# NCERT Solutions for Class 6 Maths Chapter 11 Algebra (Ex 11.1) Exercise 11.1

## NCERT Solutions for Class 6 Maths Chapter 11 Algebra (Ex 11.1) Exercise 11.1

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 by Extramarks, provide information on algebraic concepts. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 introduces mathematical topics that explain algebraic concepts. Students learn about variables through the formation of various patterns in Class 6th Math Chapter 11.1.

• A variable’s value is not fixed; it can take on various values.
• In any practical setting, one can express relations using a variable. Additionally, it enables one to generalize a number of widely used mathematical and geometrical rules.

Students learn about the use of variables in common rules before delving deeper into the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. Some of the Geometrical Rules covered in Class 6 Maths Exercise 11.1 are:

• The perimeter of a Square
• The perimeter of a Rectangle

Arithmetic Rules covered in Class 6 Maths 11.1 are:

• Commutativity of addition of two numbers
• Commutativity of multiplication of two numbers
• Distributivity of numbers

The concepts of Using Expressions with Variables are highlighted in  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. An equation is then thoroughly described in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 using matchstick designs that are provided after that. The two grounds covered in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are as follows:

• How do equations function?
• An Equation’s solution

### Access Other Exercises of Class 6 Maths Chapter 11

 Chapter 11 – Algebra Exercises Exercise 11.2 5 Questions & Solutions Exercise 11.3 6 Questions & Solutions Exercise 11.4 3 Questions & Solutions Exercise 11.5 5 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 11 Algebra (Ex 11.1) Exercise 11.1

Before beginning to develop a thorough understanding of expressions and equations, the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 can be referred to by students for a better understanding of the mathematical concepts. Finding the rules that specify the amount of matchsticks needed to create matchstick patterns, or utilising the variable to write the rules, are just a few examples of the many attributes that are the basis for the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. Extramarks’ experts aim to familiarise students with the concept of a variable and how to use it to create mathematical equations with the help of  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. In the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1, the notion of a variable is explained through simple and illustrated examples employing everyday objects.

Students can hone their logic and analytical abilities by practising  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. This NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 can be used to comprehend a total of 11 extremely straightforward questions that are introduced in the Chapter 11 exercise. This may enable students to comprehensively understand variables, which are the most crucial elements of Algebra. Students should thoroughly complete the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 that are accessible in  PDF format on the Extramarks website or mobile application.

Other study material and learning resources may be accessed from the Extramarks website along with the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1, such as the following:

• NCERT Solutions Class 6 Maths Chapter 11 Ex 11.2
• NCERT Solutions Class 6 Maths Chapter 11 Ex 11.3
• NCERT Solutions Class 6 Maths Chapter 11 Ex 11.4
• NCERT Solutions Class 6 Maths Chapter 11 Ex 11.5

Through the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 students can have a thorough understanding of the concepts related to Algebra which can in turn help students score better in their final examination. Students’ analytical and logical skills may improve by consistently practising the exercise problems and solutions. Before moving on to the next exercise,  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 must be practised by students. The concepts of variables are described in a thorough and comprehensive manner in Chapter 11.

Students will have no trouble understanding the idea of variables in Maths once they have finished practising the questions in the Chapter 11 exercise with the assistance of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 also provide a basis for understanding Algebra and its features. Because Algebra has so many practical applications, it is essential for students to consistently practise the concerned exercises.

## Access NCERT Solutions For Class 6 Maths Chapter 11 – Algebra

The topic Algebra is introduced in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. The topic of algebra, as well as algebraic expressions and their characteristics, is thoroughly covered in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. Through the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1, students learn how to employ letters, how they help us construct rules and formulae, and how they might represent numbers and unknowable amounts. Students can study how to solve problems by performing operations on the letters that stand in for numbers with the help of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1.

Matchstick Patterns, Variables, and Introduction to Algebra are the topics covered in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are recommended to students for their preparation for the Maths examination of Class 6. All of the answers are fully explained in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 which is available on the Extramarks website and mobile application.

Each exercise question is thoroughly addressed in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 assists students in finishing the assignments, turning in their homework, and getting ready for their CBSE Class 6 tests and semester examinations.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are created by subject matter specialists at Extramarks. For an overview of NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1, students can refer to the Extramarks website and mobile application.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are available on the Extramarks website and mobile application, so students can check them if they run into any problems when attempting to answer the questions of exercise 11.1 of Chapter 11. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 may be utilised by students to clear any doubts they may have. By clicking the link provided on the Extramarks website and mobile application, students can download the PDF of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1.

Students may download the PDF files of the required study material from the Extramarks website, so they can view it later when necessary, even without an internet connection. Additionally, they can use PDF files for last-minute exam preparation. On the Extramarks website and mobile application, students can find the PDF file of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1.

## NCERT Solutions for Class 6 Maths Chapter 11 Algebra (Ex 11.1) Exercise 11.1

Students can find detailed answers to each question in the exercise by using Extramarks’ NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. These comprehensive NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are created by experienced subject-matter experts at Extramarks using their years of knowledge.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 include accurate and simple-to-understand explanations. These NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are available to students to assist them in completing the chapter exercise. Below are some of the main advantages of using Extramarks’ NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1:

• The most recent CBSE board regulations are taken into consideration while preparing the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1.
• The subject matter specialists who have in-depth knowledge of Class 6 Maths concepts have provided the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1.
• Experts have given the answers to the questions in exercise 11.1 of Chapter 11. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are elaborate and extensive for the better understanding of students.
• The Class 6 Ex 11.1 PDFs are useful for review for the final Maths exam.
• The NCERT Solutions For Class 6 Maths Chapter 11 Exercise 11.1 enable students to comprehend the concept of each topic from the standpoint of the exam.
• Solutions of Maths Class 6 Chapter 11 Exercise 11.1 are accessible for students of Class 6 for their preparation.
• Students studying for competitive exams can also obtain assistance from the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1.

Introduction to Algebra, Matchstick Patterns and Variables are the foundations of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1. To better grasp what the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 are about, students are advised to first go through the chapter theory and summary.

• Getting Started with Algebra

Students will explore the use of letters in the mathematical field of algebra. By conducting operations on the letters that stand in for numbers in algebra, they learn how to figure out unknown values.

• Pattern of Matchsticks

The number of matchsticks needed to construct the ‘n’ number of these patterns can be determined by creating matchstick patterns, counting the number of matchsticks required to form each shape or pattern, and formulating a rule.

• How do variables work?

The word “variable” refers to something that can change or vary. A variable’s value is not constant. It can have several values. The above-mentioned “n” number is a variable. Its value is arbitrary and could be 1, 2, 3, 4, etc. We use the variable “n” to specify the rule for the necessary number of matchsticks. An illustration of a variable is “n.” The letter “n” can be substituted with any other letter to represent  number with an unknown amount.

The questions posed by this exercise notions of matchstick patterns and the idea of variables are addressed in  NCERT Class 6 Maths Chapter 11 Exercise 11.1. In the area of Maths known as algebra, students discover how to use letters to create equations. The professionals at Extramarks have crafted  Class 6 Maths Chapter 11 Exercise 11.1 since they have extensive knowledge of the concepts covered in each question in Class 6 Maths 11.1.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 provide a basic introduction to Algebra for students in Class 6. The area of Maths known as Algebra deals with mathematical operations on letters, while also introducing the concepts of variables and constants. The letters employed in algebra are referred to as variables. The value of a variable can change; it is not fixed. Students can use a variable to express relations in any real-world situation.

Many fundamental geometrical and mathematical concepts can be generalised by students by applying variables. According to a series of instructions, Class 6 will learn how to write an equation. A condition on a variable is represented by a mathematical equation. An equation’s LHS and RHS are separated by the equal sign. The fundamental concept of algebra is the replacement of numbers by symbols (or other particular things). Students can learn how to arrive at a solution or conclusion by using a variable or other uncertain value in algebra. Class 6 students learned the following fresh ideas in the Maths chapter:

• Variable: Usually, a letter, most frequently a “x,” is used to denote this. The aforementioned circumstances determine its value.
• An algebraic expression, a collection of constants and variables, denotes a mathematical state or event.
• Algebraic formulas essential procedures
• Equations

Algebra is a branch of Maths that focuses on symbols and the methods for altering them. Manipulating equations or algebraic expressions is a part of algebra. Learning algebra helps students develop critical and logical thinking skills so that they can tackle a variety of problems in both academic and professional contexts. It makes way for an alternative subject. The majority of fields necessitate a basic comprehension of Maths. Significant algebraic concepts include:

• How to use fractional and decimal values to add, subtract, multiply, and divide them
• Computer power and root rules
• Exponentiated expressions: A simplified approach
• How to work out equations involving just one variable and several variables
• Variable inequality solutions
• How to create a line graph using the point-slope form and the slope-intercept formula
• How to use the quadratic formula to solve the problem to discover the roots

The following are some of the subjects that are covered in Algebra in Class 6 Maths Ch 11 Ex 11.1:

• Getting Started with Algebra
• The Matchstick Issues
• Concept of a variable
• Variables are used in common rules
• Principles of geometry
• Rules of maths
• Variables in expressions
• Applications of phrases in real life
• What is the formula?
• A response to an equation

Algebra is the study of letter usage, and it helps in problem-solving. Class 6 Chapter 11 Algebra notes explain the topics thoroughly by using a pictorial and graphical representation. These notes may be accessed by students from the Extramarks website. The fundamental ideas of algebra for Class 6 are covered in the NCERT Solutions, along with its formula and examples.

The fundamental principles covered in Algebra for Class 6 such as constructing expressions with variables, and evaluating them with one or two variables will lay a solid foundation for more complex ideas in higher education.

One of the significant concepts covered in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 based on Algebra is the use of letters that can represent any number without indicating a particular number. Basic arithmetic requires algebraic procedures. This fundamental idea is the foundation for all mathematical operations, from adding two numbers to working out complex research sums. Geometrical problems are among the many equations that are built on algebraic ideas. The best method to make sure you understand the concepts presented above is to answer every question in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 based on Algebra. The step-by-step NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.1 based on Algebra for all of the problems, can also be downloaded in PDF format from the Extramarks website and mobile application.

Q.1 Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.

$\begin{array}{l}\left(a\right)\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{T}\mathrm{as}\overline{\text{\hspace{0.17em}}|\text{\hspace{0.17em}}}\\ \left(b\right)\text{\hspace{0.17em}}\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{Z}\mathrm{as}\overline{\underset{¯}{\text{\hspace{0.17em}}\overline{)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}}\text{\hspace{0.17em}}}\\ \left(c\right)\text{\hspace{0.17em}}\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{U}\mathrm{as}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\underset{¯}{|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}|}\text{\hspace{0.17em}}\\ \left(d\right)\text{\hspace{0.17em}}\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{V}\mathrm{as}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}/\\ \left(e\right)\text{\hspace{0.17em}}\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{E}\mathrm{as}\text{\hspace{0.17em}}\frac{|\text{\hspace{0.17em}}\overline{\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\text{\hspace{0.17em}}}{|\text{\hspace{0.17em}}\underset{¯}{\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\\ \left(f\right)\text{\hspace{0.17em}}\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{S}\mathrm{as}\frac{|\text{\hspace{0.17em}}\overline{\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\text{\hspace{0.17em}}}{\underset{¯}{\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}|}\\ \left(g\right)\text{\hspace{0.17em}}\mathrm{A}\mathrm{pattern}\mathrm{of}\mathrm{letter}\mathrm{A}\mathrm{as}\frac{|\text{\hspace{0.17em}}\overline{\text{}\text{}\text{}\text{}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\text{\hspace{0.17em}}|\text{\hspace{0.17em}}}{|\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}|\text{\hspace{0.17em}}\text{\hspace{0.17em}}}\end{array}$

Ans.

(a) In the formation of pattern of letter T, we can see that it will require two matchsticks.

 Number of T 1 2 3 4 5 6 – Required matchsticks 2 4 6 8 10 12 –

Therefore, the pattern is 2n.

(b) In the formation of pattern of letter Z, we can see that it will require three matchsticks.

 Number of Z 1 2 3 4 5 6 – Required matchsticks 3 6 9 12 15 18 –

Therefore, the pattern is 3n.

(c) In the formation of pattern of letter U, we can see that it will require three matchsticks.

 Number of U 1 2 3 4 5 6 – Required matchsticks 3 6 9 12 15 18 –

Therefore, the pattern is 3n.

(d) In the formation of pattern of letter V, we cansee that it will require two matchsticks.

 Number of V 1 2 3 4 5 6 – Required matchsticks 2 4 6 8 10 12 –

Therefore, the pattern is 2n.

(e) In the formation of pattern of letter E, we can see that it will require five matchsticks.

 Number of E 1 2 3 4 5 6 – Required matchsticks 5 10 15 20 25 30 –

Therefore, the pattern is 5n.
(f) In the formation of pattern of letter S, we can see that it will require five matchsticks.

 Number of S 1 2 3 4 5 6 – Required matchsticks 5 10 15 20 25 30 –

Therefore, the pattern is 5n.

(g) In the formation of pattern of letter A, we can see that it will require six matchsticks.

 Number of A 1 2 3 4 5 6 – Required matchsticks 6 12 18 24 30 36 –

Therefore, the pattern is 6n.

Q.2 We already know the rule for the pattern of letters 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.

In the formation of pattern of letter L, we can see that it will require two matchsticks.

 Number of T 1 2 3 4 5 6 – Required matchsticks 2 4 6 8 10 12 –

Therefore, the pattern is 2n. V and T are the letters in Q.1, which give us the same rule as that given by L. This is happened because in the formation of letters L, T and V, we require only two matchsticks in each.

Q.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 number of rows be n.
Number of cadets in each row = 5
Number of cadets in n rows = 5n
The general rule to get the number of cadets in n rows is 5n.

Q.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 number of boxes b.
Number of mangoes in each box = 50
Number of mangoes in b boxes = 50b
The general rule to get the number of mangoes in n boxes is 5n.

Q.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.

Let number of students be s.
Each student got pencils = 5
s students got pencils = 5s
Therefore, 5s pencils are needed to distribute in s students.

Q.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.

Let the flying time of a bird be t minutes.
Distance covered by the bird in one minute = 1 km
Distance covered by the bird in t minutes = t km
Therefore, the distance covered by a bird in t minutes is t km.

Q.7 Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots) with chalk powder. She has 9 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.

Number of dots in a row = 9
Number of rows = r
Number of dots in r rows = 9r
Number of dots in 8 rows = 9 x 8
= 72
Number of dots in 10 rows = 9 x 10 = 90

Q.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 age of Radha = x years
Difference between the age of Leela and Radha = 4 years
Therefore, age of Leela = Age of Radha – 4
= (x – 4) years

Q.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.

Number of laddus gave away by mother = l
Remaining laddus with mother = 5

Q.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 oranges in smaller box = x
Number of boxes filled by oranges = 2
Remaining oranges after filling 2 smaller boxes = 10
Total oranges in a big box = 2x + 10

Q.11 (a) Look at the following matchstick pattern of squares (Fig 11.6). 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. (b) Fig 11.7 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) We see that number of matchsticks in given pattern are 4, 7, 10 and 13, which are 1 more than thrice of the number of square. Therefore, the pattern is (3n + 1), where n is the number of squares in pattern.

(b) We see that number of matchsticks in given pattern are 3, 5, 7 and 9, which are 1 more than twice of the number of triangles. Therefore, the pattern is (2n + 1), where n is the number of triangles in pattern.