Class 6 Maths Chapter 11 Algebra PDF Solutions and Exercises
NCERT for Algebra Class 6 Maths Chapter 11 Solutions by Vedantu, introduces students to the foundational concepts of algebra, a crucial branch of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations.
Table of Content
NCERT Solutions for Class 6 Maths chapter 11 covers the basics of terms, constants, and variables, teaching students how to form and simplify algebraic expressions. It also introduces simple equations and their solutions, providing a solid foundation for understanding more complex algebraic concepts in the future. By learning algebra, students develop critical problem-solving skills and the ability to apply mathematical reasoning to real-life situations.
Glance on Physics Chapter 11 Class 6 - Algebra
NCERT Solutions for Class 6 Maths Chapter 11 Algebra begins by explaining the basics of algebra, including terms, constants, and variables.
This Chapter Algebra class 6 teaches how to form algebraic expressions and understand their components. Simplifying algebraic expressions using addition, subtraction, multiplication, and division is a key focus, helping students manipulate and solve these expressions efficiently.
Simple equations are introduced, teaching students how to solve them by finding the value of the unknown variable. This involves basic techniques that are essential for solving more complex algebraic equations in higher grades.
The chapter also emphasizes the practical applications of algebra in solving real-life problems. This includes understanding patterns, relationships, and how algebra can be used in various scenarios.
This article contains chapter notes, important questions, exemplar solutions, exercises, and video links for Chapter 11 - Algebra, which you can download as PDFs.
There is one exercise (11 fully solved questions) in class 6th maths chapter 11 Algebra.
Access Exercise wise NCERT Solutions for Chapter 11 Maths Class 6
Exercise 11.1: This exercise gives an introduction to Variables and Expression. The objective is to understand the concept of variables and how to form algebraic expressions. Key Concepts is identifying variables and constants. Forming simple algebraic expressions from given statements. Understanding basic operations involving variables.
Access NCERT Solutions for Class 6 Maths Chapter 11 – Algebra
Exercise 11.1
1. Find this rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write this rule.
(a). A pattern of letter T
Ans. It is observed that number of matchsticks required is $2$. Hence, the pattern of letter T is \[2n\].
(b) A pattern of letter Z
Ans. It is observed that number of matchsticks required is $3$. Hence, the pattern of letter Z is \[3n\].
(c) A pattern of letter U
Ans. It is observed that number of matchsticks required is $3$. Hence, the pattern of letter V is \[3n\].
(d) A pattern of letter V
Ans. It is observed that number of matchsticks required is $2$. Hence, the pattern of letter V is \[2n\].
(e) A pattern of letter E
Ans. It is observed that number of matchsticks required is $5$. Hence, the pattern of letter E is \[5n\].
(f) A pattern of letter S
Ans. It is observed that number of matchsticks required is $5$. Hence, the pattern of letter S is \[5n\].
(g) A pattern of letter A
Ans. It is observed that number of matchsticks required is $6$. Hence, the pattern of letter A 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 Observe that letter L requires $2$ matchsticks. Hence, it has pattern \[2n\]. Letters ‘T’ and ‘V’ similarly require $2$ matchsticks and hence has pattern \[2n\].
3. Cadets are marching in a parade. There are \[\mathbf{5}\]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. Number of cadets= Number of cadets in each row × Number of rows
Number of rows= $n$
Number of cadets in each row=$5$ (∵Given)
∴ Total number of cadets= $5\times n=5n$
4. If there are \[\mathbf{50}\] 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. Number of mangoes= Number of mangoes in each box × Number of boxes
Number of boxes= b
Number of mangoes in each box= $50$ (∵Given)
∴ Total number of mangoes= $50\times b=50b$
5. The teacher distributes \[\mathbf{5}\] pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students)
Ans. Number of pencils needed= Number of pencils distributed per student × Number of students
Number of students= s
Number of pencils distributed per student= $5$ (∵Given)
∴ Total number of pencils needed= $5\times s=5s$
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. Distance covered by birds (in km) = speed × time
Time (in minutes) = t
Speed (in km/min) =$1$ km/min (∵Given)
∴ Total distance = $1\times t=t$km
7. Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as in figure). She has \[\mathbf{8}\] dots in a row. How many dots will her Rangoli have for r rows? How many dots are there if there are \[\mathbf{8}\] rows? If there are \[\mathbf{10}\] rows?
Ans. Number of dots = Number of dots in each row × Number of rows
Number of rows= r
Number of dots in each row= $8$ (∵Given)
∴ Total number of dots= $8\times r=8r$……(Equation 1)
For $8$ rows,
$r=8$
Total number of dots= \[8\times r=8\times 8=64\]……(∵ From Equation 1)
For $10$ rows,
$r=10$
Total number of dots= \[8\times r=8\times 10=80\]……(∵ From Equation 1)
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
Given that, Leela is 4 years younger than Radha.
Hence, Leela’s age = \[\left( x-4 \right)\] 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. Total laddus mother made = laddus given to guests and family + remaining laddus
Laddus given to guests and family = l
Laddus remaining = 5 (∵Given)
∴ Total laddus = 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 x, what is the number of oranges in the larger box?
Ans. Number of smaller boxes = 2
Number of oranges in 1 small box = \[x\]
Oranges remaining outside = 10
Total number of oranges in larger box = (number of smaller boxes) × (number of oranges in 1 smaller box) + oranges remaining outside
∴ Total oranges in larger box =$2x+10$
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. If we remove the last vertical stick, we are left with a pattern of C.
Letter C has 3 matchsticks which gives us pattern $3n$.
Now, add the removed vertical stick. This gives us the required equation$3n+1$.
(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. We can see that the figures have 1 matchstick more than twice the number of triangles in the pattern.
Hence, required equation is $2n+1$. (where, n is the number of triangles)
Overview of Deleted Syllabus for CBSE Class 6 Maths Algebra
Class 6 Maths Chapter Algebra: Exercises Breakdown
Conclusion
NCERT Solutions for Class 6 Maths Algebra provides a fundamental understanding of algebraic concepts, including variables, constants, algebraic expressions, and simple equations. By mastering these basics, students gain essential problem-solving skills and the ability to represent and analyse mathematical relationships symbolically. This chapter lays a critical foundation for more advanced algebraic studies, ensuring that students are well-prepared to tackle complex mathematical challenges in their future academic pursuits. In previous year's question papers, there were typically around 2–3 questions related to Algebra.
Other Study Material for CBSE Class 6 Maths Chapter 11
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 - 2025-26
1. How should I use the Vedantu NCERT Solutions for Class 6 Maths Chapter 11 to prepare for exams?
To use these NCERT Solutions effectively, first try to solve the exercise problems from the textbook on your own. Then, compare your method with the step-by-step solutions provided by Vedantu. Focus on understanding the logic behind each step, especially how to form expressions and balance equations. This practice ensures you grasp the correct methodology as per the 2025-26 CBSE guidelines and can tackle any similar problem in your exams.
2. What is the correct step-by-step method to solve a simple equation in Chapter 11?
The NCERT textbook introduces solving equations by finding a value for the variable that makes the equation true. The core principle is to keep the equation balanced. For an equation like m + 3 = 10, the step-by-step method is:
- Identify the operation performed on the variable (here, 3 is added to m).
- To isolate the variable 'm', perform the inverse operation on both sides of the equation.
- Subtract 3 from both the Left Hand Side (LHS) and the Right Hand Side (RHS): m + 3 - 3 = 10 - 3.
- This simplifies to m = 7, which is the solution to the equation.
3. How are variables used to define general rules for geometry as shown in the NCERT solutions?
In Class 6 Maths Chapter 11, variables are used to generalise formulas. For example, instead of calculating the perimeter of a specific square with a side of 5 cm, we use a variable, like 's', to represent the side length. The perimeter can then be expressed as the rule P = 4s. This single algebraic rule applies to any square, no matter the length of its side, demonstrating how variables help create universal formulas in geometry.
4. What are the main types of problems covered in the exercises of NCERT Class 6 Maths Chapter 11: Algebra?
The NCERT solutions for this chapter guide you through solving several key types of problems, including:
- Forming algebraic expressions from simple real-world statements.
- Identifying variables and constants in given expressions.
- Creating rules for patterns, such as matchstick designs.
- Translating statements into equations.
- Finding the solution to simple equations using the trial-and-error method and balancing.
5. Why is it important to show each step when solving an algebraic equation, instead of just writing the final answer?
Showing each step is crucial because it demonstrates your understanding of the balancing principle in equations, which is a fundamental concept of algebra. According to the CBSE evaluation pattern, marks are often awarded for the correct method, not just the final answer. Writing down each step helps you track your work, easily spot any mistakes, and builds a strong foundation for solving more complex equations in higher classes.
6. How do the matchstick pattern problems in the NCERT book help in understanding algebraic expressions?
The matchstick pattern problems are a practical introduction to algebra. They help you move from a concrete visual pattern to an abstract rule. By observing how the number of matchsticks changes with the number of shapes, you learn to identify a relationship and express it using a variable. For instance, finding that the rule for a chain of 'C' shapes is 3n (where 'n' is the number of Cs) is your first step in creating and understanding algebraic expressions.
7. What is the key difference between an 'algebraic expression' and an 'equation' as explained in NCERT Chapter 11?
The key difference lies in the presence of an equals sign (=). An 'algebraic expression' is a combination of numbers, variables, and operations, like y + 8 or 5x - 2; it does not have a fixed value. An 'equation', however, is a statement that sets two expressions equal to each other, such as y + 8 = 12. An equation states a condition for a variable and can be solved to find the specific value of that variable which makes the statement true.
