CBSE students can refer to NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Textbook Questions and Answers are provided by experts in order to help students secure good marks in exams.
Class 7 Maths NCERT Solutions Chapter 12 Algebraic Expressions Ex 12.1
Question 1.
Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
- Subtraction of z from y.
- One-half of the sum of numbers x and y.
- The number z multiplied by itself
- One-fourth of the product of numbers p and q.
- Numbers x and y both squared and added.
- Number 5 added to three times the product of numbers m and n.
- Product of numbers y and z subtracted from 10.
- Sum of numbers a and b subtracted from their product.
Solution:
- y – z
- \(\frac { 1 }{ 2 } \) ( x + y )
- z2
- \(\frac { 1 }{ 4 } \) pq
- x2 + y2
- 3mn + 5
- 10 – yz
- ab – ( a + b )
Question 2.
(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
(a) x – 3
Solution:
(b) 1 + x + x2
Solution:
(c) y – y3
Solution:
(d) 5xy2 + 7x2y
Solution:
(e) – ab + 2b2 – 3a2
Solution:
(ii) Identify terms and factors in the expressions given below :
(a) -4x + 5
(b) -4x + 5y
(c) 5y + 3y2
(d) xy + 2x2 y2
(e) pq + q
(f) 1.2ab – 2.4b + 3.6a
(g) \(\frac{3}{4}\) x + \(\frac{1}{4}\)
(h) 0.1p2 + 0.2q2
Solution:
Question 3.
Identify the numerical coefficients terms (other than constants) in the following expressions :
(i) 5 – 3t2
(ii) 1 + t + t2 + f3
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) – p2q2 + 7 pq
(vi) 1.2a + 0.8b
(vii) 3.14r2
(viii) 2 (l + b)
(ix) 0.1y + 0.01y2
Solution:
Question 4.
(a) Identify terms that 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
Solution:
(b) Identify terms that contain y2 and give the coefficient of y2.
(i) 8 – xy2
(ii) 5y2 + 7x
(iii) 2x2y – 15xy2 + 7y2
Solution:
Question 5.
Classify into monomials, binomials, and 4y 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
Solution:
We know that an algebraic expression containing only one term is called a monomial. So, the monomials are : (ii), (iv), and (viii).
We know that an algebraic expression containing two terms is called a binomial. So, the binomials are : (i), (vi), (vii), (x) and (xi).
We know that an algebraic expression containing three terms is called a trinomial. So, the trinomial are : (iii), (v), (ix) and (xii).
Question 6.
State whether a given pair of terms j is of like or unlike terms:
- 1,100
- -7x, \(\frac { 5 }{ 2 } \) x
- -29 x, -29 y
- 14 xy, 42 yx
- 4m2p, 4mp2
- 12xz, 12x2 z2.
Solution:
- Like
- Like
- Unlike
- Like
- Unlike
- Unlike
Question 7.
Identify like terms in the following:
(a) – xy2, -4yx2, 8x2, 2xy2, 7y, – 11x2, – 100x, – 11yx, 20x2y, – 6x2, y, 2xy, 3x
Solution:
In the given terms, like terms are grouped as under :
(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q,- 23, 12q2p2, – 5p2, 41, 2405p, 78qp, 13p2q, qp2, 701p2
Solution:
In the given terms, like terms are grouped as under :