Posted by RBSE Solutions for Class 6 Maths Chapter 11: Algebra introduces students to basic algebraic concepts, which serve as the foundation for advanced mathematics. This chapter covers the introduction to variables, forming simple equations, and understanding expressions. The solutions provided are designed to help students learn how to solve algebraic problems step-by-step, making the concepts clear and engaging.
Key Concepts Covered in Chapter 11: Algebra
- Understanding Variables and Constants
- Formation of Algebraic Expressions
- Simple Equations and Their Solutions
- Practical Applications of Algebra in Real Life
- Using Variables to Represent Quantities
Algebra helps students develop critical thinking and problem-solving skills, which are crucial for future mathematical studies.
Detailed RBSE Class 6 Solutions for Chapter 11: Algebra
Below are detailed solutions for each problem in Chapter 11. These solutions offer step-by-step explanations that make it easy for students to grasp algebraic concepts and solve questions confidently.
NCERT Solutions for Class 6 Chapter 11: Algebra Exercise 11.1
Table of Contents
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
(b) A pattern of letter Z as
(c) A pattern of letter U as
(d) A pattern of letter Vas
(e) A pattern of letter E as
(f) A pattern of letter S as
(g) A pattern of letter A as
Solutions:
(a)
From the figure, we observe that two matchsticks are required to make the letter T. Hence, the pattern is 2n
(b)
From the figure, we observe that three matchsticks are required to make the letter Z. Hence, the pattern is 3n
(c)
From the figure, we observe that three matchsticks are required to make the letter U. Hence, the pattern is 3n
(d)
From the figure, we observe that two matchsticks are required to make the letter V. Hence, the pattern is 2n
(e)
From the figure, we observe that 5 matchsticks are required to make the letter E. Hence, the pattern is 5n
(f)
From the figure, we observe that 5 matchsticks are required to make the letter S. Hence, the pattern is 5n
(g)
From the figure, we observe that 6 matchsticks are required to make the letter A. Hence, the pattern is 6n
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?
Solutions:
We know that T require only two matchsticks. So, the pattern for the letter T is 2n. Among all the letters given in question 1, only T and V are the letters which require two matchsticks. Hence, (a) and (d).
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)
Solutions:
Let n be the number of rows
Number of cadets in a row = 5
Total number of cadets = number of cadets in a row × number of rows
= 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.)
Solutions:
Let b be the number of boxes
Number of mangoes in a box = 50
Total number of mangoes = number of mangoes in a box × number of boxes
= 50b
5. The teacher distributes 5 pencils per students. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
Solutions:
Let s be the number of students
Pencils given to each student = 5
Total number of pencils = number of pencils given to each student × number of students
= 5s
6. A bird flies 1 kilometer in one minute. Can you express the distance covered by the birds in terms of its flying time in minutes? (Use t for flying time in minutes.)
Solutions:
Let t minutes be the flying times
Distance covered in one minute = 1 km
Distance covered in t minutes = Distance covered in one minute × Flying time
= 1 × t
= t km
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?
Solutions:
Number of dots in a row = 9
Number of rows = r
Total number of dots in r rows = Number of dots in a row × number of rows
= 9r
Number of dots in 8 rows = 8 × 9
= 72
Number of dots in 10 rows = 10 × 9
= 90
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.
Solutions:
Let Radha’s age be x years
Leela’s age = 4 years younger than Radha
= (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?
Solutions:
Number of laddus mother gave = l
Remaining laddus = 5
Total number of laddus = number of laddus given away by mother + number of laddus remaining
= (l + 5) laddus
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?
Solutions:
Number of oranges in a small box = x
Number of oranges in two small boxes = 2x
Number of oranges remaining = 10
Number of oranges in large box = number of oranges in two small boxes + number of oranges remained
= 2x + 10
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. (Hint: If you remove vertical stick at the end, you will get a pattern of Cs)
(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.
Solutions:
(a) We may observe that in the given matchstick pattern, the number of matchsticks are 4, 7, 10 and 13, which is 1 more than thrice the number of squares in the pattern
Therefore, the pattern is 3x + 1, where x is the number of squares
(b) We may observe that in the given matchstick pattern, the number of matchsticks are 3, 5, 7 and 9, which is 1 more than twice the number of triangles in the pattern.
Therefore, the pattern is 2x + 1, where x is the number of triangles.
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Benefits of RBSE Class 6 Chapter 11 Solutions
- Easy Learning: Step-by-step explanations simplify complex algebraic concepts.
- Improved Problem-Solving: Practicing these solutions sharpens analytical skills.
- Practical Knowledge: Understanding algebra helps students apply mathematical reasoning to real-world problems.
FAQs on RBSE Solutions for Class 6 Maths Chapter 11: Algebra
Q1: What is algebra, and why is it important?
A1: Algebra is a branch of mathematics that deals with symbols and variables to represent numbers in equations and expressions. It is important because it helps in understanding relationships between quantities and solving real-life problems.
Q2: How does Chapter 11 help Class 6 students?
A2: This chapter introduces students to basic algebraic expressions and equations, which serve as a foundation for more complex math concepts in higher classes.
Q3: Where can I find detailed RBSE solutions for Class 6 Chapter 11?
A3: You can access comprehensive, step-by-step solutions on rbsesolution.in, where each question is explained for easy understanding.
Q4: What are variables and constants in algebra?
A4: In algebra, a variable is a symbol (like x or y) that represents an unknown value, while a constant is a fixed number.
Q5: How can learning algebra help students in daily life?
A5: Algebra helps students solve real-world problems involving unknowns, such as budgeting, calculating distances, and making predictions based on patterns.
Conclusion
The RBSE Solutions for Class 6 Maths Chapter 11: Algebra provide students with a fundamental understanding of variables, expressions, and equations. These solutions are designed to make algebra accessible and enjoyable, giving students the confidence to tackle more complex mathematical challenges in the future. With these foundational skills, students can apply algebra to real-life situations, enhancing both their academic and practical understanding.