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

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1.

Board	CBSE
Textbook	NCERT
Class	Class 7
Subject	Maths
Chapter	Chapter 12
Chapter Name	Algebraic Expressions
Exercise	Ex 12.1
Number of Questions Solved	7
Category	NCERT Solutions

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

Question 1.
Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations.
(i) Subtraction of z from y.
Solution:
y – z

(ii) One-half of the sum of numbers x and y.
Solution:
\(\frac{1}{2}\) (x -y)

(iii) The number z multiplied by itself.
Solution:
z × z i.e., z²

(iv) One-fourth of the product of numbers p and q.
Solution:
\(\frac{1}{4}\) pq

(v) Numbers x and y both squared and added.
Solution:
x² + y²

(vi) Number 5 added to three times the product of numbers m and n.
Solution:
3mn + 5

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

(viii) Sum of numbers a and 6 subtracted from their product.
Solution:
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
(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) \(\frac { 3 }{ 4 } \) x + \(\frac { 1 }{ 4 } \)
(h) 0.1 p² + 0.2 q²

Solution:

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

5 – 3t²
1 + t + t² + t³
x + 2xy + 3y
100m + 1000n
-p²q² + 7pq
1.2 a + 0.8 b
3.14 r²
2 (l + b)
0.1 y + 0.01 y².

Solution:

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

y²x + y
13y² – 8yx
x + y + 2
5 + z + zx
1 + x + xy
12xy² + 25
7x + xy².

(b) Identify terms which contain y² and give the coefficient of y².

8 – xy²
5y² + 7x
2x²y – 15xy² + 7y²

Solution:

Question 5.
Classify into monomials, binomials and trinomials.

4y – 7z
y²
x + y – xy
100
ab – a – b
5 – 3t
4p²q – 4pq²
7mn
z² – 3z + 8 a² + b²
z² + z
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 is of like or unlike terms :
(i) 1, 100
Solution:
Like

(ii) -7x, \(\frac{5}{2}\)x
Solution:
Like

(iii) – 29x, – 29y
Solution:
Unlike

(iv)14xy, 42yx
Solution:
Like

(v) 4m²p, 4mp²
Answer:
Unlike

(vi) 12xz, 12x²z²
Solution:
Unlike

(i) 4y – 7z.
This expression is a binomial because it contains two terms: 4y and – Iz.
(ii) y².
This expression is a monomial because it contains only one term: y²
(iii) x + y – xy.
This expression is a trinomial because it contains three terms: x, y, and – xy.
(iv) 100.
This expression is a monomial because it contains only one term: 100
(v) ab – a – b.
This expression is a trinomial because it contains three terms: ab, -a, and -b
(vi) 5 – 3t.
This expression is a binomial because it contains two terms : 5 and – 31.
(vii) 4p²q – 4pq².
This expression is a binomial because it contains two terms: 4p²q and – 4pq².
(viii) 7mn.
This expression is a monomial because it contains only one term : 7mn.
(ix) z² – 3z + 8.
This expression is a trinomial because it contains three terms : z², – 3z and 8.
(x) a² + b².
This expression is a binomial because it contains two terms: a² and b².
(xi) z² + z.
This expression is a binomial because it contains two terms : z² and z.
(xii) 1 + x + x².
This expression is a trinomial because it contains three terms: 1, x, and x².

Question 6.
State whether a given pair of terms is of like or unlike terms :
(i) 1, 100
Solution:
Like

(ii) -7x, \(\frac{5}{2}\)x
Solution:
Like

(iii) – 29x, – 29y
Solution:
Unlike

(iv)14xy, 42yx
Solution:
Like

(v) 4m²p, 4mp²
Answer:
Unlike

(vi) 12xz, 12x²z²
Solution:
Unlike

Question 7.
Identify like terms in the following :
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 10
Solution:

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