NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions - Download PDF

NCERT Solutions for Maths Chapter 12 Algebraic Expressions Class 7th Topic 12.2

Question: Describe how the following expressions are obtained:

Answer:

the above expression is obtained by adding 7xy with 5. Here 7xy is obtained by multiplying 7,x and y

the above expression is obtained by subtracting the product of 5 and x from the product of 4,x and x

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Topic 12.3

Question:1 What are the terms in the following expressions? Show how the terms are formed. Draw a tree diagram for each expression:

Answer: The terms in the expression are

is obtained by adding the product of 8 and y with the product of 3 x and x

the tree diagram for the expression is given below

has two terms 7mn and 4 and the expression is obtained by subtracting 4 from the product of 7,m and n. The tree diagram is shown below.

has only one term, that is the expression itself.

The expression is formed by multiplying 4 terms 2, x, x and y. The tree diagrams are shown below

Question:2 Write three expressions each having 4 terms.

Answer: We can write as many expressions we need with 4 terms. Following are a few examples of expression with 4 terms

Question: Identify the coefficients of the terms of following expressions:

Answer: i) has two terms 4x and -3y

the coefficient of x is 4 and the coefficient of y is -3

ii) a+b+5 has 3 terms a,b and a constant that is 5.

the coefficient of a is 1 and b is also 1. Constant terms have no coefficient

iii) 2y+5 has two terms 2y and 5 which is constant.

The coefficient of y is 2. Constant terms have no coefficient

iv) 2xy has only one term which is 2xy and the coefficient of xy is 2

NCERT Solutions for Maths Chapter 12 Algebraic Expressions Class 7th Topic 12.4

Question:1(i) Group the like terms together from the following:

, , , , , , , ,

Answer: The like terms are grouped below

Group 1: , ,

Group 2: , ,

Group 3: , ,

NCERT Solutions for Class 7th Math Chapter 12 Algebraic Expressions Topic 12.5 Monomials, Binomials, Trinomials and Polynomials

Question: Classify the following expressions as a monomial, a binomial or a trinomial:

Answer: Monomial: a, xy, 7

binomial: a+b, xy+5, 4mn+7

Trinomial: ab+a+b, 5x ² -x+2, 4pq-3q+5p, 4m-7n+10

Polynomial with 4 terms: ab+a+b-5

NCERT Solutions for Class 7th Math Chapter 12 Algebraic Expression Exercise 12.1

Question: 1(i) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Subtraction of from .

Answer: Subtraction of z from y:

Question: 1(ii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation.

One-half of the sum of numbers and .

Answer: Sum of numbers x and y = x + y

One half of the sum of numbers x and y

Question: 1(iii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

The number multiplied by itself.

Answer:

The number multiplied by itself

Question: 1(iv) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

One-fourth of the product of numbers and .

Answer: Product of the numbers p and q

One-fourth of the product of numbers p and q

Question: 1(v) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Numbers and both squared and added.

Answer: Number x squared =

Number y squared =

Numbers x and y both squared and added =

Question:1(vi) Get the algebraic expressions in the following cases using variables, constants and arithmetic operation.

Number 5 added to three times the product of numbers and .

Answer: Product of numbers m and n

Number 5 added to three times the product of numbers and =

Question:1(vii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Product of numbers and subtracted from .

Answer: Product of numbers y and z

Product of numbers y and z subtracted from 10

Question: 1(viii) Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.

Sum of numbers and subtracted from their product.

Answer: Sum of numbers a and b = a + b

Product of the numbers a and b

Sum of numbers and subtracted from their product .

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams. (a)

Answer: Expression : x - 3

Terms in the above expression: x and -3

Tree diagram for the given expression

Question: 2 (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (b)

Answer: Expression:

Tems in the above expression:

Factors of x ² : x and x

Tree diagram for the given expression

Question:2(i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (c)

Answer: Expression: y - y ³

Terms in the above expression: y and -y ³

Factors of -y ³ : -1, y, y and y

Tree diagram for the given expression

Question: 2 (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams. (d)

Answer: Expression: 5xy ² + 7x ² y

Terms in the above expression: 5xy ² and 7x ² y

Factors of 5xy ² : 5, x, y and y

Factors of 7x ² y: 7, x, x and y

Tree diagram for the given expression

Question: 2 (i) Identify the terms and their factors in the following expressions

Show the terms and factors by tree diagrams (e)

Answer:

Expression: -ab + 2ab ² - 3a ²

Terms in the above expression: -ab, 2ab ² and -3a ²

Factors of -ab: -1, a and b

Factors of 2ab ² : 2, a, b and b

Factors of -3a ² : -1, 3, a and a

Tree diagram for the given expression

Question: 2 (ii) Identify terms and factors in the expressions given below:

(a)

Answer: Expression: -4x + 5

Terms in the above expression: -4x and 5

Factors of -4x: -1, 4 and x

Factors of 5: 5

Question: 2 (ii) Identify terms and factors in the expressions given below:

(b)

Answer: Expression: -4x + 5y

Terms in the above expression: -4x and 5y

Factors of -4x: -1, 4 and x

Factors of 5y: 5 and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(c)

Answer: Expression: 5y + 3y ²

Terms in the above expression: 5y and 3y ²

Factors of 5y: 5 and y

Factors of 3y ² : 3, y and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(d)

Answer: Expression: xy + 2x ² y ²

Terms in the above expression: xy and 2x ² y ²

Factors of xy: x and y

Factors of 2x ² y ² : 2, x, x, y and y

Question: 2 (ii) Identify terms and factors in the expressions given below:

(e)

Answer: Expression: pq + q

Tems in the above expression: pq and q

Factors of pq: p and q

Factors of q: q

Question: 2 (ii) Identify terms and factors in the expressions given below:

(f)

Answer: Expression: 1.2ab - 2.4b + 3.6a

Tems in the above expression: 1.2ab, -2.4b and 3.6a

Factors of 1.2ab: 1.2, a and b

Factors of -2.4b: -1, 2.4 and b

Factors of 3.6a: 3.6 and a

Question: 2( ii) Identify terms and factors in the expressions given below:

(g)

Answer: Expression:

Terms in the above expression: and

Factors of : and x

Factors of :

Question: 2 (ii) Identify terms and factors in the expressions given below:

(h)

Answer: Expression: 0.1p ² + 0.2q ²

Tems in the above expression:0.1p ² and 0.2q ²

Factors of 0.1p ² : 0.1, p and p

Factors of 0.2q ² : 0.2, q and q

Question:3(i) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 5 - 3t ²

Tems in the above expression: 5 and -3t ²

Coefficient of -3t ² : -3

Question:3(ii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 1 + t + t ² + t ³

Terms in the above expression: 1, t, t ² and t ³

Coefficient of t is 1

Coefficient of t ² is 1

Coefficient of t ³ : is 1

Question: 3(iii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: x + 2xy + 3y

Terms in the above expression: x, 2xy and 3y

Coefficient of x: 1

Coefficient of 2xy: 2

Coefficient of 3y: 3

Question: 3(iv) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 100m + 1000n

Terms in the above expression: 100m and 1000n

Coefficient of 100m: 100

Coefficient of 1000n: 1000

Question: 3(v) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: -p ² q ² + 7pq

Tems in the above expression: -p ² q ² and 7pq

Coefficient of -p ² q ² : -1

Coefficient of 7pq: 7

Question:3(vi) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 1.2a + 0.8b

Terms in the above expression: 1.2a and 0.8b

Coefficient of 1.2a: 1.2

Coefficient of 0.8b: 0.8

Question:3(vii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 3.14r ²

Terms in the above expression: 3.14r ²

Coefficient of 3.14r ² is 3.1

Question: 3(viii) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 2(l + b) = 2l + 2b

Tems in the above expression: 2l and 2b

Coefficient of 2l: 2

Coefficient of 2b: 2

Question: 3(ix) Identify the numerical coefficients of terms (other than constants) in the following expressions:

Answer: Expression: 0.1y + 0.01y ²

Tems in the above expression: 0.1y and 0.01y ²

Coefficient of 0.1y is 0.1

Coefficient of 0.01y ² is 0.01

Question: 4 (a) Identify terms which contain x and give the coefficient of x.

(i)

Answer: Expression: y ² x + y

Terms with x: y ² x

Coefficient of x in y ² x: y ²

Question:4(a) Identify terms which contain x and give the coefficient of x.

(ii)

Answer: Expression: 13y ² - 8yx

Terms with x: -8yx

Coefficient of x in -8yx: -8y

Question: 4 (a) Identify terms which contain x and give the coefficient of x.

(iii)

Answer: Expression: x + y + 2

Terms with x: x

Coefficient of x in x: 1

Question: 4 (a) Identify terms which contain x and give the coefficient of x.

(iv)

Answer: Expression: 5 + z + zx

Terms with x: zx

Coefficient of x in zx: z

Question: 4 (a) Identify terms which contain x and give the coefficient of x .

(v)

Answer: Expression: 1 + x + xy

Terms with x: x and xy

Coefficient of x in x: 1

Coefficient of x in xy: y

Question:4(a) Identify terms which contain x and give the coefficient of x.

(vi)

Answer: Expression: 12xy ² + 5

Terms with x: 12xy ²

Coefficient of x in 12xy ² : 12y ²

Question:4(a) Identify terms which contain x and give the coefficient of x.

(vii)

Answer: Expression: 7x + xy ²

Terms with x: 7x and xy ²

Coefficient of x in 7x: 7

Coefficient of x in xy ² : y ²

Question: 4 (b) Identify terms which contain and give the coefficient of .

(i)

Answer: Expression: 8 - xy ²

Terms with y ² : -xy ²

Coefficient of y ² in -xy ² : -x

Question: 4 (b) Identify terms which contain and give the coefficient of .

(ii)

Answer: Expression: 5y ² + 7x

Terms with y ² : 5y ²

Coefficient of y ² in 5y ² : 5

Question: 4 (b) Identify terms which contain and give the coefficient of .

(iii)

Answer: Expression: 2x ² y -15xy ² + 7y ²

Terms with y ² : -15xy ² and 7y ²

Coefficient of y ² in -15xy ² : -15x

Coefficient of y ² in 7y ² : 7

Question:5 Classify into monomials, binomials and trinomials.

(i) 4y – 7z

(ii) y ²

(iii) x + y – xy

(iv) 100

(v) ab – a – b

(vi) 5 – 3t

(vii) 4p ² q – 4pq ²

(viii) 7mn

(ix) z ² – 3z + 8

(x) a ² + b ²

(xi) z ² + z

(xii) 1 + x + x ²

Answer: (i) 4y – 7z

Binomial

(ii) y ²

Monomial

(iii) x + y – xy

Trinomial

(iv) 100

Monomial

(v) ab – a – b

Trinomial

(vi) 5 – 3t

Binomial

(vii) 4p ² q – 4pq ²

Binomial

(viii) 7mn

Monomial

(ix) z ² – 3z + 8

Trinomial

(x) a ² + b ²

Binomial

(xi) z ² + z

Binomial

(xii) 1 + x + x ²

Trinomial

Question:6(i) State whether a given pair of terms is of like or unlike terms.

Answer: (i) are Like terms.

Question:6(ii) State whether a given pair of terms is of like or unlike terms.

Answer: (ii) are Like terms

Question:6(iii) State whether a given pair of terms is of like or unlike terms.

Answer: Unlike since y and x are unlike terms

Question: 6(iv) State whether a given pair of terms is of like or unlike terms.

Answer: Like terms, since both the terms contain xy and only the coefficient is different

Question: 6(v) State whether a given pair of terms is of like or unlike terms.

Answer: Unlike since are different

Question: 6(vi) State whether a given pair of terms is of like or unlike terms.

Answer: Unlike since are unlike terms

Question:7(a) Identify like terms in the following:

Answer: Like terms are

(i) -xy ² and 2xy ²

(ii) -4x ² y and 20x ² y

(iii) 8x ² , -11x ² and -6x ²

(iv) 7y and y

(v) -100x and 3x

(vi) -11yx and 2xy

Question:7(b) Identify like terms in the following:

Answer: Like terms are

(i) 10pq, -7qp and 78qp

(ii) 7p and 2405p

(iii) 8q and -100q

(iv) -p ² q ² and 12q ² p ²

(vii) -23 and 41

(viii) -5p ² and 701p ²

(ix) 13p ² q and qp ²

NCERT Solutions for Class 7th Math Chapter 12 Algebraic Expressions Topic 12.6

Question:(i) Add and subtract

Answer: Adding

Will give the result as follows

Subtracting

Will give the result as follows

Question:(ii) Add and subtract

Answer: Adding the following terms

we will get

Subtracting

We will get

NCERT Solutions for Chapter 12 Maths Class 7 Algebraic Expression Exercise: 12.2

Question: 1(i) Simplify combining like terms:

Answer: 21b - 32 + 7b -20b

= (21 + 7 - 20)b -32

= 8b - 32

The simplified expression is 8b - 32.

Question:1(ii) Simplify combining like terms:

Answer:

-z ² + 13z ² - 5z + 7z ³ - 15z

= (-1 + 13)z ² + (-5 - 15)z +7z ³

=12z ² - 20z + 7z ³

The simplified expression is 12z ² - 20z + 7z ³

Question:1(iii) Simplify combining like terms:

Answer: p - (p - q) - q - (q - p)

= p - p + q - q - q + p

= p - p + p + q - q -q

= p - q

The simplified expression is p - q.

Question: 1(iv) Simplify combining like terms:

Answer: 3a - 2b - ab - (a - b + ab) + 3ab + b - a

= 3a - 2b - ab - a + b - ab + 3ab + b - a

= (3 - 1 - 1)a + (-2 + 1 +1)b + (-1 - 1 + 3)ab

= a + ab

The simplified expression is a + ab.

Question:1(v) Simplify combining like terms:

Answer: 5x ² y - 5x ² + 3yx ² - 3y ² + x ² - y ² + 8xy ² - 3y ²

= (5 + 3 )x ² y + (-5 + 1)x ² + (-3 - 1 - 3)y ² + 8xy ²

= 8x ² y - 4x ² - 7y ² + 8xy ²

The simplified expression is 8x ² y - 4x ² - 7y ² + 8xy ²

Question:1(vi) Simplify combining like terms:

Answer: (3y ² + 5y - 4) - (8y - y ² - 4)

= 3y ² + 5y - 4 - 8y + y ² + 4

= (3 + 1)y ² + (5 - 8)y - 4 + 4

= 4y ² - 3y

The simplified expression is 4y ² - 3y

Question:2 Add:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Answer: The given terms are added as follows

Question:3 Subtract:

(i) from

(ii) from

(iii) from

(iv) from

(v) from

(vi) from

(vii) from

(viii) from

Answer: The given terms are subtracted as follows

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Question: 4 (a) What should be added to to obtain

Answer: Let the term be a which must be added to x ² + xy + y ² to obtain 2x ² + 3xy

x ² + 2xy - y ² should be added to x ² + xy + y ² to obtain 2x ² + 3xy

Question: 4 (b) What should be subtracted from to get

Answer: Let the term be c which must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

5a + b - 6 must be subtracted from 2a + 8b + 10 to get -3a + 7b + 16

Question: 5 What should be taken away from to obtain

Answer: Let the term be a which must be taken away from 3x ² - 4y ² + 5xy + 20 to obtain -x ² - y ² + 6xy + 20

4x ² - 3y ² - xy must be taken away from 3x ² - 4y ² + 5xy + 20 to obtain -x ² - y ² + 6xy + 20

Question:6(a) From the sum of and , subtract

Answer:

On subtracting 3x - y - 11 from the sum of 3x - y + 11 and -y - 11 we get -y + 11

Question: 6 (b) From the sum of and subtract the sum of and .

Answer:

On subtracting the sum of and from the sum of and we get

NCERT Solutions for Chapter 12 Maths Class 7th Algebraic Expression Exercise 12.3

Question:1(i) If find the value of:

Answer: (i) m - 2

= 2 - 2

= 0

If m = 2 the value of m - 2 = 0

Question:1(ii) If find the value of:

Answer:

If m = 2 the value of 3m - 5 = 1

Question:1(iii) If find the value of:

Answer:

If m = 2 the value of 9 - 5m = -1

Question: 1(iv) If find the value of:

Answer:

If m = 2 the value of 3m ² - 2m - 7 = 1

Question: 1(v) If find the value of: (v) If find the value of:

Answer:

= 5 - 4

= 1

If m = 2 the value of

Question:2(i) If find the value of:

Answer:

If p = -2 the value of 4p + 7 = -1

Question: 2(ii) If find the value of:

Answer:

If p = -2 the value of -3p ² + 4p + 7 = -13

Question: 2(iii) If , find the value of:

Answer:

If p = -2 the value of -2p ³ - 3p ² + 4p + 7 = 3

Question: 3(i) Find the value of the following expressions, when :

Answer:

If x = -1 the value of 2x - 7 = -9

Question: 3(ii) Find the value of the following expressions, when

Answer:

-x + 2

= -( -1 ) + 2

= 1 + 2

= 3

If x = -1 the value of -x + 2 = 3

Question:3(iii) Find the value of the following expressions, when :

Answer:

If x = -1 the value of x ² + 2x + 1 = 0

Question:3(iv) Find the value of the following expressions, when :

Answer:

So the value at x=-1 is 1

Question: 4(i) If find the value of:

Answer:

a ² + b ²

= ( 2 ) ² + ( -2 ) ²

= 4 + 4

= 8

If a = 2 and b = -2 the value of a ² + b ² = 8

Question: 4(ii) If find the value of:

Answer:

If a = 2 and b = -2 the value of a ² + ab + b ² = 4

Question:4(iii) If find the value of

Answer:

a ² - b ²

= 2 ² - ( -2 ) ²

= 4 - 4

= 0

If a = 2 and b = -2 the value of a ² - b ² = 0

Question: 5(i) When find the value of the given expressions:

Answer:

When a = 0 and b = -1 the value of the given expression 2a + 2b = -2

Question: 5(ii) When find the value of the given expressions:

Answer:

When a = 0 and b = -1 the value of the given expression 2a ² + b ² + 1 = 2

Question: 5(iii) When , find the value of the given expressions:

Answer:

When a = 0 and b = -1 the value of the given expression 2a ² b + 2ab ² + ab = 0

Question:5(iv) When find the value of the given expressions:

Answer:

When a = 0 and b = -1 the value of the given expression a ² + ab + 2 = 2

Question: 6(i) Simplify the expressions and find the value if is equal to

Answer:

If x is equal to 2 the value of x + 7 + 4( x - 5 ) = -3

Question: 6(ii) Simplify the expressions and find the value if is equal to

Answer:

If x is equal to 2 the value of 3( x + 2 ) + 5x - 7 = 15

Question: 6(iii) Simplify the expressions and find the value if is equal to

Answer:

If x is equal to 2 the value of 6x + 5( x - 2 ) = 12

Question: 6(iv) Simplify the expressions and find the value if is equal to

Answer:

If x is equal to 2 the value of 4( 2x - 1 ) + 3x + 11 = 29

Question: 7 Simplify these expressions and find their values if

(i)

(ii)

(iii)

(iv)

(v)

Answer:

The expression is simplified as follows and also obtained their values

(i)

(ii)

(iii)

(iv)

(v)

Question: 8 (i) If find the value of

Answer:

If z = 10 the value of z ³ - 3( z - 10 ) = 1000

Question: 8 (ii) If find the value of

Answer:

If p = -10 the value of p ² - 2p - 100 = 20

Question: 9 What should be the value of a if the value of equals to , when

Answer:

Therefore for a = -5 when the value of x=0

Question: 10 Simplify the expression and find its value when and

Answer:

When a = 5 and b = -3 the value 2( a ² + ab ) + 3 - ab = 38

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expression Exercise 12.4

Question:1 Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

Answer:

The number of segments required to form n of each digits shown above are 5n + 1, 3n + 1 and 5n + 2

When n = 5

When n = 10

When n = 100

Question: 2 Use the given algebraic expression to complete the table of number patterns.

Answer: Below you can find the table of number patterns: