NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

• Class 7 Maths Algebraic Expressions Exercise 12.1
• Class 7 Maths Algebraic Expressions Exercise 12.2
• Class 7 Maths Algebraic Expressions Exercise 12.3
• Class 7 Maths Algebraic Expressions Exercise 12.4

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1
Ex 12.1 Class 7 Maths Question 1.
Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
(i) Subtraction of z from y.
(ii) One half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and 2 subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.
Solution:
(i) Subtraction of z from y
Expression: y – z

(ii) One half of the sum of numbers x and y
Expression: \(\frac{1}{2}(x+y) \text { or } \frac{x+y}{2}\)

(iii) The number 2 multiplied by itself.
Expression: z × z = z ²

(iv) One-fourth of the product of numbers p and q
Expression: \(\frac{1}{4} p q \text { or } \frac{p q}{4}\)

(v) Numbers x and y both squared and added
Expression: x ² + y ²

(vi) Number 5 added to three times the product of number m and n
Expression: 3mn + 5

(vii) Product of numbers y and z subtracted from 10
Expression: 10 – yz

(viii) Sum of numbers a and 6 subtracted from their product
Expression: Sum = a + b, Product = ab
∴ Required expression
= ab – (a + b)
= ab – a- b

Ex 12.1 Class 7 Maths Question 2.
(i) Identify the terms and their factors in the following expressions show the terms and factors by tree diagrams.
(a) x – 3
(b) 1 + x + x ²
(c) y – y ³
(d) 5xy ² + 7x ² y
(e) -ab + 2b ² – 3a ²
Solution:

(ii) Identify terms and factors in the expression
given below:
(a) -4x + 5
(b) -4x + 5y
(c) 5y + 3y ²
(d) xy + 2x ² y ²
(e) pq + q
(f) 1.2ab – 2.4b + 3.6a
(g) \(\frac{3}{4} x+\frac{1}{4}\)
(h) 0.1p ² + 0.2q ²
Solution:

Ex 12.1 Class 7 Maths Question 3.
Identify the numerical coefficients of terms (other than constants) in the following:
(i) 5 – 3t ²
(ii) 1 + t + t ² + t ³
(iv) 100m + 1000n
(v) -p ² q ² + 7pq
(vi) 1.2 a + 0.86
(vii) 3.14r ²
(viii) 2(l + b)
(ix) 0.1y + 0.01y ²
Solution:

Ex 12.1 Class 7 Maths Question 4.
(a) Identify terms which contain x and give the
coefficient of x.
(i) y ² x + y
(ii) 13y ² – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12 xy ² + 25
(vii) 7x + xy ²
Solution:

(b) Identify terms which contain y ² and give the coefficients of y ² .
(i) 8 – xy ²
(ii) 5y ² + 7x
(iii) 2x ² y – 15xy ² + 7y ²
Solution:

Ex 12.1 Class 7 Maths Question 5.
Classify into monomials, binomials and trinomials:
(i) 4y – 7x
(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
Solution:
(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

Ex 12.1 Class 7 Maths Question 6.
State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) -7x, \(\frac{5}{2}\)x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m ² p, 4mp ²
(vi) 12xz, 12 x ² y ²
Solution:
(i) 1, 100 – Like
(ii) -7x, \(\frac{5}{2}\)x – Like
(iii) -29x, -29y – Unlike
(iv) 14xy, 42yx – Like
(v) 4m ² p, 4mp ² – Unlike
(vi) 12xz, 12x ² z ² – Unlike

Ex 12.1 Class 7 Maths Question 7.
Identify like terms in the following:
(a)-xy ² , -4yx ² , 8x ² , 2xy ² , 7y ² , -11x ² , -100x, -11yx, 20x ² y, -6x ² , y, 2xy, 3x
(b) 10pq, 7p, 8q, -p ² q ² , -7qp, -100q, -23, 12q ² p ² , -5p ² , 41, 2405p, 78qp, 13p ² q, qp ² , 701p ²
Solution:
(a) Like terms are:
(i) -xy ² , 2xy ²
(ii) -4yx ² , 20x ² y
(iii)8x ² , -11x ² , -6x ²
(iv) 7y, y
(v) -100x, 3x
(vi) -11yx, 2xy

(b) Like terms are:
(i) 10pq, – 7qp, 78qp
(ii) 7p, 2405p
(iii) 8q, -100q
(iv) -p ² q ² , 12 q ² p ²
(v) -23, 41
(vi) -5p ² , 701p ²
(vii) 13p ² q, qp ²

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