# NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4

## NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4

The Extramarks NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 provides insight into algebraic ideas. The introduction section of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 introduces a fascinating subject, the Matchsticks Pattern, which aids in the explanation of the Algebraic notion. Matchsticks are used to create a variety of patterns that help the students grasp the idea of variables.

The introductory section of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 helps students explore the following areas:

• Variables have changing values; they don’t have stable values.
• In any real-world scenario, relations can be expressed using a variable. It also enables the universal expression of a number of widely used mathematical and geometrical rules.

Students will learn about the use of Variables in Common Rules before going on to Exercise 11.2 in class.

Below is an overview of the Geometrical rules:

• rectangle with a square perimeter
• Border of a rectangle
• Mathematical principles This comprises
• Commutativity of two-number addition and multiplication
• The diversity of numbers

The ideas of Expressions with Variables and Using Expressions are highlighted. After that, a thorough explanation of the equation is provided with the aid of matchstick patterns. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 covers two areas:

• How do equations work?
• Solution of an Equation

A condition on a variable is what an equation is. It is stated by claiming that a variable expression equals a fixed number. A solution to an equation is the value of the variable in the equation that satisfies the equation. This NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 explains the trial-and-error approach, which aids in finding an equation solution.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 by Extramarks has fun activities, and questions with diverse patterns can help students better understand the chapter.

What Have We Discussed? is the title of the section at the end of  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 that lists all the chapter’s key points.

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

 Chapter 11 – Algebra Exercises Exercise 11.1 11 Questions & Solutions Exercise 11.2 5 Questions & Solutions Exercise 11.3 6 Questions & Solutions Exercise 11.5 5 Questions & Solutions

## NCERT Solutions for Class 6 Maths Chapter 11 Algebra (Ex 11.4) Exercise 11.4

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 is a simple yet crucial activity. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 demonstrates how to transform a real-world circumstance into a mathematical problem and the related algebraic equation. The questions in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 are carefully chosen to provide students the chance to apply Maths to real-world issues that can arise. Additionally, the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 helps students become comfortable with transforming problem sums into algebraic expressions. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 establishes the groundwork for the subsequent activity, which incorporates equations.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 are essential for examinations. They must therefore be thoroughly solved. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 are necessary for a deeper understanding of complex Maths. Students must practise the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 activity multiple times in order to solidify the concepts in their minds.

Class 6 Math Chapter 11 Exercise 11.4 in Algebra can be a difficult subject because it requires students to create expressions that are at a high level. However, as the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 will aid in the development of their analytical skills, learners will find the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 engaging.

After completing the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4, students will be able to use the algebraic idea in a variety of contexts. In the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4, students will run into a wide range of issues that will serve as a stimulus for them to learn more. Additionally, it is suggested that they read through the examples of the  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 that have been solved before attempting the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 problems.

## Access NCERT Solutions for Class 6 Maths Chapter 11-Algebra

The academic specialists at Extramarks have solved the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 that may be found on their website and mobile application. These NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 will make it easier for students to complete their homework and other assignments on time.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 is divided into 30 ideas, and Extramarks offers 1500+ practice questions from 50+ books, 30+ video solutions, and more for the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4. Additionally, Extramarks offers examinations broken down by chapters and topics to help with thorough preparation of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4. Both English and Hindi versions of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 are accessible at Extramarks.

Below are a few points to remember while solving the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4:

• Literal numbers or Literals are the letters that are used to represent numbers.
• All the laws (and signs) of addition, subtraction, multiplication, and division of numbers as well as the characteristics of these operations are observed by both the literal numbers themselves as well as combinations of literal numbers and numbers.
• In the equation x99, 99 is referred to as the Index or Exponent and xx as the Base. In a5a5, the Base is aa and the Index or Exponent is 55.
• A constant is a symbol with a set numerical value.
• A variable is a symbol without a predetermined numerical value.

## NCERT Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.4

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 introduces Class 6 students to algebra, a crucial area of Maths. According to theory, algebra as a field of Maths dates back to around 1550 BC, or more than 3500 years ago, when Egyptians first began employing symbols to represent unknowable numbers. Algebra is the branch of Maths that studies arithmetic operations on letters with the idea of variables and constants. Variables are the names given to the letters used in algebra. A variable’s value is not fixed; it can take on various values. In any practical setting, students can express relations using a variable.

With the help of variables, students are able to generalise a number of fundamental geometrical and Mathematical principles. Class 6 students will learn how to construct an equation using a set of instructions with the help of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4. A condition on a variable is indicated by an equation. The equal sign is located between the LHS and RHS of an equation. Algebra’s central concept is the substitution of symbols for numbers (or other particular things). Algebra is taught to students to help them learn how to use a variable, or something uncertain, to come to a conclusion or solution. The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 based on Algebra exposes Class 6 students to the following fresh ideas:

• Variable: This is typically indicated by a letter, most frequently an “x.” Its value is subject to the circumstances stated.
• A mathematical condition or circumstance is indicated by an algebraic expression, which is a grouping of constants and variables.
• Fundamental operations for Algebraic expressions
• Equations

Students may learn the fundamentals of using expressions practically in daily life through  NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4. These are a few of the essential ideas that are crucial for exam preparation. Students can use the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 created by Extramarks teachers to complete exercise-by-exercise questions on a daily basis to become familiar with these ideas and earn high marks in the examinations.

In the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 by Extramarks, along with Numbers, Variables (or letters) are first introduced in Algebra. Algebra plays a key part in Maths because it is a requirement for more advanced arithmetic and is a crucial topic to take into account. Up until this moment, the focus of the lesson on numbers, their operations, and properties was on working with numbers and shapes. The primary characteristic of algebra is the use of letters, which makes it possible to create formulas and rules. The letters in this chapter can be used to describe any number; they are not restricted to any particular number, which is their main benefit. Letters can also stand in for undefined quantities.

Algebra in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 by Extramarks, uses a variety of techniques to identify unknown facts in order to solve problems and deal with other issues. Additionally, as letters are representations of numbers, operations on them can be carried out in the same manner as operations on numbers. As a result, it is possible to research algebraic expressions and their properties. Additionally, the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 by Extramarks is incredibly beneficial for problem-solving. Subject-matter specialists at Extramarks have offered the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 for student use. With the aid of the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 by Extramarks available on the Extramarks website and mobile application, students can complete a thorough review of Chapter 11 Algebra.

The following is a list of all the exercises in Chapter 11 of Class 6 Maths:

• NCERT Solutions Class 6 Maths Chapter 11 Ex 11.1
• 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

Using letters that can correspond to any number without designating a specific number is one of the important ideas addressed in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 . Algebraic operations are necessary for basic arithmetic. All Mathematical operations, from adding two numbers to resolving intricate research sums, rely on this crucial concept. Algebraic concepts form the foundation of a variety of equations, including geometry difficulties. Answering all of the questions in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 is the best way to ensure that students comprehend the ideas outlined above. The section-by-section NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 for all of the issues can also be downloaded as a PDF file.

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• Class 6 Maths Chapter 11 Ex 11.1 –11 Questions
• Class 6 Maths Chapter 11 Ex 11.2 – 5 Questions
• Class 6 Maths Chapter 11 Ex 11.3 – 6 Questions
• Class 6 Maths Chapter 11 Ex 11.4 – 3 Questions
• Class 6 Maths Chapter 11 Ex 11.5 – 5 Questions

The use of variables in basic geometrical operations, like calculating a rectangle’s or square’s perimeter, commutative addition and multiplication of two and three numbers, distributivity of numbers, and equation construction are the subjects covered in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 centered on Algebra.

There are 30 questions in all in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4. 12 are simple sums, 8 are of medium difficulty, and 10 are difficult sums.

The NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4 centered on Algebraic Formulae are necessary for gaining a thorough understanding of the algebraic tools. The majority of the formulas relate to various arithmetic operation features. Students will learn how to calculate a square and a rectangle’s perimeters through the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4. Students also attempt to solve an expression using just one variable. The following are some significant formulas and properties mentioned in the NCERT Solutions Class 6 Maths Chapter 11 Exercise 11.4:

• The square’s perimeter is equal to 4 times the length of its sides.
• The rectangle’s perimeter is 2(l + b), where l and b are its length and width, respectively.
• A + B = B + A is the commutativity of the addition of the two numbers a and b.
• A x B = B x A is a commutative formula for multiplying two numbers, a and b.
• Speed (s) equals distance/time (d/t).

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(a) Take Sarita’s present age to be y years
(i) What will be her age 5 years from now?
(ii) What was her age 3 years back?
(iii) Sarita’s grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is 2 years younger than grandfather. What is grandmother’s age?
(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. What is her father’s age?

(b) The length of a rectangular hall is 4 meters less than 3 times the breadth of the hall. What is the length, if the breadth is b meters?

(c) A rectangular box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.

(d) Meena, Beena and Leena are climbing the steps to the hill top. Meena is at step s, Beena is 8 steps ahead and Leena 7 steps behind. Where are Beena and Meena? The total number of steps to the hill top is 10 less than 4 times what Meena has reached. Express the total number of steps using s.

(e) A bus travels at v km per hour. It is going from Daspur to Beespur. After the bus has travelled 5 hours, Beespur is still 20 km away. What is the distance from Daspur to Beespur? Express it using v.

Ans.

(a) Present age of Sarita = y years
(i) Age of Sarita after 5 years = (y + 5) years
(ii) Age of Sarita 3 years back = (y – 5) years
(iii) Age of Sarita’s grandfather = 6 times of y = 6y years
(iv)The Grandmother is 2 years younger than grandfather. So, Age of the grandmother = (6x – 2) years
(v) Sarita’s father’s age is 5 years more than 3 times Sarita’s age. So, father’s age = (3y + 5) years

(b) The breadth of rectangular hall = b m The length of rectangular hall = (3b – 4) m

(c) Height of the box = h cm
Length of the box = 5h cm
Breadth of the box = (h – 10) cm

(d) Meena is at steps = s
Since, Beena is 8 steps ahead. Then Beena is at steps = (s + 8)
Since, Leena is 7 steps behind to Meena. So, Leena is at steps = (s – 7)
Total number of steps = (4s – 10)

e) Speed of bus = v km/hr
Distance covered by bus in 5 hours = time x speed
= 5v
Remaining distance = 20 km
Total distance between Daspur to Beespur = (5v + 20) km

Q.2 Change the following statements using expressions into statements in ordinary language.
(For example, Given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language – Nalin scores 15 runs more than Salim.)
(a) A notebook costs â‚¹ p. A book costs â‚¹ 3p.
(b) Tony puts q marbles on the table. He has 8q marbles in his box.
(c) Our class has n students. The school has 20n students.
(d) Jaggu is z years old. His uncle is 4z years old and his aunt is (4z – 3) years old.
(e) In an arrangement of dots there are r rows. Each row contains 5 dots.

Ans.

(a) The cost of a book is three times the cost of a notebook.
(b) The box of tony contains 8 times the number of marbles on the table.
(c) The total students in the school is 20 times of the students of our class.
(d) Jaggu’s uncle is 4 times older than Jaggu. Jaggu’s unty is 3 years younger than his uncle.
(e) Number of rows = r
Number of dots in a row = 5
Total number of dots = 5r
Therefore, total number of dots is 5 times of the total number of rows.

Q.3 (a) Given Munnu’s age to be x years, can you guess what (x – 2) may show? Can you guess what (x + 4) may show? What (3 x + 7) may show?

$\begin{array}{l}\text{(b) Given Sara’s age today to be y years. Think of her}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}age in the future or in the past.}\\ \text{What will the following expression indicate?}\\ y+7,y–3,y+4\frac{1}{2},y–2\frac{1}{2}.\\ \text{(c) Given n students in the class like football, what}\\ \text{may 2n show? What may}\frac{\text{2n}}{}\text{show?}\end{array}$

Ans.

(a) The present age of Mannu is x years. Age of any person is 2 years less than the age of Mannu i.e., (x – 2) years.
Age of any person is 4 years more than the age of Mannu i.e., (x + 4) years.
Age of any person is 7 years more than thrice of the age of Mannu i.e., (3x + 7) years.
(b) The present age of Sara = y years
(y + 7) is the age of Sara after 7 years.
(y – 3) is the age of Sara before 3 years.

$\begin{array}{l}\left(y+4\frac{1}{2}\right)\text{is the age of Sara after 4}\frac{1}{2}\text{years}\text{.}\\ \left(y-2\frac{1}{2}\right)\text{is the age of Sara before 2}\frac{1}{2}\text{years}\text{.}\end{array}$

(c) n students like football, but 2n students may like other game or football. Similarly, (n/2) students may like any other game out of the number of students who like football.