Class 7, Maths, Chapter 12, Exercise 12.1 Solutions
Q.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 numbers m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.
Ans:
(i) Subtraction of z from y.
= Y – z
(ii) One-half of the sum of numbers x and y.
$=\frac{x+y}{2}$
(iii) The number z multiplied by itself.
=z × z = z2
(iv) One-fourth of the product of numbers p and q.
$\mathsf{=}\frac{\mathsf{1}}{\mathsf{4}}\mathsf{(p\times q)=}\frac{\mathsf{pq}}{\mathsf{4}}$
(v) Numbers x and y both squared and added.
= x2 + y2
(vi) Number 5 added to three times the product of numbers m and n.
= 3mn + 5
(vii) Product of numbers y and z subtracted from 10.
= 10 – (y x z) = 10 – yz
(viii) Sum of numbers a and b subtracted from their product.
= (a x b) – (a + b) = ab- (a + b)
Q.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 + x2
(c) y – y3
(d) 5xy2 + 7x2y
(e) – ab + 2b2 – 3a2
(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5
(b) – 4x + 5y
(c) 5y + 3y2
(d) xy + 2x2y2
(e) pq + q
(f) 1.2 ab – 2.4 b + 3.6 a
(g) $\frac{\mathsf{3}}{\mathsf{4}}\mathsf{x+}\frac{\mathsf{1}}{\mathsf{4}}$
(h) 0.1p2 + 0.2q2
(ii)
Q.3. Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t2
(ii) 1 + t + t2 + t3
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) – p2q2 + 7pq
(vi) 1.2 a + 0.8 b
(vii) 3.14 r2
(viii) 2 (l + b)
(ix) 0.1 y + 0.01 y2
Ans:
Q.4. (a) Identify terms which contain x and give the coefficient of x.
(i) y2x + y
(ii) 13y2 – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12xy2 + 25
(vii) 7x + xy2
(b) Identify terms which contain y2 and give the coefficient of y2.
(i) 8 – xy2
(ii) 5y2 + 7x
(iii) 2x2y – 15xy2 + 7y2
Ans:
(a)
(b)
Q.5. Classify into monomials, binomials and trinomials.
(i) 4y – 7z
(ii) y2
(iii) x + y – xy
(iv) 100
(v) ab – a – b
(vi) 5 – 3t
(vii) 4p2q – 4pq2
(viii) 7mn
(ix) z2 – 3z + 8
(x) a2 + b2
(xi) z2 + z
(xii) 1 + x + x2
Ans:
Monomials: An expression with only one term is called a monomial.
Binomials: An expression with only two term is called a binomial.
Trinomials: An expression with only three term is called a trinomial.
Q.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) 4m2p, 4mp2
(vi) 12xz, 12x2z2
Ans:
Like terms: When term have the same algebraic factors, they are like terms.
All constant are like terms.
Unlike terms: The terms have different algebraic factors, they are unlike terms.
Q.7. Identify like terms in the following:
(a) – xy2, – 4yx2, 8x2, 2xy2, 7y, – 11x2, – 100x, – 11yx, 20x2y, – 6x2, y, 2xy, 3x
(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2
Ans:
(a) Like terms: When term have the same algebraic factors, they are like terms.
(i) -xy2, 2xy2
(ii) -4yx2, 20x2y
(iii) 8x2,-11x2, -6x2
(iv) 7y, y
(v) -100x, 3x
(vi) -11yx, 2xy
(b) Like terms: When term have the same algebraic factors, they are like terms.
(i) 10 pq, -7pq,78qp
(ii) 7p, 2405p
(iii) 8q,-100q
(iv) -p2q2,12q2 p2
(v) -23,41
(vi) -5p2,701p2
(vii) 13p2q, qp2
NCERT Solutions For Class 7 Maths, Chapter 12 Algebraic Expressions (All Exercises)
Class 7, Maths, Chapter 12, Algebraic Expressions
Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.1 ← You are here
Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.2
Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.3
Class 7, Maths, Chapter 12, Algebraic Expressions, Exercise 12.4