Telangana SCERT Class 6 Maths Chapter 9 Solution – Introduction to Algebra. Here in this post we provides Class 6 Maths Introduction to Algebra Telangana State Board Solution. Telangana State Board English Class VI Medium Students can download this Solution to Solve out Improve Your Learning Questions and Answers.
Telangana State Board Class 6 Maths Chapter 9 Introduction to Algebra Solution:
EXERCISE – 9.1
1.) Find the rule which gives the number of match sticks required to make the following match sticks patterns.
(i) A pattern of letter ‘T’
ANSWER:
Here, we have to find rule which gives the number of match sticks required to make the pattern of letter ‘T’.
We require 2 sticks to make letter ‘T’.
The rule for letter ‘T’ is “2 m”
Where m is s the number of faces and it can take any value i.e. 1, 2, 3, 4,………
(ii) A pattern of letter ‘E’
ANSWER:
Here, we have to find rule which gives the number of match sticks required to make the pattern of letter ‘E’.
We require 4 sticks to make letter ‘E’.
The rule for letter ‘E’ is “4 m”
Where m is s the number of faces and it can take any value i.e. 1, 2, 3, 4 …
(iii) A pattern of letter ‘Z’
ANSWER:
Here, we have to find rule which gives the number of match sticks required to make the pattern of letter ‘Z’.
We require 3 sticks to make letter ‘Z’.
The rule for letter ‘Z’ is “3 m”
Where m is s the number of faces and it can take any value i.e. 1, 2, 3, 4 …
2.) Make a rule between the number of blades required and the number of fans (say n) in a hall?
ANSWER:
There are total 3 blades for 1 fan.
Now, n is number of fans in a hall.
We make rule between the number of blades required and the number of fans = 3 x n
Rule between the number of blades required and the number of fans = 3n
3.) Find a rule for the following patterns between number of shapes formed and number of match sticks required.
ANSWER:
From given shapes,
1st pattern require 2 match sticks.
2nd pattern require 4 match sticks.
3rd pattern require 6 match sticks.
We find rule.
Rule = 2 x s
s = number of shapes join.
ANSWER:
From given shapes,
1st pattern require 3 match sticks.
2nd pattern require 6 match sticks.
3rd pattern require 9 match sticks.
We find rule.
Rule = 3 x s
s = number of shapes join.
4.) The cost of one pen is Rs.7 then what is the rule for the cost of ‘n’ pens.
ANSWER:
Given, the cost of one pen is Rs.7
We have to find the rule for the cost of ‘n’ pens.
The rule for the cost of ‘n’ pens = 7 x n
5.) The cost of one bag is Rs.90 what is the rule for the cost of ‘m’ bags?
ANSWER:
Given, the cost of one bag is Rs.90
We have to find the rule for the cost of ‘m’ bags
The rule for the cost of ‘m’ bags = 90 x m
6.) The rule for purchase of books is that the cost of q books is Rs. 23q; then find the price of one book?
ANSWER:
Given, the cost of q books is Rs. 23q
We have to find the price of one book.
The price of one book = Rs. 23q / q
The price of one book = Rs. 23
7.) John says that he has two books less than Gayathri. Write the relationship using letter x.
ANSWER:
Given that, John says that he has two books less than Gayathri.
Let, Gayathri’s books be x.
John’s book = (x – 2)
8.) Rekha has 3 books more than twice the books with Suresh. Write the relationship using letter y.
ANSWER:
Given that, Rekha has 3 books more than twice the books with Suresh.
Let, Suresh’s book be y.
Rekha’s book = 2y + 3
9.) A teacher distributes 6 pencils per student. Can you find how many pencils are needed for the given number of students (use ‘z’ for the number of students).
ANSWER:
Given that, a teacher distributes 6 pencils per student.
We have to find how many pencils are needed for the given number of students.
Let, number of students be Z.
Pencils are needed for the ‘Z’ number of students = 6 Z
10.) Complete each table to generate the given functional relationship.
ANSWER:
We have to fill given table by calculation.
Given that 3x + 2
We put value of x= 1, 2, 3 …
For x = 2
3x + 2 = 3 x 2 + 2 = 8
For x = 3
3x + 2 = 3 x 3 + 2 = 11
For x = 4
3x + 2 = 3 x 4 + 2 = 14
For x = 5
3x + 2 = 3 x 5 + 2 = 17
For x = 9
3x + 2 = 3 x 9 + 2 = 29
Now
3x + 2 = 38
3x = 38 – 2
3x = 36
X = 36 / 3
X = 12
Table value = 8, 11, 14, 17, 29, 12
ANSWER:
We have to fill given table by calculation.
Given that 5a – 1
We put value of a = 1, 2, 3 …
For a = 3
5a – 1 = 5 x 3 – 1 = 14
For a = 6
5a – 1 = 5 x 6 – 1 = 29
For a = 7
5a – 1 = 5 x 7 – 1 = 34
For a = 8
5a – 1 = 5 x 8 – 1 = 39
For a = 9
5a – 1 = 5 x 9 – 1 = 44
Now,
5a – 1 = 49
5a = 49 + 1
5a = 50
a = 10
Table value = 14, 29, 34, 39, 44, 10
11.) Observe the following pattern.
Count the number of line segments in each shape.
(i) How many line segments will the ninth shape contain?
ANSWER:
19 line segments will the ninth shape contain.
(ii) Write the rule for the above pattern.
ANSWER:
The rule for given pattern is 3 + 2 (n – 1) = 2n+1
EXERCISE -9.2
1.) Write the expressions for the following statements
(i) q is multiplied by 5
ANSWER:
Here, we are write the expressions for given statement.
q is multiplied by 5 = 5q
(ii) y is divided by 4
ANSWER:
Here, we are write the expressions for given statement.
y is divided by 4 = y / 4
(iii) One fourth of the product of numbers p and q
ANSWER:
Here, we are write the expressions for given statement.
One fourth of the product of numbers p and q = pq/4
(iv) 5 is added to the three times z
ANSWER:
Here, we are write the expressions for given statement.
5 is added to the three times z = 3z+5
(v) 9 times ‘n’ is added to ’10’
ANSWER:
Here, we are write the expressions for given statement.
9 times ‘n’ is added to ’10’ = 9n + 10
(vi) 16 is subtracted from two times ‘y’
ANSWER:
Here, we are write the expressions for given statement.
16 is subtracted from two times ‘y’ = 2y – 16
(vii) ‘y’ is multiplied by 10 and then x is added to the product
ANSWER:
Here, we are write the expressions for given statement.
‘y’ is multiplied by 10 and then x is added to the product = 10y + x
2.) Write two statements each for the following expressions
(i) y – 11
ANSWER:
We have to write statement for the given expressions.
y – 11 = 11 is subtracted from ‘y’
(ii) 10a
ANSWER:
We have to write statement for the given expressions.
10a = a is multiplied by 10
(iii) x / 5
ANSWER:
We have to write statement for the given expressions.
x / 5 = x is divided by 5
(iv) 3m + 11
ANSWER:
We have to write statement for the given expressions.
3m + 11 = 3 times ‘m’ is added to ’11’
(v) 2y – 5
ANSWER:
We have to write statement for the given expressions.
2y – 5 = 5 is subtracted from two times ‘y’
3.) Peter has ‘p’ number of balls. Number of balls with David is 3 times the balls with Peter. Write this as an expression.
ANSWER:
Given, Peter has ‘p’ number of balls. Number of balls with David is 3 times the balls with Peter.
We write expression = 3p
4.) Sita has 3 more note books than Githa. Find the number of books that Sita has? Use any letter for the number of books that Gita has.
ANSWER:
Given, Sita has 3 more note books than Githa.
Let, Githa has x note books.
Sita’s note books = x + 3
5.) Cadets are marching in a parade. There are 5 cadets in each row. What is the rule for the number of cadets, for a given number of rows? Use ‘n’ for the number of rows.
ANSWER:
Given, There are 5 cadets in each row.
We have to find the rule for the number of cadets, for a given number of rows.
The rule = 5n
EXERCISE – 9.3
1.) State which of the following are equations.
(i) x – 3 = 7
ANSWER:
This expression contains variable and number hence it is equation.
(ii) l + 5 > 9
ANSWER:
This expression does not contains variable and number hence it is not equation.
(iii) p-4 < 10
ANSWER:
This expression contains variable and number but comparison is there, hence it is not equation.
(iv) 5 + m = -6
ANSWER:
This expression contains variable and number hence it is equation.
(v) 2s – 2 = 12
ANSWER:
This expression contains variable and number hence it is equation.
(vi) 3x +5 > 13
ANSWER:
This expression contains variable and number but comparison is there, hence it is not equation.
(vii) 3x < 15
ANSWER:
This expression contains variable and number but comparison is there, hence it is not equation.
(viii) 2x – 5 = 3
ANSWER:
This expression contains variable and number hence it is equation.
(ix) 7y + 1 < 22
ANSWER:
This expression contains variable and number but comparison is there, hence it is not equation.
(x) -3z + 6 = 12
ANSWER:
This expression contains variable and number hence it is equation.
(xi) 2x – 3y = 3
ANSWER:
This expression contains variable and number hence it is equation.
(xii) z = 4
ANSWER:
This expression contains variable and number hence it is equation.
2.) Write LHS and RHS of the following equations.
(i) x-5 =6
ANSWER:
We have to write LHS and RHS of the given equation.
X-5 = 6
LHS = X-5
RHS = 6
(ii) 4y = 12
ANSWER:
We have to write LHS and RHS of the given equation.
4y = 12
LHS = 4y
RHS = 12
(iii) 2z + 3 = 7
ANSWER:
We have to write LHS and RHS of the given equation.
2z + 3 = 7
LHS = 2z + 3
RHS = 7
(iv) 3p = 24
ANSWER:
We have to write LHS and RHS of the given equation.
3p = 24
LHS = 3p
RHS = 24
(v) 4 = x – 2
ANSWER:
We have to write LHS and RHS of the given equation.
4 = x – 2
LHS = 4
RHS = x – 2
(vi) 2a – 3 = -5
ANSWER:
We have to write LHS and RHS of the given equation.
2a – 3 = -5
LHS = 2a – 3
RHS = -5
3.) Solve the following equation by Trial & Error Method.
(i) x + 3 = 5
ANSWER:
We solve x + 3 = 5
X = 5 – 3
X = 2
(ii) y – 2 = 7
ANSWER:
We solve y – 2 = 7
y = 7 + 2
y = 9
(iii) a- 2 = 6
ANSWER:
We solve a – 2 = 6
a = 6 + 2
a = 8
(iv) 5y = 15
ANSWER:
We solve 5y = 15
y = 15 / 5
y = 3
(v) 6n = 30
ANSWER:
We solve 6n = 30
n = 30 / 6
n = 5
(vi) 3z = 27
ANSWER:
We solve 3z = 27
Z = 27 / 3
Z = 9
Did you miss: Chapter 10 Solution? Here Link