NCERT solution class 7 chapter 12 Algebraic expressions 12.1 mathematics

EXERCISE 12.1

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"Algebraic Expressions" Chapter 12 - Introduction - NCERT Class 7th Maths Solutions

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Q 1, Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Page No 234:

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) 
(iii) z²
(iv) 
(v) x² + y²
(vi) 5 + 3 (mn)
(vii) 10 − yz
(viii) ab − (a + b)

Q 2 (i), Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Q 2 (ii), Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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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)  (e) − ab + 2b² − 3a²
(ii) Identify terms and factors in the expressions given below:
(a) − 4x + 5 (b) − 4x + 5y (c) 5y + 3y²
(d)  (e) pq + q
(f) 1.2 ab − 2.4 b + 3.6 a (g) 
(h) 0.1p² + 0.2 q²

Answer:

(i)
(a)

(b)

(c)

(d)

(e)

(ii)

Row	Expression	Terms	Factors
(a)	− 4x + 5	− 4x 5	− 4, x 5
(b)	− 4x + 5y	− 4x 5y	− 4, x 5, y
(c)	5y + 3y2	5y 3y2	5, y 3, y, y
(d)	xy + 2x2y2	xy 2x2y2	x, y 2, x, x, y, y
(e)	pq + q	pq q	p, q q
(f)	1.2ab − 2.4b + 3.6a	1.2ab − 2.4b 3.6a	1.2, a, b − 2.4, b 3.6, a
(g)
(h)	0.1p2 + 0.2q2	0.1p2 0.2q2	0.1, p, p 0.2, q, q

Q 3, Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Page No 235:

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) 3.14 r² (viii) 2 (l + b) (ix) 0.1y + 0.01 y²

Answer:

Row	Expression	Terms	Coefficients
(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)	100m + 1000n	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)	3.14 r2	3.14 r2	3.14
(viii)	2(l + b)	2l 2b	2 2
(ix)	0.1y + 0.01y2	0.1y 0.01y2	0.1 0.01

Q 4 (A Part), Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Q 4 (B Part), Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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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 (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

Answer:

(a)

Row	Expression	Terms with x	Coefficient of x
(i)	y2x + y	y2x	y2
(ii)	13y2 − 8yx	− 8yx	−8y
(iii)	x + y + 2	x	1
(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)

Row	Expression	Terms with y2	Coefficient of y2
(i)	8 − xy2	−xy2	− x
(ii)	5y2 + 7x	5y2	5
(iii)	2x2y + 7y2 −15xy2	7y2 −15xy2	7 −15x

Q 5, Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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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:

The monomials, binomials, and trinomials have 1, 2, and 3 unlike terms in it respectively.
(i) 4y − 7z
Binomial
(ii) y²
Monomial
(iii) x + y − xy
Trinomial
(iv) 100
Monomial
(v) ab − a − b
Trinomial
(vi) 5 − 3t
Binomial
(vii) 4p²q − 4pq²
Binomial
(viii) 7mn
Monomial
(ix) z² − 3z + 8
Trinomial
(x) a² + b²
Binomial
(xi) z² + z
Binomial
(xii) 1 + x + x²
Trinomial

Q 6, Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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Question 6:

State whether a given pair of terms is of like or unlike terms.
(i) 1, 100 (ii)  (iii) − 29x, − 29y
(iv) 14xy, 42yx (v) 4m²p, 4mp² (vi) 12xz, 12 x²z²

Answer:

The terms which have the same algebraic factors are called like terms. However, when the terms have different algebraic factors, these are called unlike terms.
(i) 1, 100
Like
(ii) − 7x, 
Like
(iii) −29x, −29y
Unlike
(iv) 14xy, 42yx
Like
(v) 4m²p, 4mp²
Unlike
(vi) 12xz, 12x²z²
Unlike

Q 7, Ex 12.1 - Algebraic Expressions - Chapter 12 - Maths Class 7th - NCERT

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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, − 7qp, − 100q, − 23, 12q²p², − 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²

Answer:

(a) −xy², 2xy²
−4yx², 20x²y
8x², −11x², −6x²
7y, y
−100x, 3x
−11xy, 2xy
(b) 10pq, −7qp, 78qp
7p, 2405p
8q, −100q
−p²q², 12p²q²
−23, 41
−5p², 701p²
13p²q, qp²