NCERT Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.1

NCERT Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.1 provides answers to the questions related to the concepts of Matchstick patterns and the ideas of variables present in this exercise. Algebra is a branch of Mathematics where the students learn about the method of using letters in the form of equations. The NCERT Solutions Class 6 Maths are created by BYJU’S faculty having vast knowledge about the concepts covered under each exercise of Chapter 11 Algebra.

NCERT Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.1

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Access NCERT Solutions for Class 6 Chapter 11: Algebra 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

(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.

Also, explore –

NCERT Solutions for Class 6 Maths Chapter 11

NCERT Solutions for Class 6

NCERT Solutions