### NCERT Solutions Class 6 Maths 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 a letter T. Hence, the pattern is 2n

(b)

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

(c)

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

(d)

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

(e)

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

(f)

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

(g)

From the figure we observe that 6 matchsticks are required to make a 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 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).

**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 time

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 remained = 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 the thrice of 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 the twice of the number of triangles in the pattern.

Therefore, the pattern is 2x + 1, where x is the number of triangles.

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