Chapter 11: Algebra

Q1Multiple choice

Find the rule which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.

(e) A pattern of letter E as
NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 5

(f) A pattern of letter S as
NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 6

(g) A pattern of letter A as
NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 7

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Correct option: A

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Worked solution

(a)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 8

From the figure we observe that two matchsticks are required to make a letter T. Hence, the pattern is 2n

(b)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 9

From the figure we observe that three matchsticks are required to make a letter Z. Hence, the pattern is 3n

(c)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 10

From the figure we observe that three matchsticks are required to make a letter U. Hence, the pattern is 3n

(d)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 11

From the figure we observe that two matchsticks are required to make a letter V. Hence, the pattern is 2n

(e)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 12

From the figure we observe that 5 matchsticks are required to make a letter E. Hence, the pattern is 5n

(f)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 13

From the figure we observe that 5 matchsticks are required to make a letter S. Hence, the pattern is 5n

(g)

NCERT Solutions for Class 6 Maths Chapter 11 Exercise 11.1 - 14

From the figure we observe that 6 matchsticks are required to make a letter A. Hence, the pattern is 6n

Q2Written answer

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?

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Worked solution

We know that T requires only two matchsticks. So, the pattern for 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).

Q3Written answer

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)

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Worked solution

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

Q4Written answer

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.)

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Worked solution

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

Q5Written answer

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.)

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Worked solution

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

Q6Written answer

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.)

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Worked solution

Let t minutes be the flying time

Distance covered in one minute = 1 km

Distance covered in t minutes = Distance covered in one minute × Flying time

= 1 × t

= t km

Q7Written answer

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?

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Worked solution

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

Q8Written answer

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.

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Worked solution

Let Radha’s age be x years

Leela’s age = 4 years younger than Radha

= (x – 4) years

Q9Written answer

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?

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Worked solution

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

Q10Written answer

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?

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Worked solution

Number of oranges in a small box = x

Number of oranges in two small boxes = 2x

Number of oranges remained = 10

Number of oranges in large box = number of oranges in two small boxes + number of oranges remained

= 2x + 10

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Exercise 11.1