PSEB Class 6 Maths Chapter 7 Algebra Questions and Answers Solution
PSEB Punjab Board Class 6 Maths Textbook Solution Chapter 7 Algebra Exercise Questions and Answers. We have also included some Additional questions, so that students can prepare more strongly.
Exercise 7.1
1.) Find the rule which gives the number of matchsticks required to make the following’n’ matchstick patterns. Use a variables to write the rule:-
A pattern of letter T as
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 n”
(ii) A pattern of letter E as
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 “4n”
(iii) A pattern of letter F as
ANSWER:
Here, we have to find rule which gives the number of match sticks required to make the pattern of letter ‘F’.
We require 3 sticks to make letter ‘F’.
The rule for letter ‘F’ is “3n”
(iv) A pattern of letter C as
ANSWER:
Here, we have to find rule which gives the number of match sticks required to make the pattern of letter ‘C’.
We require 3 sticks to make letter ‘C’.
The rule for letter ‘C’ is “3n”
(v) A pattern of letter S as
ANSWER:
Here, we have to find rule which gives the number of match sticks required to make the pattern of letter ‘S’.
We require 5 sticks to make letter ‘S’.
The rule for letter ‘S’ is “5n”
2.) Students are sitting in rows. There are 12 students in a row. What is the rule which gives the number of students in ‘n’ rows? (Represent by table)
ANSWER:
Given that,
There are 12 students in a row.
We have to find rule which gives the number of students in ‘n’ rows
Rule which gives the number of students in ‘n’ rows = 12n
3.) The teacher distributes 3 pencils to a student. What is the rule which gives the number of pencils, if there are ‘a’ number of students?
ANSWER:
Given that,
The teacher distributes 3 pencils to a student.
We have to find rule which gives the number of pencils, if there are ‘a’ number of students
Rule which gives the number of pencils = 3a
4.) There are 8 pens in a pen stand. What is the rule that gives the total cost of the pens. If the cost of each pen is represented by a variable ‘c’?
ANSWER:
Given that,
There are 8 pens in a pen stand.
The cost of each pen is represented by a variable ‘c’
We have to find rule that gives the total cost of the pens.
Rule that gives the total cost of the pens = 8c
5.) Gurleen is drawing pictures by joining dots. To make one picture, she has to join 5 dots. Find the rule that gives the number of dots, if the number of pictures is represented by the symbol ‘p’.
ANSWER:
Given that,
Gurleen is drawing pictures by joining dots. To make one picture, she has to join 5 dots.
Number of pictures is represented by the symbol ‘p’.
We have to find rule that gives the number of dots.
Rule that gives the number of dots = 5p
6.) The cost of a dozen bananas is 50. Find the rule of total cost of bananas if there are ‘d’ dozens bananas.
ANSWER:
Given that,
The cost of a dozen bananas is 50.
There are’d’ dozens bananas
We have to find rule that gives total cost of bananas.
Rule that gives total cost of bananas = 50d
7.) Look at the following matchsticks patterns of squares given below. The squares are not separate as there are two adjoined adjacent squares have a common match stick. 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 patterns of C)
ANSWER:
By observing patterns we have to find the rule that gives the number of matchsticks in terms of the number of squares.
Rule that gives the number of matchsticks in terms of the number of squares = 1+3x or 3x+1
Exercise 7.2
1.) Each side of equilateral triangle is denoted by ‘a’ then express the perimeter of the triangle using ‘a’.
ANSWER:
Given that,
Each side of equilateral triangle is denoted by ‘a’
We have to find perimeter of the triangle using ‘a’.
We know,
Perimeter of the triangle = Sum of all outer sides
Perimeter of the equilateral triangle = 3a
2.) An isosceles triangle is shown. Express its perimeter in terms of “l” and “b”
ANSWER:
Given that,
An isosceles triangle.
We have to find perimeter of the isosceles triangle in terms of “l” and “b”
Perimeter of the isosceles triangle =2l + b
3.) Each side of regular hexagon is denoted by ‘S’ then express the perimeter of the regular hexagon using ‘S’.
ANSWER:
Given that,
Each side of regular hexagon is denoted by ‘S’
We have to find perimeter of the regular hexagon using ‘S’.
We know,
Perimeter of the regular hexagon = Sum of all outer sides
Perimeter of the regular hexagon = 6S
4.) The cube has 6 faces and all of them are identify squares. If ‘l’ is the length of an edge of a cube, find the total length of all edges of the cube in terms of ‘l’.
ANSWER:
Given that,
The cube has 6 faces and all of them are identify squares. If ‘l’ is the length of an edge of a cube.
We have to find total length of all edges of the cube in terms of ‘l’
Total length of all edges of the cube in terms of ‘l’ = 12l
5.) Write communtative property of addition using variables x and y.
ANSWER:
We have to write communtative property of addition using variables x and y.
Communtative property of addition using variables x and y = x+y = y+x
6.) Write associative property of multiplication using variables I, m and n.
ANSWER:
We have to write associative property of multiplication using variables I, m and n.
Associative property of multiplication using variables I, m and n = l x (m x n) = (l x m) x n
7.) Write distributive property of multiplication over addition in terms of variables p, q and r respectively.
ANSWER:
We have to write distributive property of multiplication over addition in terms of variables p, q and r
Distributive property of multiplication over addition in terms of variables p, q and r =
p x (q+r)=p x q+p x r
Exercise 7.3
1.) Pick the algebraic expressions and the arithmetic expressions from the following:
(i) 2l-3
ANSWER:
We know,
Expression contains variable and number is called algebraic expressions.
2l-3 is algebraic expressions.
(ii) 5 x 3+8
ANSWER:
We know,
Expression which contains only numbers is called arithmetic expressions.
5 x 3 + 8 is arithmetic expression.
(iii) 6-3x
ANSWER:
We know,
Expression contains variable and number is called algebraic expressions.
6-3x is algebraic expressions.
(iv) 5l
ANSWER:
We know,
Expression contains variable and number is called algebraic expressions.
5l is algebraic expressions.
(v) 2 x (21-18)+9
ANSWER:
We know,
Expression which contains only numbers is called arithmetic expressions.
2 x (21-18)+ 9 is arithmetic expression.
(vi) 6a/5 + 2
ANSWER:
We know,
Expression contains variable and number is called algebraic expressions.
6a/5 + 2 is algebraic expressions.
(vii) 7 x 20 / 5 + 3
ANSWER:
We know,
Expression which contains only numbers is called arithmetic expressions.
7 x 20 / 5 + 3 is arithmetic expression.
(viii) 8
ANSWER:
We know,
Expression which contains only numbers is called arithmetic expressions.
8 is arithmetic expression.
2.) Write the terms for the following expressions:
(i) 2y+5z
ANSWER:
We have to write terms for the 2y+5z.
Terms for the 2y+5z = 2y, 5z
(ii) 6x-3y+8
ANSWER:
We have to write terms for the 6x-3y+8
Terms for the 6x-3y+8 = 6x,-3y, 8
(iii) 7a
ANSWER:
We have to write terms for the 7a
Terms for the 7a = 7a
(iv) 3l-5m+2n
ANSWER:
We have to write terms for the 3l-5m+2n
Terms for the 3l-5m+2n = 3l,-5m, 2n
(v) 2l/3+x
ANSWER:
We have to write terms for the 2l/3+x
Terms for the 2l/3+x = 2l/3, x
3.) Tell how the following expressions are formed.
(i) a+11
ANSWER:
We have to write how the expressions are formed.
a+11 = a is increased by 11
(ii) 12-x
ANSWER:
We have to write how the expressions are formed.
12-x = x is subtracted from 12
(iii) 3z+8
ANSWER:
We have to write how the expressions are formed.
3z+8 = Three times of z is increased by 8
(iv) 6-5l
ANSWER:
We have to write how the expressions are formed.
6-5l = 5 times l is subtracted from 6
(v) 5a/4
ANSWER:
We have to write how the expressions are formed.
5a/4 = 5 times a is divided by 4.
4.) Give expressions for the following:
(i) 10 is added to p
ANSWER:
We have to write expression.
10 is added to p = p+10
(ii) 5 is subtracted from y
ANSWER:
We have to write expression.
5 is subtracted from y = y-5
(iii) d is divided by 3
ANSWER:
We have to write expression.
d is divided by 3 = d/3
(iv) l is multiplied by-6
ANSWER:
We have to write expression.
l is multiplied by-6 = -6l
(v) m is subtracted from 1
ANSWER:
We have to write expression.
m is subtracted from 1 = 1 – m
(vi) 11 is added to 3x
ANSWER:
We have to write expression.
11 is added to 3x = 3x + 11
(vii) y is multiplied by – 2 and then 2 is added to the result
ANSWER:
We have to write expression.
y is multiplied by – 2 and then 2 is added to the result = -2y+2
(viii) c is divided by 5 and then 7 is multiplied to the result
ANSWER:
We have to write expression.
c is divided by 5 and then 7 is multiplied to the result = 7(c/5)
(ix) x is multiplied by 3 then subtracted this result from y
ANSWER:
We have to write expression.
x is multiplied by 3 then subtracted this result from y = y-3x
(x) a is added to b then c is multiplied with this result
ANSWER:
We have to write expression.
a is added to b then c is multiplied with this result = (a+b)c
5.) Write the number which is 15 less than y.
ANSWER:
We have to write the number which is 15 less than y.
The number which is 15 less than y. = y-15
6.) Write the number which is 3 more than a.
ANSWER:
We have to write the number which is 3 more than a.
The number which is 3 more than a = a+3
7.) Find the number which is I more than twice of x.
ANSWER:
We have to write the number which is 1 more than twice of x.
The number which is 1 more than twice of x = 2x+1
8.) Find the number which is 7 less than 5 times of y.
ANSWER:
We have to write the number which is 7 less than 5 times of y.
The number which is 7 less than 5 times of y = 5y-7
9.) Somi’s present age is ‘a’ years. Express the following in algebraic form:
(i) Her age after 15 years.
ANSWER:
Given that, Somi’s present age is ‘a’ years
We have to find her age after 15 years.
Her age after 15 years. = a+15
(ii) Her age 2 years ago.
ANSWER:
Given that, Somi’s present age is ‘a’ years
We have to find her age 2 years ago.
Her age 2 years ago = a – 2
(iii) If Somi’s father’s age is 5 more than twice of her present age, express her father’s age.
ANSWER:
Given that, Somi’s present age is ‘a’ years
Somi’s father’s age is 5 more than twice of her present age,
We have to find her father’s age.
Her father’s age = 2a+5
(iv) If Somi’s sister is 4 years younger to her. Express her sister’s age.
ANSWER:
Given that, Somi’s present age is ‘a’ years
Somi’s sister is 4 years younger to her.
We have to find her sister’s age.
Her sister’s age. = a-4
(v) If Somi’s mother is 3 less than 3 times her present age. Express her mother’s age.
ANSWER:
Given that, Somi’s present age is ‘a’ years
Somi’s mother is 3 less than 3 times her present age.
We have to find her mother’s age.
Her mother’s age. = 3a-3
10.) The length of a floor is 10 more than two times of breadth what is the length if breadth is lmetres.
ANSWER:
Given that,
The length of a floor is 10 more than two times of breadth.
We have to find the length if breadth is l metres.
The length of a floor = 2l+10 metres.
Exercise 7.4
1.) Write the following statements as algebraic equations:-
(i) The sum of x and 3 gives 10.
ANSWER:
We have to write statement as algebraic equations.
The sum of x and 3 gives 10 = x+3=10
(ii) 5 less than a number ‘a’ is 12.
ANSWER:
We have to write statement as algebraic equations.
5 less than a number ‘a’ is 12. = a-5=12
(iii) 2 more than 5 times of p gives 32.
ANSWER:
We have to write statement as algebraic equations.
2 more than 5 times of p gives 32. =5p+2=32
(iv) Half of a number is 10.
ANSWER:
We have to write statement as algebraic equations.
Half of a number is 10. = x/2 = 10
(v) Twice of a number added to 3 gives 17.
ANSWER:
We have to write statement as algebraic equations.
Twice of a number added to 3 gives 17 = 2x+3=17
2.) Write the LHS and RHS for the following equations:-
(i) l+5=8
ANSWER:
We have to write LHS and RHS for the l+5=8
LHS= l+5, RHS = 8
(ii) 13=2m+3
ANSWER:
We have to write LHS and RHS for the 13=2m+3
LHS = 13, RHS = 2m +3
(iii) t/4 = 6
ANSWER:
We have to write LHS and RHS for the t/4 = 6
LHS = t/4, RHS = 6
(iv) 2h-5=13
ANSWER:
We have to write LHS and RHS for the 2h-5=13
LHS = 2h – 5, RHS = 13
(v) 5x/7 = 15
ANSWER:
We have to write LHS and RHS for the 5x/7 = 15
LHS = 5x/7, RHS = 15
3.) Solve the following equations by trial and error method:
(i) x+2=7
ANSWER:
We have to solve equations by trial and error method
x+2=7
we put x = 3
3+2=5, x = 3 not satisfy equation.
we put x = 4
4+2=6, x = 4 not satisfy equation.
we put x = 5
5+2=7, x = 5 satisfy equation.
(ii) 5p=20
ANSWER:
We have to solve equations by trial and error method
5p=20
We put p = 2
5p= 5 x 2 = 10, p = 2 not satisfy equation.
We put p = 3
5p= 5 x 3 = 15, p = 3 not satisfy equation.
We put p = 4
5p= 5 x 4 = 20, p = 4 satisfy equation.
(iii) a/5 =2
ANSWER:
We have to solve equations by trial and error method
a/5 = 2
We put a = 6
a/5 = 6/5, a = 6 not satisfy equation.
We put a = 8
a/5 = 8/5, a = 8 not satisfy equation.
We put a = 10
a/5 = 10/5 = 2, a = 10 satisfy equation.
(iv) 2l-4=8
ANSWER:
We have to solve equations by trial and error method
2l-4=8
We put l = 4
2l-4=8 = 8 – 4 = 4
l = 4 not satisfy equation.
We put l = 5
2l-4=8 = 10 – 4 = 6
l = 5 not satisfy equation.
We put l = 6
2l-4=8 = 12 – 4 = 8
l = 6 satisfy equation.
(v) 3x+2=11
ANSWER:
We have to solve equations by trial and error method
3x+2=11
We put x = 1
3x+2=11 = 3 + 2 = 5
x = 1 not satisfy equation.
We put x = 2
3x+2=11 = 3 x 2 + 2 = 8
x = 2 not satisfy equation.
We put x = 3
3x+2=11 = 3 x 3 + 2 = 11
x = 3 satisfy equation.
4.) Solve the following equations by systematic method.
(i) z-4=10
ANSWER:
We have to solve z-4=10 by systematic method.
Z-4=10
z = 10 + 4
z = 14
(ii) a+3=15
ANSWER:
We have to solve a+3=15 by systematic method.
a+3=15
a = 15 – 3
a = 12
(iii) 4m=20
ANSWER:
We have to solve 4m=20 by systematic method.
4m=20
m = 20 / 4
m = 5
(iv) 3x-3=15
ANSWER:
We have to solve 3x-3=15 by systematic method.
3x-3=15
3x = 15 + 3
3x = 18
X = 18/3
X = 6
(v) 4x+5=13
ANSWER:
We have to solve 4x+5=13 by systematic method.
4x+5=13
4x = 13 – 5
4x = 8
X = 8/4
X = 2
5.) Solve the following equation by transposition:
(i) x-5=6
ANSWER:
We have to solve x-5=6 by transposition.
X-5=6
x = 6 + 5
x = 11
(ii) Y+2=3
ANSWER:
We have to solve Y+2=3 by transposition.
Y+2=3
Y = 3 – 2
Y = 1
(iii) 5x=10
ANSWER:
We have to solve 5x=10 by transposition.
5x=10
X = 10 / 5
X = 2
(iv) a/6 = 4
ANSWER:
We have to solve a/6 = 4 by transposition
a/6 = 4
a = 6 x 4
a = 24
(v) 4y-2=30
ANSWER:
We have to solve 4y-2=30 by transposition
4y-2=30
4y = 30 + 2
4y = 32
Y = 32 / 4
Y = 8
6.) Solve the following equations:
(i) X+7=11
ANSWER:
We have to solve X+7=11
X+7=11
X = 11 – 7
X = 4
(ii) x-3=15
ANSWER:
We have to solve x-3=15
X-3=15
x = 15 + 3
x = 18
(iii) x-2=13
ANSWER:
We have to solve x-2=13
x-2=13
x = 13 + 2
x = 15
(iv) 6x=18
ANSWER:
We have to solve 6x=18
6x=18
X = 18/6
X = 3
(v) 3x=24
ANSWER:
We have to solve 3x=24
3x=24
X = 24/3
X = 8
(vi) x/4 =7
ANSWER:
We have to solve x/4 =7
x/4 =7
x = 7 x 4
x = 28
(vii) x/8 = 5
ANSWER:
We have to solve x/8 = 5
x/8 = 5
x = 5 x 8
x = 40
(viii) 2x-5=17
ANSWER:
We have to solve 2x-5=17
2x-5=17
2x = 17 + 5
2x = 22
X = 22/2
X = 11
(ix) 4x+5=21
ANSWER:
We have to solve 4x+5=21
4x+5=21
4x = 21 – 5
4x = 16
X = 16 / 4
X = 4
(x) 5x-2=13
ANSWER:
We have to solve 5x-2=13
5x-2=13
5x = 13 + 2
5x = 15
X = 15/5
X = 3
Multiple Choice Questions
1.) Each side of square is represented by ‘s’ then perimeter of square is:
(a) 4+s
(b) s-4
(c) 4s
(d) s
ANSWER: (c) 4s
2.) Write commutative property of multiplication using variables x and y
(a) xy=yx
(b) x+y=y+x
(c) x+y
(d) xy
ANSWER: (a) xy=yx
3.) How many terms in expression 7l-3
(a) 1
(b) 3
(c) 2
(d) 4
ANSWER: (c) 2
4.) 5 is subtracted from m=
(a) 5-m
(b) m+5
(c) 5+m
(d) m-5
ANSWER: (d) m-5
5.) Multiply p by 3 then 2 is added =
(a) 2p+3
(b) 3p-2
(c) 3p+2
(d) 2p-3
ANSWER: (c) 3p+2
6.) If Armaan’s present age is x years then what will be his age after 4 years?
(a) x-4
(b) X+ 4
(c) 4x
(d) 4-x
ANSWER: (b) X+ 4
7.) Write as algebraic equation: 7 more than 4 times of y gives 23.
(a) 4+7y=23
(b) 7+y=23
(c) 4y-7=23
(d) 4y+7=23
ANSWER: (d) 4y+7=23
8.) Find x if x-3=2
(a) 3
(b) 6
(c) 5
(d) 2
ANSWER: (c) 5
9.) Solve; 4l-3=5
(a) 3
(b) 4
(c) 1
(d) 2
ANSWER: (d) 2
10.) a/4 = 5 then a=
(a) 5
(b) 20
(c) 4
(d) 18
ANSWER: (b) 20