern is \[3n\]
(d) A pattern of letter V as V
Ans: In the given below diagram we can see that there are 2 matchsticks.
Hence, the pattern is \[2n\]
(e) A pattern of letter E as E
Ans: In the given below diagram we can see that there are 5 matchsticks.
Hence, the pattern is \[5n\]
(f) A pattern of letter S as S
Ans: In the given below diagram we can see that there are 5 matchsticks.
Hence, the pattern is \[5n\]
(g) A pattern of letter R as R
Ans: In the given below diagram we can see that there are 6 matchsticks.
Hence, the pattern is \[6n\]
2. We already know the rule for the pattern of letter L, C and F. Some of the letters from Q.1 (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Ans: We know that L requires 2 matchsticks, hence it has a pattern \[2n\]. As we solved in above questions the letter $T$ and $V$ has the same pattern \[2n\].
3. Cadets are marching in a parade. There are 5 cadets in a row. What is the rule, which gives the number of cadets, given the number of rows? (Use n for the number of rows)
Ans: Let us consider that there is a $n$ number of rows.
Cadets in each row are $5$.
Hence the total number of cadets
$ = 5n$
4. If there are 50 mangoes in a box, how will you write the total number of mangoes in terms of the number of boxes? (Use b for the number of boxes)
Ans: Let us consider that there is a $b$ number of rows.
The number of mangoes in each box is $50$.
Hence the total number of mangoes
$ = 50b$
5. The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students)
Ans: The number of students is $s$.
The number of pencils for each student is $5$.
Hence the total number of pencils needed are
$ = 5s$
6. A bird flies 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use t for flying time in minutes)
Ans: Time taken by a bird is $t$ minutes.
The speed of a bird is 1 km per minute.
Distance covered by bird
$ = {\text{speed }} \times {\text{ time}} = 1 \times t = t\;km$
7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as in figure). She has 8 dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are 8 rows? If there are 10 rows?
Ans: Dots in each row is $8$.
The number of rows is $r$.
The number of dots is $8\;r$
If there are 8 rows, the number of dots is given by
$ = 8 \times 8 = 64\,{\text{dots}}$.
If there are 10 rows, the number of dots
$ = 8 \times 10 = 80\,{\text{dots}}$.
8. Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take Radha’s age to be x years.
Ans: Let Radha’s age be $x$ years.
Since Leela’s age is equal to 4 years younger than Radha.
Then Leela’s age is $x - 4$ years.
9. Mother has made laddus. She gives some laddus to guests and family members; still 5 laddus remain. If the number of laddus mother gave away is l, how many laddus did she make?
Ans: The number of laddus given away by the mother is $l$.
Laddus remaining is $5$.
A total number of laddus is the sum of the number of laddus given away by the mother and the number of laddus remaining.
Hence, the total number of laddus is $l + 5$
10. Oranges are to be transferred from larger boxes into smaller boxes. When a large box is emptied, the oranges from it fill two smaller boxes and still 10 oranges remain outside. If the number of oranges in a small box are taken to be larger x, what is the number of oranges in the box?
Ans: The number of oranges in one box is $x$.
The number of boxes is 2
The total number of oranges inboxes is $2x$.
The remaining oranges are $10$
Hence the number of oranges $ = 2x + 10$
11. (a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common matchstick. Observe the patterns and find the rule that gives the number of matchsticks in terms of the number of squares. (Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)
Ans:
(a) 4 matchsticks.
(b) 7 matchsticks.
(c) 10 matchsticks.
(c) 13 matchsticks.
Hence the required equation is $3x + 1$, where x is the number of squares.
(b) Figs. Below gives a matchstick pattern of triangles. As in Exercise 11 (a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.
Ans:
(a) 3 matchsticks.
(b) 5 matchsticks.
(c) 7 matchsticks.
(c) 9 matchsticks.
Conclusion
In conclusion, Class 6 Maths Exercise 11.1 Solutions provides a comprehensive introduction to the basics of algebra. By working through class 6 exercise 11.1, students gain a clear understanding of variables and constants, and how to use them in forming and solving simple algebraic expressions and equations. This foundational knowledge is important as it prepares students for more complex algebraic concepts in higher grades.
CBSE Class 6 Maths Chapter 11 Other Study Materials
Chapter-Specific NCERT Solutions for Class 6 Maths
Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.
FAQs on NCERT Solutions For Class 6 Maths Chapter 11 Algebra Exercise 11.1 - 2025-26
1. What are the key topics for which I can find solutions in NCERT Class 6 Maths Chapter 11, Algebra?
The NCERT Solutions for Class 6 Maths Chapter 11 provide step-by-step answers for all problems related to the core concepts of Algebra. The key topics covered include:
Introduction to variables using patterns (like matchstick patterns).
Forming algebraic expressions with variables and arithmetic operations.
Understanding the practical use of expressions in everyday situations.
Defining an equation and understanding its components (LHS and RHS).
Finding the solution of an equation using the trial and error method.
2. How many exercises are there in Class 6 Maths Chapter 11, and do the NCERT Solutions cover all of them?
According to the latest CBSE syllabus for 2025-26, Class 6 Maths Chapter 11 (Algebra) has five exercises: 11.1, 11.2, 11.3, 11.4, and 11.5. Vedantu provides detailed, step-by-step NCERT Solutions for all the questions in every single exercise, ensuring comprehensive coverage of the entire chapter.
3. How do the NCERT Solutions for Chapter 11 explain the correct method for solving a simple equation?
The NCERT Solutions for this chapter primarily introduce the 'trial and error' method for solving equations, which is foundational for Class 6. The solutions demonstrate the process clearly:
First, understand that an equation has a Left-Hand Side (LHS) and a Right-Hand Side (RHS).
Next, you substitute different values for the variable.
Finally, you check for which value the LHS becomes exactly equal to the RHS. That value is the solution to the equation.
4. How do you translate a word problem into an algebraic equation as shown in the Chapter 11 exercises?
Translating a word problem into an equation involves a few logical steps which are clearly explained in the solutions. First, you must identify the unknown quantity and represent it with a variable (like 'x', 'y', or 'n'). Then, you translate the relationships described in words (e.g., '5 more than a number', 'twice a number') into mathematical operations. For example, 'Sarita has 10 more marbles than Ameena' becomes m + 10, where 'm' is the number of marbles Ameena has.
5. What is the main difference between an 'algebraic expression' and an 'equation' in Class 6 Maths?
The key difference lies in the equals sign (=). An algebraic expression is a combination of numbers, variables, and operations, like 'x + 20' or '3n - 5'. It does not have a specific value. An equation, however, is a statement that two expressions are equal, such as 'x + 20 = 25'. An equation has a condition and is only true for a specific value of the variable, which is called its solution.
6. Why is the 'trial and error' method, used in NCERT Chapter 11 solutions, an important first step for solving equations?
The 'trial and error' method is a crucial introductory concept because it helps build a strong intuitive understanding of what a 'solution' actually is. By testing different values, you physically see how the balance of an equation works. It shows that only one specific value for the variable will satisfy the condition (LHS = RHS), which is the fundamental principle of solving any equation. This conceptual clarity is more important at this stage than learning complex rules.
7. When solving problems from Chapter 11, what is a common mistake students make with variables?
A common mistake is confusing a variable with a specific unknown number. It's important to remember that a variable like 'n' can represent any number in an expression or a general rule (like 2n for the perimeter of a square). However, in an equation, the variable holds a specific value that you need to find. The NCERT solutions help clarify this distinction by applying variables in both contexts across different exercises.
8. Why are Vedantu’s NCERT Solutions for Class 6 Maths Chapter 11 helpful for exam preparation?
For the 2025-26 session, these solutions are particularly helpful because Algebra is a new and abstract topic for Class 6 students. The solutions provide clear, step-by-step methods that make complex ideas easy to grasp. They ensure students don't just find the answer but also understand the correct methodology as per the CBSE curriculum. This builds a strong foundation, prevents common errors, and helps score better marks in exams.
