NCERT Solutions for Maths Class 6 Chapter 11 Algebra Exercise 11.1 - FREE PDF Download
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.
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
1. How many questions are present in NCERT solutions for class 6 Maths chapter 11 Algebra?
In Class 6 Chapter 6 there is only one exercise and that is -
Exercise 11.1 - 11 questions
Students can find the solutions to these questions here. The solution for Class 6 Maths Exercise 11.1 solutions are provided and are written in an easy manner which will help students in clarifying all their doubts.
2. How many questions have long solutions (more than 180 words) in NCERT Solutions for Class 6 Maths Chapter 11 Algebra?
Chapter 11 of Class 6 NCERT Algebra has the following long answer type exercise questions-
Exercise 11.1 - 2 ( 1 and 11)
The detailed stepwise explanation prepared by subject experts to all these questions can be found on Vedantu’s website. All the material is also available on the Vedantu app. All the resources are free of cost.
3. What are variables and how are they related to an equation in class 6 exercise 11.1?
The concept of variables is very important in Algebra. A variable is something that does not have a fixed value and can vary. Variables allow us to express many rules in geometry and arithmetic. An equation is satisfied for a definite value of a variable therefore it is a condition on a variable. The solution of an equation is obtained when a variable satisfies the equation and the LHS and RHS become equal.
4. What are the important concepts in Class 6 Maths Chapter 11 Algebra?
Students learn the concept of variables and how it enable us to express relations in mathematics and geometry. Variables are numbers and therefore common operations such as addition, and multiplication. Subtraction and division can be done on them. Students also learn about equations and how to solve them. An equation has two sides, the LHS and RHS separated by an equal sign. The LHS and RHS of an equation are equal only for a definite value of a variable.
5. Why should I refer to NCERT Solutions in Chapter 11 of Class 6 Algebra?
Vedantu provides well-explained solutions designed by experts which helps students in clarifying their doubts and achieving good marks in the exams. The benefits of following the solution for this chapter are that algebra is a new concept for students and they may find it difficult to grasp. However, the solutions provided are well organised and explained in detail step by step so that students need not be afraid of the topic but enjoy learning it.
6. What is a constant in algebra?
A constant is a fixed value that does not change. In algebraic expressions, it is usually represented by a number.
7. Why are variables used in algebra answer it according to class 6 maths ch 11 ex 11.1.
Variables are used to generalize mathematical problems and make it easier to represent and solve equations involving unknown values.
8. What is an algebraic expression?
As we studied in Class 6 Math Exercise 11.1, An algebraic expression is a combination of variables, constants, and arithmetic operations (such as addition, subtraction, multiplication, and division).
9. How do you solve a simple algebraic equation?
According to Class 6 Math Exercise 11.1, To solve a simple algebraic equation, you need to isolate the variable on one side of the equation by performing inverse operations on both sides.
10. Give me an example of a simple algebraic expression.
An example of a simple algebraic expression is 2x+3, where x is the variable.
