Students can practice TS SCERT Class 6 Maths Solutions Chapter 9 Introduction to Algebra Ex 9.1 to get the best methods of solving problems.
TS 6th Class Maths Solutions Chapter 9 Introduction to Algebra Exercise 9.1
Question 1.
Find the rule which gives the number of matchsticks required to make the following matchsticks patterns.
(i) A pattern of letter ‘T’
Answer:
The rule which gives the number of sticks required to make the pattern T is 2n.
(ii) A pattern of letter ‘E’
Answer:
The rule which gives the number of sticks required to make the pattern E is 5n.
(iii) A pattern of letter ‘Z’
Answer:
The rule which gives the number of sticks required to make the pattern Z is 3n.
Question 2.
Make a rule between the number of blades required and the number of fans (say n) in a hall ?
Answer:
The number of blades that a fan has = 3
Number of fans = n (say)
∴ The number of blades for ‘n’ fans = 3 × n = 3n
The required rule is 3n.
Question 3.
Find a rule for the following patterns between number of shapes formed and number of matchsticks required.
(a)
Answer:
The first shape has 2 matchsticks, the second shape 4 and the third shape 6.
∴ The required rule 2s.
(‘s’ stands for number of shapes.)
(b)
Answer:
The first shape has 3 matchsticks, the second shape 6 and the third shape 9.
∴ The required rule is 3s.
(‘s’ stands for number of shapes.)
Question 4.
The cost of one pen is ₹ 7 then what is the rule for the cost of ‘n’ pens.
Answer:
Cost of one pen is Rs. 7.
Cost of ‘n’ pens = 7 × n = 7n
The rule for cost of n’ pens is 7n.
Question 5.
The cost of one bag is ₹ 90, what is the rule for the cost of ‘m’ bags ?
Answer:
The cost of one bag = Rs. 90.
Cost of ‘m’ bags = 90 × m = 90m
The rule for the cost of ‘m’ bags is 90m.
Question 6.
The rule for purchase of books is-that the cost of q books is ₹ 23; then find the price of one book ?
Answer:
Cost of ‘q’ books = Rs. 23
∴ Cost of one book = \(\frac{23}{q}\)
The rule for the price of one book is \(\frac{23}{q}\).
Question 7.
John says that he has two books less than Gayathri. Write the relationship using letter x.
Answer:
Let the number of books that Gayathri has be x.
Then the number of books that John has = (x – 2)
(∵ John says that he has two books less than Gayathri)
The required relationship is (x – 2).
Question 8.
Rekha has 3 books more than twice the books with Suresh. Write the relationship using letter y.
Answer:
Let the number of books with Suresh be ‘y’.
Twice the number of books with Suresh = 2 × y – 2y.
As per the problem, the number of ‘ books that Rekha has = (2y + 3)
The required relationship is 2y + 3.
Question 9.
A teacher distributes 6 pencils per student. Can you find how many pencils are needed for the given number of students (use V for the number of students).
Answer:
Let the number of students be ’z’.
The teacher gives 6 pencils to each student.
The number of pencils that are given to ‘z’ students = 6 × z = 6z
The rule that is required is 6z.
Question 10.
Complete each table to generate the given functional relationship.
Answer:
Question 11.
Observe the following pattern.
Count the number of line segments in each shape.
(i) How many line segments will the 9th shape contain ?
(ii) Write the rule for the above pattern.
Answer:
(i) Shape – 1 contains 3 line segments.
Shape – 2 contains 5 line segments.
Shape – 3 contains 7 line segments.
Shape – 4 contains 9 line segments.
Shape – 5 contains 11 line segments.
Shape – 6 contains 13 line segments.
Shape – 7 contains 15 line segments.
Shape – 8 contains 17 line segments.
Shape – 9 contains 19 line segments.
The number of line segments that 9 such shapes contains is 99.
(∵ 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)
(ii) The rule for the above pattern is 3 + 2(n – 1).