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

These NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Questions and Answers are prepared by our highly skilled subject experts.

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

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 z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.
Answer:
(i) y – z
(ii) \(\frac { 1 }{ 2 }\)(x + y)
(iii) z2
(iv) \(\frac { 1 }{ 4 }\)pq
(v) x2 + y2
(vi) 5 + 3mn
(vii) 10 – yz
(viii) ab – (a + b)

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

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) 1.2ab- 2.4 b + 3.6a
(g) \(\frac { 3 }{ 4 }\)x + \(\frac { 1 }{ 4 }\)
(h) 0.1p2 + 0.2p2
Answer:
(i) (a) x – 3
Terms : x; – 3 Factors x; -3
1 + x + x2
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 1

(b) 1 + x + x2
Terms = 1; x; x2
Factors = 1; x; x, x (x2 )
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 2

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

(c) y-y3
Terms: y; -y3
Factors y;-1,y,y,y
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 3

(d) 5xy2 + 7x2 y
Terms: 5xy2; 7x2 y
Factors: 5, x, y, y; 7, x, x, y
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 4

(e) -ab + 2b2 – 3a2
Terms: -ab; 2b2, -3a2
Factors: -1, a, b; 2; b; b; 3, a, a
NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 5

(ii)

Expression Terms Factors
(a) -4x + 5 -4x
5
-4x and z
5 and y
(b) – 4x + 5y -4x
5y
– 4 and z
5 and y
(c) 5y + 3y2 5y
3y2
5 and y
3, y and y
(d) xy + 2x2 y2 Xy
2x2y2
x and y
2, x.x, y and y
(e) pq + q Pq
q
p and q
q
(f) 1.2ab – 2.4 b + 3.6a 1.2ab
– 2.4 b
3.6a
1.2, a and b.
-2.4 and b
3.6 and a
(g) \(\frac{3}{4}\)x + \(\frac{1}{4}\) \(\frac{3}{4}\)x
\(\frac{1}{4}\)
\(\frac{3}{4}\) and x
\(\frac{1}{4}\)
(h) 0.lp2 + 0.2q2 0.1p2
0.2q2
0.1, p,p
0.2, q and q

Question 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) 1.2a + 0.8b
(vii) 3.14r2
(viii) 2(l + b)
(ix) 0.1y + 0.01y2
Answer:

Expression Terms (other than constant) Numerical coefficient
(i) 5 – 3t2 – 3t2 -3
(ii) 1 + t + t2 + t3 t
t2
t3
1
1
1
(iii) x + 2xy + 3y x
2xy
3y
1
2
3
(iv) 100 m + lOOOn 100m
1000n
100
1000
(v) -p2q2 + 7pq -p2q2
7pq
-1
7
(vi) 1.2a + 0.8b 1.2a
0.8b
1.2
0.8
(vii) 3.14r2 3.14r2 3.14
(viii) 2(l + b) 2l
2b
2
2
(ix) 0.1y + 0.01y2 0.1y
0.01y2
0.1
0.01

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

Question 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
(iv) 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
Answer:

Expression Term containing x Coefficient of x
(i) y2x + y y2x y2
(ii) x + y + 2 – 8yx – 8y
(iii) 5 + z + zx x l
(iv) 5 + z + zx zx Z
(v) 1 + x + xy x
xy
1
y
(vi) 12xy2+ 25 12xy2 12y2
(vii) 7x + xy2 7x
xy2
7
y2

(b)

Expression Term containing y2 Coefficient of y2
(i) 8 – xy2 -xy2 -X
(ii) 5y2 + 7x 5y2 5
(iii) 2x2y – 15xy2 + 7y2 – 15xy2 7f – 15x 7

Question 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
Answer:
(i) 4y – 7z
The expression 4y – 7z is having two unlike terms (4y and – 7z)
∴ It is a binomial.

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

(ii) y2
The expression y2 is having only one term (y2)
∴ It is a monomial.

(iii) x + y – xy
The expression x + y – xy is having three terms (x, y and – xy)
∴ It is a trinomial.

(iv) 100
The expression 100 is having only one term (100)
∴ It is a monomial.

(v) ab – a – b.
The expression ab – a – b is having three terms (ab, -a, and -b)
∴ The expression is a trinomial.

(vi) 5 – 3t
The expression 5 – 3t is having two terms (5 and -3t)
∴ It is a binomial expression.

(vii) 4p2q – 4pq2
The expression 4p2q – 4pq2 is having
two unlike terms (4p2q and – 4pq2)
∴ The expression is a binomial.

(viii) 7mn
The expression 7mn is having only one term (ie 7mn)
∴ The expression is a monomial.

(ix) z2– 3z + 8
The expression z2 – 3z + 8 is having three terms (ie z2, – 3z and 8)
∴ The expression is a trinomial.

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

(x) a2 + b2
The expression (a2 + b2) is having two unlike terms (a2 and b2)
∴ It is a binomial expression.

(xi) z2 + z
The expression z2 + z is having two unlike terms (z2 and z)
∴ The expression in binomial.

(xii) 1 + x + x2
The expression 1 + x + x2 is having three terms (1, x and x2)
∴ The expression is a trinomial.

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) 4m2p, 4mp2
(vi) 12xz, 12x2z2
Answer:
(i) 1, 100 is a pair of like terms.
(ii) \(\frac { 5 }{ 2 }\)x is a pair of like terms.
(iii) – 29x, – 29y is a pair of unlike terms.
(iv) 14xy, 42yx is a pair of like terms.
(v) 4m2p, 4mp2 is a pair of unlike terms.
(vi) 12xz; 12x2z2 is a pair of unlike terms.

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

Question 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, -7pq, -100q, -23, 12q2p2, -5p2, 41, 2405p, 78qp,
13p2q, qp2,701p2
Answer:
(a) -xy2 and 2xy2, – 4yx2 and 20x2 y, 8x2, -11x2 and – 6x2; 7y and y; lOOx and 3x; -1 lyx and 2xy are like terms.
(b) 10pq, – 7pq and 78qp.
7p and 2405p; 8q and 100q; – p2q2 and 12q2p2; – 23 and 41; – 5p2 and 701p2; 13p2q and qp2 are like terms.

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