NCERT Solutions 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.)

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.

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

Class 6 Maths Chapter Algebra: Exercises Breakdown

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.