MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1

Question 1.
Find the rule which gives the number of matchsticks required to make the following matchstick patterns. Use a variable to write the rule.
(a) A pattern of letter T as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 1
(b) A pattern of letter Z as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 2
(c) A pattern of letter U as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 3
(d) A pattern of letter V as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 4
(e) A pattern of letter E as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 5
(f) A pattern of letter S as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 6
(g) A pattern of letter A as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 7
Solution:
(a) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 8
∴ Number of matchsticks required to
make a pattern of letter T as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 9

(b) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 10
∴ Number of matchsticks required to make a pattern of letter Z as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 11

(c) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 12
∴Number of matchsticks required to make a pattern of letter U as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 13

(d) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 14
Number of matchsticks required to make a pattern of letter V as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 15

(e) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 16
∴ Number of matchsticks required to make a pattern of letter E as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 17

(f) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 18
∴ Number of matchsticks required to make a pattern of letter S as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 19

(g) Number of matchsticks required to make one MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 20
∴ Number of matchsticks required to make a pattern of letter A as MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 21

Question 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?
Solution:
Part (a) & (d) i.e., letter T and V have same rule as that given by L.
Because the number of matchsticks required in each of them is 2.

Question 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.)
Solution:
Let number of rows = n
Number of cadets in each row = 5
Therefore, total number of cadets = 5M

MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1

Question 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.)
Solution:
Let number of boxes = b
Number of mangoes in each box = 50
Therefore, total number of mangoes = 50b

Question 5.
The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use s for the number of students.)
Solution:
Let number of students = s
Number of pencils distributed to each student = 5
Therefore, total number of pencils needed = 5s

Question 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.)
Solution:
Let flying time of the bird be t minutes.
Distance covered by the bird in 1 minute = 1 km
∴ Distance covered by the bird in t minutes = 1 × t km = t km

MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1

Question 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?
Solution:
Number of dots in each row = 9
Number of rows = r
Therefore, total number of dots = 9r
When there are 8 rows, then number of dots = 9 × 8 = 72
When there are 10 rows, then number of dots = 9 × 10 = 90

Question 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.
Solution:
Radha’s age = x years
Since, Leela is 4 years younger than Radha.
Therefore, Leela’s age = (x – 4) years.

Question 9.
Mother has made laddus. She gives Vome 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?
Solution:
Number of laddus gave away = l
Number of remaining laddus = 5
∴ Total number of laddus = (l + 5)

MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1

Question 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?
Solution:
Number of oranges in a small box = x
Number of smaller boxes = 2
Therefore, total number of oranges in smaller boxes = 2x
Number of remaining oranges = 10
Thus, number of oranges in the larger box = 2x + 10

Question 11.
(a) Look at the following matchstick pattern of squares (see fig.).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.)
MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 22
(b) The given figure 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.
MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 23
Solution:
(a)
MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 24
If we remove 1 matchstick from each figure, then they make multiples of 3, i.e., 3, 6, 9, 12, …………
So the required equation = 3x + 1, where x is number of squares.

(b)
MP Board Class 6th Maths Solutions Chapter 11 Algebra Ex 11.1 25
If we remove 1 matchstick from each figure, then they make multiples of 2, i.e., 2, 4, 6, 8, ………..
So the required equation = 2x + 1, where x is number of triangles.

MP Board Class 6th Maths Solutions