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NCERT Solutions Class 6 Maths Chapter 11 Algebra

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Last updated date: 12th Jul 2024
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NCERT Solutions for Maths Class 6 Chapter 11 Algebra - FREE PDF Download

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.

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Table of Content
1. NCERT Solutions for Maths Class 6 Chapter 11 Algebra - FREE PDF Download
2. Glance on Physics Chapter 11 Class 6 - Algebra
3. Access Exercise wise NCERT Solutions for Chapter 11 Maths Class 6
4. Exercise Under NCERT Solutions for Class 6 Maths Chapter 11 Algebra
5. Access NCERT Solutions for Class 6 Maths Chapter 11 – Algebra
6. Overview of Deleted Syllabus for CBSE Class 6 Maths Algebra
7. Class 6 Maths Chapter Algebra: Exercises Breakdown
8. Other Study Material for CBSE Class 6 Maths Chapter 11
9. Chapter-Specific NCERT Solutions for Class 6 Maths
FAQs


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

Current Syllabus Exercises of Class 6 Maths Chapter 11

NCERT Solutions of Class 6 Maths Algebra Exercise 11.1

Exercise Under NCERT Solutions for Class 6 Maths Chapter 11 Algebra

  • 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.)


matchstick pattern of squares


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.


matchstick pattern 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

Chapter

Dropped Topics

Algebra

11.6 Use of variables in common rules

11.7 Expressions with variables

11.8 Using expressions practically

11.9 What is an equation?

11.10 Solution of an equation


Class 6 Maths Chapter Algebra: Exercises Breakdown

Exercise

Number of Questions

Exercise 11.1

11 Questions & Solutions


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 Class 6 Maths Chapter 11 Algebra

1. What is algebra in class 6 chapter 11?

Algebra is a branch of mathematics where letters and symbols are used to represent numbers and quantities in formulas and equations. Algebra class 6 helps in generalizing arithmetic operations and solving problems involving unknown values.

2. Who invented algebra in class 6 chapter 11?

In algebra class 6 NCERT PDF solutions, Algebra was developed by the Persian mathematician Al-Khwarizmi in the 9th century. His works introduced the systematic solution of linear and quadratic equations, earning him the title "father of algebra."

3. What is class 6 chapter 11 algebra called?

Algebra Class 6 is often referred to as the language of mathematics because it uses symbols and letters to describe relationships and solve equations. It allows for the generalization of arithmetic operations and is fundamental in advanced mathematical studies.

4. How is class 6 chapter 11 algebra used in real life?

Class 6 Chapter 11 Algebra is used in various real-life situations such as calculating distances, budgeting expenses, determining the dimensions of objects, and solving problems related to speed and time. Class 6 math chapter 11 is essential in fields like engineering, science, economics, and technology for modelling and solving practical problems.

5. What is algebra in class 6 chapter 11?

In Class 6 chapter 11 algebra, students understand the basics of using symbols and letters to represent numbers. It covers forming and simplifying algebraic expressions, understanding variables and constants, and solving simple equations. In class 6 maths chapter 11 PDF, foundational knowledge prepares students for more complex algebraic concepts in higher grades.

6. What types of problems are included in class 6 chapter 11 algebra exercises?

  • Forming Algebraic Expressions: Creating expressions from given statements.

  • Simplifying Expressions: Combining like terms and applying basic operations.

  • Solving Simple Equations: Finding the value of the unknown variable.

  • Real-life Applications: Translating word problems into algebraic expressions and solving them.

7. Why is learning algebra important as discussed in Algebra class 6 NCERT PDF solutions?

Learning algebra in Algebra Class 6 NCERT PDF solutions is important because it develops logical thinking and problem-solving skills. It is essential for understanding more advanced mathematical concepts and has practical applications in various fields such as science, engineering, and economics.

8. What is a variable in algebra mentioned in class 6 maths chapter 11 PDF?

From class 6 maths chapter 11 PDF, a variable in algebra is a symbol or letter that represents an unknown value. It can take different values depending on the context of the problem.

9. Why are variables important in Algebra class 6 math chapter 11?

Variables are important in Algebra Class 6 math chapter 11 because they allow us to generalize mathematical relationships and solve problems involving unknown values. They enable us to create formulas and equations that can be applied to a wide range of situations.